CINXE.COM

<!DOCTYPE html><html lang="en"><head><meta charSet="utf-8"/><meta name="viewport" content="width=device-width"/><title>Wolfram|Alpha: Making the world’s knowledge computable</title><meta name="description" content="Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…"/><meta property="og:url" content="URL: (The exact URL for your query string)"/><meta property="og:type" content="website"/><meta property="og:title" content="Wolfram|Alpha: Making the world’s knowledge computable"/><meta property="og:description" content="Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels."/><meta property="og:image" content="https://www.wolframalpha.com/_next/static/images/share_3eSzXbxb.png"/><meta name="keywords" content="Wolfram Alpha"/><meta name="twitter:description" content="Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels."/><meta name="twitter:title" content="Wolfram|Alpha: Making the world’s knowledge computable"/><meta name="twitter:site" content="@Wolfram_Alpha"/><meta name="twitter:card" content="summary_large_image"/><meta name="twitter:image" content="https://www.wolframalpha.com/_next/static/images/share_3eSzXbxb.png"/><meta name="apple-itunes-app" content="app-id=548861535"/><link rel="shortcut icon" href="/_next/static/images/favicon_1zbE9hjk.ico"/><meta name="next-head-count" content="17"/><meta name="bingbot" content="nocache"/><link rel="preload" href="/_next/static/css/f6600fb4102e0fe6.css" as="style"/><link rel="stylesheet" href="/_next/static/css/f6600fb4102e0fe6.css" data-n-g=""/><noscript data-n-css=""></noscript><script defer="" nomodule="" src="/_next/static/chunks/polyfills-c67a75d1b6f99dc8.js"></script><script src="/_next/static/chunks/webpack-4e2e9c6131680975.js" defer=""></script><script src="/_next/static/chunks/framework-c41ea8a791274584.js" defer=""></script><script src="/_next/static/chunks/main-0a967061d7d98d3b.js" defer=""></script><script src="/_next/static/chunks/pages/_app-8259c5b240b4f9f9.js" defer=""></script><script src="/_next/static/chunks/2603-bb394855ba3d6115.js" defer=""></script><script src="/_next/static/chunks/pages/termsofuse/pro-c599165094ba3d6b.js" defer=""></script><script src="/_next/static/TArlO3n_zK_862JVBqVpv/_buildManifest.js" defer=""></script><script src="/_next/static/TArlO3n_zK_862JVBqVpv/_ssgManifest.js" defer=""></script><style data-styled="" data-styled-version="5.3.11">.ehESuO{background:#ffffff;color:#000000;}/*!sc*/ data-styled.g1[id="sc-21c13e9a-0"]{content:"ehESuO,"}/*!sc*/ .dsKfRP{color:#535353;}/*!sc*/ .eQkcfp{color:#333333;}/*!sc*/ data-styled.g2[id="sc-21c13e9a-1"]{content:"dsKfRP,eQkcfp,"}/*!sc*/ .czjJqi{color:#cb1000;background-color:transparent;border-color:#cb1000;}/*!sc*/ .czjJqi .mainColor{fill:#cb1000;}/*!sc*/ .czjJqi:hover{color:#ae0000;background-color:transparent;border-color:#ae0000;}/*!sc*/ .czjJqi:hover .mainColor{fill:#ae0000;}/*!sc*/ .czjJqi:active,.czjJqi.active{color:#ae0000;background-color:transparent;border-color:#ae0000;outline:none;}/*!sc*/ .czjJqi:active .mainColor,.czjJqi.active .mainColor{fill:#ae0000;}/*!sc*/ .czjJqi.disabled,.czjJqi[disabled]{opacity:0.5;pointer-events:none;cursor:pointer;color:#cb1000;background-color:transparent;border-color:#cb1000;}/*!sc*/ .czjJqi.disabled .mainColor,.czjJqi[disabled] .mainColor{fill:#cb1000;}/*!sc*/ .bZJsei{color:#ff7e00;background-color:transparent;border-color:#ff7e00;}/*!sc*/ .bZJsei .mainColor{fill:#ff7e00;}/*!sc*/ .bZJsei:hover{color:#cb1000;background-color:transparent;border-color:#cb1000;}/*!sc*/ .bZJsei:hover .mainColor{fill:#cb1000;}/*!sc*/ .bZJsei:active,.bZJsei.active{color:#cb1000;background-color:transparent;border-color:#cb1000;outline:none;}/*!sc*/ .bZJsei:active .mainColor,.bZJsei.active .mainColor{fill:#cb1000;}/*!sc*/ .bZJsei.disabled,.bZJsei[disabled]{opacity:0.5;pointer-events:none;cursor:pointer;color:#ff7e00;background-color:transparent;border-color:#ff7e00;}/*!sc*/ .bZJsei.disabled .mainColor,.bZJsei[disabled] .mainColor{fill:#ff7e00;}/*!sc*/ .klpTfJ{background-color:transparent;color:#777777;border-color:#777777;}/*!sc*/ .klpTfJ .mainColor{fill:#777777;}/*!sc*/ .klpTfJ:hover{background-color:transparent;color:#ec561a;border-color:#ec561a;}/*!sc*/ .klpTfJ:hover .mainColor{fill:#ec561a;}/*!sc*/ .klpTfJ:active,.klpTfJ.active{background-color:transparent;color:#cb1000;border-color:#cb1000;}/*!sc*/ .klpTfJ:active .mainColor,.klpTfJ.active .mainColor{fill:#cb1000;}/*!sc*/ .klpTfJ.disabled,.klpTfJ[disabled],.klpTfJ:disabled{opacity:0.5;pointer-events:none;cursor:pointer;}/*!sc*/ data-styled.g11[id="sc-c233f61b-2"]{content:"czjJqi,cJHKlg,bZJsei,klpTfJ,"}/*!sc*/ .cosuER{border:none;padding:0;display:contents;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;margin-right:10px;border:0;font-family:'Source Sans Pro',Arial,Helvetica,sans-serif;font-size:15px;line-height:1.27;vertical-align:baseline;white-space:normal;}/*!sc*/ data-styled.g12[id="sc-c233f61b-3"]{content:"lfJXKd,cosuER,"}/*!sc*/ .gkuhJX{background:#ffffff;border-color:#dfdfdf;}/*!sc*/ .cMPKhv{background:#ffffff;}/*!sc*/ data-styled.g20[id="sc-3d5da239-0"]{content:"gkuhJX,cMPKhv,"}/*!sc*/ .ECfnZ{height:0;width:0;}/*!sc*/ data-styled.g59[id="sc-78826ae-0"]{content:"ECfnZ,"}/*!sc*/ .fabaKa{width:100%;height:46px;font-size:14px;position:relative;z-index:1100;font-family:'Source Sans Pro',Arial,Helvetica,sans-serif;}/*!sc*/ data-styled.g111[id="sc-23deba95-0"]{content:"fabaKa,"}/*!sc*/ .eIjWBP{width:100%;height:100%;display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;padding:0 11px 0 20px;box-sizing:border-box;position:relative;border-bottom-width:1px;border-bottom-style:solid;}/*!sc*/ data-styled.g112[id="sc-23deba95-1"]{content:"eIjWBP,"}/*!sc*/ .fvastQ{vertical-align:text-top;display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;list-style:none;margin:0;padding:0;margin-left:8px;}/*!sc*/ data-styled.g114[id="sc-9be66fc6-0"]{content:"fvastQ,"}/*!sc*/ .jrvlPG{padding:0;margin:0 4px;height:14px;width:14px;}/*!sc*/ .jrvlPG:first-child{margin-left:0;}/*!sc*/ .jrvlPG:last-child{margin-right:0;}/*!sc*/ data-styled.g115[id="sc-9be66fc6-1"]{content:"jrvlPG,"}/*!sc*/ .ksSXcu{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;margin:0 4px 0 0px;line-height:1.33;}/*!sc*/ .ksSXcu:not(:last-child):after{content:'';display:block;height:11px;width:1px;background:#777777;margin-left:4px;}/*!sc*/ .hBBSJU{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;margin:0 4px 0 0px;line-height:1.33;}/*!sc*/ data-styled.g116[id="sc-87bc1c62-0"]{content:"ksSXcu,hBBSJU,"}/*!sc*/ .kqXe{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;padding:3px;margin:3px 0;border:0;}/*!sc*/ data-styled.g117[id="sc-87bc1c62-1"]{content:"kqXe,"}/*!sc*/ .ejuFmI{padding:4px;white-space:nowrap;color:#777777;}/*!sc*/ data-styled.g118[id="sc-105e6ee4-0"]{content:"ejuFmI,"}/*!sc*/ .dhgquj{margin-right:2px;}/*!sc*/ data-styled.g119[id="sc-105e6ee4-1"]{content:"dhgquj,"}/*!sc*/ .bqpxBo{width:112px;height:25px;margin-right:5px;}/*!sc*/ .bqpxBo .sc-70463ee1-0{fill:#777777;}/*!sc*/ .bqpxBo .sc-70463ee1-1{fill:#cb1000;}/*!sc*/ data-styled.g122[id="sc-2983807f-0"]{content:"bqpxBo,"}/*!sc*/ .dfMBtc{font-family:'Source Sans Pro',Arial,Helvetica,sans-serif;padding:0;margin:0;list-style:none;display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;margin-bottom:5px;font-size:12px;font-weight:600;}/*!sc*/ .LJgzy{font-family:'Source Sans Pro',Arial,Helvetica,sans-serif;padding:0;margin:0;list-style:none;display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;margin-bottom:5px;font-size:12px;font-weight:400;}/*!sc*/ .cunmhB{font-family:'Source Sans Pro',Arial,Helvetica,sans-serif;padding:0;margin:0;list-style:none;display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;margin-top:0;font-size:12px;font-weight:600;}/*!sc*/ data-styled.g123[id="sc-aea496ab-0"]{content:"dfMBtc,LJgzy,cunmhB,"}/*!sc*/ .hkxlVw{width:100%;display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-flex-direction:column;-ms-flex-direction:column;flex-direction:column;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;-webkit-box-pack:center;-webkit-justify-content:center;-ms-flex-pack:center;justify-content:center;z-index:2;padding:30px 0;}/*!sc*/ data-styled.g124[id="sc-d3c8c5f1-0"]{content:"hkxlVw,"}/*!sc*/ body,html{margin:0;padding:0;border:0;font:inherit;vertical-align:baseline;box-sizing:border-box;background:#ffffff;}/*!sc*/ data-styled.g125[id="sc-global-kVCJVd1"]{content:"sc-global-kVCJVd1,"}/*!sc*/ .iJLvQa{position:fixed;height:100%;width:100%;z-index:999999;}/*!sc*/ data-styled.g130[id="sc-7725dd90-0"]{content:"iJLvQa,"}/*!sc*/ .bxdiWb{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-flex-direction:column;-ms-flex-direction:column;flex-direction:column;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;position:absolute;top:19%;left:0;right:0;}/*!sc*/ @media (max-width:610px){.bxdiWb{margin:0 20px;}}/*!sc*/ data-styled.g131[id="sc-7725dd90-1"]{content:"bxdiWb,"}/*!sc*/ .eVjfbT{max-width:450px;}/*!sc*/ @media (max-width:610px){.eVjfbT{max-width:100%;}}/*!sc*/ data-styled.g132[id="sc-7725dd90-2"]{content:"eVjfbT,"}/*!sc*/ .FTXyR{font-family:WebRoboto,"Hiragino Kaku Gothic ProN","ヒラギノ角ゴ ProN",Meiryo,メイリオ,Arial,Helvetica,sans-serif;font-size:21px;font-weight:400;font-size:21px;line-height:1.4;text-align:center;margin-top:40px;}/*!sc*/ data-styled.g133[id="sc-7725dd90-3"]{content:"FTXyR,"}/*!sc*/ .dZUQwe{font-family:WebRoboto,"Hiragino Kaku Gothic ProN","ヒラギノ角ゴ ProN",Meiryo,メイリオ,Arial,Helvetica,sans-serif;font-size:21px;font-weight:400;font-size:14px;display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-flex-wrap:wrap;-ms-flex-wrap:wrap;flex-wrap:wrap;-webkit-box-pack:center;-webkit-justify-content:center;-ms-flex-pack:center;justify-content:center;line-height:1.6;margin-top:15px;max-width:510px;min-width:300px;}/*!sc*/ @media (max-width:610px){.dZUQwe{display:inline;text-align:center;}}/*!sc*/ data-styled.g134[id="sc-7725dd90-4"]{content:"dZUQwe,"}/*!sc*/ .kMebOO{margin-left:0px;}/*!sc*/ @media (max-width:610px){.kMebOO{margin-left:3px;}}/*!sc*/ data-styled.g135[id="sc-7725dd90-5"]{content:"kMebOO,"}/*!sc*/ .TCgXP{font-family:WebRoboto,"Hiragino Kaku Gothic ProN","ヒラギノ角ゴ ProN",Meiryo,メイリオ,Arial,Helvetica,sans-serif;border:none;padding:0;margin-left:3px;vertical-align:baseline;-webkit-text-decoration:none;text-decoration:none;}/*!sc*/ data-styled.g136[id="sc-7725dd90-6"]{content:"TCgXP,"}/*!sc*/ .ewOIPz{-webkit-flex:1 1 auto;-ms-flex:1 1 auto;flex:1 1 auto;position:relative;line-break:strict;word-break:keep-all;}/*!sc*/ data-styled.g137[id="sc-23dd3cf1-0"]{content:"ewOIPz,"}/*!sc*/ .ecRDnw{fill:#DD1100;}/*!sc*/ .dBldzu{fill:#ff7e00;}/*!sc*/ .mONEU{fill:#F16850;}/*!sc*/ .jRFdJj{fill:#FD694F;}/*!sc*/ .kFWYpd{fill:#FF3413;}/*!sc*/ .cQecPf{fill:#DC1D23;}/*!sc*/ .dkjILK{fill:#FF9281;}/*!sc*/ .isCULA{fill:#FF8B79;}/*!sc*/ .eQOMZU{fill:#EF5240;}/*!sc*/ .gyaiVl{fill:#FF482C;}/*!sc*/ .cYHDTA{fill:#EC2101;}/*!sc*/ .kCxIqU{fill:#D21C22;}/*!sc*/ .fUFcRC{fill:#C90901;}/*!sc*/ .cbwiQK{fill:#B6171E;}/*!sc*/ .hZKnPh{fill:#B4151B;}/*!sc*/ .hoGXfN{fill:#e63320;}/*!sc*/ .hCcIpc{fill:#FF4527;}/*!sc*/ .gSWKjc{fill:#FD684D;}/*!sc*/ .dRoNkL{fill:#FD745C;}/*!sc*/ data-styled.g147[id="sc-769b8e3a-0"]{content:"ecRDnw,dBldzu,mONEU,jRFdJj,kFWYpd,cQecPf,dkjILK,isCULA,eQOMZU,gyaiVl,cYHDTA,kCxIqU,fUFcRC,cbwiQK,hZKnPh,hoGXfN,hCcIpc,gSWKjc,dRoNkL,"}/*!sc*/ .cbtMcE{margin:0 10px 0 0;padding:0;}/*!sc*/ data-styled.g148[id="sc-e8d6c2a6-0"]{content:"cbtMcE,"}/*!sc*/ .IUSAe{border:none;}/*!sc*/ data-styled.g149[id="sc-e8d6c2a6-1"]{content:"IUSAe,"}/*!sc*/ .kihPBb{width:166px;height:25px;}/*!sc*/ data-styled.g150[id="sc-e8d6c2a6-2"]{content:"kihPBb,"}/*!sc*/ .elEomH{margin:10px 0;line-height:24px;}/*!sc*/ data-styled.g958[id="sc-db8e37e7-0"]{content:"elEomH,"}/*!sc*/ .cNFBIx{list-style:none;}/*!sc*/ .cNFBIx:before{content:'';background-color:#ff7e00;width:3px;height:3px;margin-right:5px;display:inline-block;margin-bottom:0.2em;}/*!sc*/ data-styled.g959[id="sc-db8e37e7-1"]{content:"cNFBIx,"}/*!sc*/ .fLkfwp{padding:10px 0;}/*!sc*/ data-styled.g961[id="sc-6f3cc790-0"]{content:"fLkfwp,"}/*!sc*/ .hHVOvk{font-size:21px;}/*!sc*/ data-styled.g962[id="sc-6f3cc790-1"]{content:"hHVOvk,"}/*!sc*/ .gboyJs{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-flex-wrap:wrap;-ms-flex-wrap:wrap;flex-wrap:wrap;-webkit-box-pack:justify;-webkit-justify-content:space-between;-ms-flex-pack:justify;justify-content:space-between;font-size:45px;-webkit-align-items:baseline;-webkit-box-align:baseline;-ms-flex-align:baseline;align-items:baseline;}/*!sc*/ data-styled.g963[id="sc-b9cbbaae-0"]{content:"gboyJs,"}/*!sc*/ .djLtIe{margin-right:40px;margin-bottom:16px;}/*!sc*/ data-styled.g964[id="sc-b9cbbaae-1"]{content:"djLtIe,"}/*!sc*/ .lcqAgv{font-size:15px;padding:0;border:none;}/*!sc*/ data-styled.g965[id="sc-b9cbbaae-2"]{content:"lcqAgv,"}/*!sc*/ .dSIrBv{max-width:830px;margin:32px auto 0 auto;padding:15px;font-size:15px;font-family:'Source Sans Pro',Arial,Helvetica,sans-serif;}/*!sc*/ data-styled.g966[id="sc-7618632e-0"]{content:"dSIrBv,"}/*!sc*/ </style></head><body><script>window.ENV_DATA = {"serviceEnv":{"iPhoneAppStore":"https://apps.apple.com/us/app/wolfram-alpha/id548861535","androidAppStore":"https://play.google.com/store/apps/details?id=com.wolfram.android.alpha","openCodeBlog":"https://blog.wolfram.com/2016/12/12/launching-wolframalpha-open-code/","dataRepo":"https://datarepository.wolframcloud.com/","wolframCommunityDiscussion":"https://community.wolfram.com/content?curTag=wolfram%20alpha","leadAnnouncement":"https://wolfr.am/chatgpt-plugin","pricingWarningInfoTime":"1718460000000,1718546400000","pricingWarningShowTime":"1718427600000,1718600399000"},"base":"https://www.wolframalpha.com","baseJA":"https://ja.wolframalpha.com","baseDE":"https://de.wolframalpha.com","baseES":"https://es.wolframalpha.com","baseFR":"https://fr.wolframalpha.com","baseKO":"https://ko.wolframalpha.com","basePT":"https://pt.wolframalpha.com","baseRU":"https://ru.wolframalpha.com","baseTW":"https://tw.wolframalpha.com","baseZH":"https://zh.wolframalpha.com","wolfram":"https://www.wolfram.com","wolframLanguage":"https://www.wolfram.com/language","wolframLanguageES":"https://www.wolfram.com/language/index.php.es","wolframLanguageJA":"https://www.wolfram.com/language/index.php.ja","wolframMathematica":"https://www.wolfram.com/mathematica","wolframMathematicaES":"https://www.wolfram.com/mathematica/index.php.es","wolframMathematicaJA":"https://www.wolfram.com/mathematica/index.php.ja","product":"https://products.wolframalpha.com","developer":"https://developer.wolframalpha.com","account":"https://account.wolfram.com","billing":"https://billing.wolfram.com","blog":"https://blog.wolfram.com","community":"https://community.wolfram.com","connect":"https://www.wolfram.com/connect/","youtube":"https://www.youtube.com/user/WolframAlpha","company":"https://company.wolfram.com","reference":"https://reference.wolfram.com","wolframScience":"https://www.wolframscience.com/","demonstration":"https://demonstrations.wolfram.com","mathworld":"https://mathworld.wolfram.com","functions":"http://functions.wolfram.com/","walTracking":"//wal.wolfram.com","notebookApi":"https://www.open.wolframcloud.com/opencloud/files","pricing":"/pro/pricing/","pricingStudent":"/pro/pricing/students/","pricingEducator":"/pro/pricing/educators/","privacy":"https://www.wolfram.com/legal/privacy/wolfram/index.html","privacyJA":"https://www.wolfram.com/legal/privacy/wolfram/index.ja.html","geoIpApi":"/n/v1/api/geoIp","results":"/gateway","webSocketProtocol":"wss://","fetcherDomain":"gateway.wolframalpha.com","enableMathMode":true,"disableUploads":false,"randomizerApi":"/n/v1/api/randomizer","autocompleteApi":"/n/v1/api/autocomplete","sampleDataApi":"/n/v1/api/samplefiles","sourcerApi":"/n/v1/api/sourcer","cdn":"https://www.wolframcdn.com","logconfig":"production","feedbackApi":"/n/v1/api/feedback","supportApi":"/input/sendFormData.jsp","uploadExamples":"https://www.wolframalpha.com/input/pro/uploadexamples/","pressCenter":"https://company.wolfram.com/press-center/wolframalpha/","stephenWritings":"https://writings.stephenwolfram.com/category/wolfram-alpha/","captchaApi":"/n/v1/api/captcha","displayDebuggingInfo":"off","userApi":"/users","authApi":"https://gateway.wolframalpha.com/auth","fileApi":"https://files.wolframalpha.com","contact":"/contact-us","downloads":"/downloads","samplefiles":"/samplefiles/filedownload","temporaryFileApi":"/api/v1/fileinput/data","queryHistoryLimit":"20","firefoxExtension":"https://addons.mozilla.org/firefox/downloads/file/3569991/wolframalpha_search_engine-1.0.2-an+fx.xpi","edgeExtension":"https://microsoftedge.microsoft.com/addons/detail/wolframalpha-official/gnehniboaligpegecmikojohlpngkobh","chromeExtension":"https://chrome.google.com/webstore/detail/wolframalpha-official/icncamkooinmbehmkeilcccmoljfkdhp","w3MathML":"https://www.w3.org/Math/","continuedFractionReference":"https://reference.wolfram.com/language/ref/ContinuedFraction.html","piReference":"https://reference.wolfram.com/language/ref/Pi.html","interpreterReference":"https://reference.wolfram.com/language/ref/Interpreter.html","developerApps":"/portal/myapps","developerWidgets":"/portal/mywidgets","service":"r-core","calculatorBottomDerivative":"https://reference.wolfram.com/language/ref/D.html","fakeUploadDelay":1500,"wolframSolutions":"https://www.wolframsolutions.com","simpleExplorerApi":"https://api.wolframalpha.com/v1/simple","devPortalApi":"/n/v1/api/devportal","notebook":"https://www.wolfram.com/wolfram-alpha-notebook-edition","notebookES":"https://www.wolfram.com/wolfram-alpha-notebook-edition/index.php.es","cookieDomain":".wolframalpha.com","createAuthCookies":false,"authCookieAppend":"","examplesApi":"/n/v1/api/examples","secureCookie":true,"nksBlogPost":"https://blog.wolfram.com/2009/05/14/7-years-of-nksand-its-first-killer-app/","sw":"https://www.stephenwolfram.com/","disableLanguages":[],"partialTranslate":false,"oauth":"gateway","ads":["BTSBanner"],"adrollAdvId":"YK5YAN4TMJFF5ER2Q5CWAP","adrollPixId":"XO5UPJF2XBFPZFSQFDAIIA"};window.IS_TOUCH = false;</script><script>window.onerror = function() { var script = document.createElement('script'); script.setAttribute('type', 'text/javascript'); script.setAttribute('src', '/_next/static/chunks/explorerWarning.js'); document.head.appendChild(script); }</script><div id="__next"><div class="__trY"><noscript class="sc-21c13e9a-0 ehESuO sc-7725dd90-0 iJLvQa"><div class="sc-7725dd90-1 bxdiWb"><img src="/_next/static/images/running-man_2cHgyknz.png" alt="no-js-running-man-logo" class="sc-7725dd90-2 eVjfbT"/><span class="sc-21c13e9a-1 dsKfRP sc-7725dd90-3 FTXyR">Uh oh! Wolfram|Alpha doesn't run without JavaScript.</span><div class="sc-21c13e9a-1 dsKfRP sc-7725dd90-4 dZUQwe">Please enable JavaScript. If you don't know how, you can find instructions<a href="https://enable-javascript.com/" target="_blank" class="_3BQD noScriptInstructionsLink _ZJzB sc-c233f61b-2 sc-c233f61b-3 czjJqi lfJXKd sc-7725dd90-6 TCgXP"><span class="sc-c233f61b-0 zsCsP">here</span></a>.<span class="sc-7725dd90-5 kMebOO">Once you've done that, refresh this page to start using Wolfram|Alpha.</span></div></div></noscript><header class="sc-23deba95-0 fabaKa"><nav class="sc-23deba95-1 eIjWBP sc-3d5da239-0 gkuhJX"><h1 class="sc-e8d6c2a6-0 cbtMcE"><a href="https://www.wolframalpha.com" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 cJHKlg lfJXKd sc-e8d6c2a6-1 IUSAe"><svg class="sc-e8d6c2a6-2 kihPBb" viewBox="0 0 295 45" fill="none"><path d="M81.702 6.885h-4.27l-5.275 22.848-5.299-22.654-.046-.194h-4.738L56.822 29.55 51.638 6.885h-4.34l6.886 29.402.046.194h4.898l5.264-22.471 5.207 22.277.034.194h4.99l6.999-29.288.08-.308zm9.431 6.417c-3.174 0-5.64 1.005-7.342 2.992-1.69 1.975-2.546 4.99-2.546 8.974 0 3.985.856 6.897 2.535 8.872 1.69 1.987 4.168 2.992 7.353 2.992 3.186 0 5.652-1.017 7.32-3.026 1.655-1.998 2.5-4.978 2.5-8.838 0-3.86-.834-6.908-2.49-8.917-1.666-2.021-4.132-3.037-7.33-3.037v-.012zm4.225 18.223c-.925 1.313-2.306 1.953-4.225 1.953-2.01 0-3.425-.651-4.328-1.976-.901-1.335-1.358-3.448-1.358-6.257 0-2.808.48-5.07 1.415-6.382.915-1.29 2.353-1.953 4.282-1.953 1.93 0 3.266.64 4.214 1.941.947 1.313 1.427 3.46 1.427 6.394 0 2.935-.468 4.944-1.404 6.269l-.023.011zm13.725-26.844h-4.065v31.8h4.065V4.68zm17.572.183c-1.278-.56-2.728-.845-4.327-.845-2.569 0-4.396.662-5.424 1.976-1.027 1.29-1.541 3.322-1.541 6.028v1.896h-3.209v3.516h3.209v19.023h4.065V17.447h4.852V13.93h-4.852v-1.895c0-1.759.217-2.946.662-3.517.422-.56 1.199-.845 2.329-.845.468 0 .994.08 1.587.228a6.877 6.877 0 011.462.526l.251.137 1.131-3.597-.206-.091.011-.012zm11.076 8.724a6.395 6.395 0 00-3.814 1.233 25.137 25.137 0 00-2.774 2.329v-3.231h-4.065v22.55h4.065V21.078c1.267-1.268 2.387-2.147 3.334-2.626a6.622 6.622 0 012.98-.72c.685 0 1.211.08 1.565.229l.273.114.88-3.94-.16-.09c-.571-.309-1.347-.469-2.284-.469v.012zm19.023 1.495c-1.404-1.187-3.722-1.78-6.908-1.78-2.055 0-3.802.33-5.195 1.004-1.404.674-2.477 1.655-3.163 2.911l-.114.206 3.346 2.055.125-.217c.331-.57.879-1.107 1.644-1.598.754-.491 1.862-.742 3.277-.742 1.599 0 2.855.296 3.757.89.856.571 1.302 1.667 1.302 3.266v.845l-5.161.468c-2.147.251-3.802.685-4.944 1.279-1.154.605-2.044 1.427-2.661 2.466-.605 1.04-.913 2.352-.913 3.905 0 2.055.593 3.768 1.758 5.092 1.176 1.336 2.854 2.01 5.001 2.01 1.45 0 2.775-.331 3.928-.993a20.156 20.156 0 002.992-2.124v2.466h4.064V21.261c0-2.89-.719-4.967-2.123-6.155l-.012-.023zm-7.753 18.315c-1.233 0-2.169-.274-2.774-.8-.594-.525-.891-1.415-.891-2.648 0-1.313.445-2.284 1.359-2.97.925-.696 2.58-1.14 4.898-1.346l3.232-.309v4.99c-.434.343-.868.697-1.313 1.05-.469.377-.959.708-1.462 1.005a9.923 9.923 0 01-1.53.742 4.166 4.166 0 01-1.519.286zm42.921-16.625c-.388-1.119-1.016-1.986-1.861-2.58-.845-.594-1.975-.89-3.345-.89a7.043 7.043 0 00-4.077 1.278c-1.084.754-2.158 1.69-3.197 2.774-.331-1.324-.913-2.329-1.747-2.968-.925-.72-2.158-1.085-3.677-1.085-1.37 0-2.683.411-3.882 1.222a18.079 18.079 0 00-2.786 2.318V13.93h-4.065v22.55h4.065V20.759c1.108-1.107 2.169-1.975 3.174-2.569.994-.594 1.873-.902 2.603-.902.788 0 1.371.137 1.725.4.354.262.605.742.765 1.404.16.708.24 2.101.24 4.145V36.47h4.064V20.747c1.405-1.313 2.558-2.238 3.415-2.73.856-.49 1.644-.741 2.317-.741.8 0 1.393.125 1.759.365.365.24.616.674.765 1.313.16.674.24 2.112.24 4.27v13.234h4.064V21.5c0-2.055-.194-3.642-.57-4.738l.011.011z" class="sc-769b8e3a-0 ecRDnw"></path><path d="M210.5 6.885h-5.343L195.143 36.47h4.453l2.454-7.57h11.396l2.501 7.57h4.578l-9.956-29.424-.057-.171-.012.011zm1.576 17.995h-8.701l4.35-13.154 4.351 13.154zm15.231-20.199h-4.065v31.8h4.065V4.68zm15.095 8.621a8.827 8.827 0 00-3.813.845 11.627 11.627 0 00-2.615 1.678V13.93h-4.065v30.6h4.065v-9.59c1.816 1.45 3.779 2.18 5.857 2.18 2.809 0 5.036-1.107 6.646-3.3 1.587-2.17 2.386-5.126 2.386-8.78 0-3.654-.742-6.657-2.215-8.666-1.484-2.044-3.596-3.072-6.257-3.072h.011zm4.271 11.83c0 2.865-.514 4.977-1.507 6.302-1.005 1.324-2.25 1.964-3.802 1.964-1.793 0-3.597-.754-5.379-2.25V19.697a12.25 12.25 0 012.581-1.86c1.005-.549 2.067-.834 3.151-.834 3.335 0 4.967 2.66 4.967 8.118l-.011.011zm19.137-11.83c-1.393 0-2.809.411-4.179 1.222a18.174 18.174 0 00-3.174 2.352V4.68h-4.065v31.8h4.065V20.769a21.84 21.84 0 013.413-2.466c1.177-.674 2.216-1.016 3.084-1.016.868 0 1.519.149 1.941.445.422.286.73.754.914 1.393.194.663.296 2.055.296 4.122v13.234h4.065V21.523c0-2.934-.514-5.058-1.53-6.303-1.028-1.267-2.66-1.907-4.83-1.907v-.01zm25.554 1.781c-1.405-1.187-3.723-1.78-6.908-1.78-2.056 0-3.802.33-5.196 1.004-1.404.674-2.477 1.655-3.162 2.911l-.114.206 3.345 2.055.125-.217c.332-.57.879-1.107 1.644-1.598.754-.491 1.862-.742 3.278-.742 1.598 0 2.855.296 3.756.89.857.571 1.302 1.667 1.302 3.266v.845l-5.161.468c-2.146.251-3.802.685-4.944 1.279-1.153.605-2.044 1.427-2.661 2.466-.604 1.04-.913 2.352-.913 3.905 0 2.055.594 3.768 1.759 5.092 1.175 1.336 2.854 2.01 5 2.01 1.451 0 2.775-.331 3.929-.993a20.15 20.15 0 002.991-2.124v2.466h4.065V21.261c0-2.89-.72-4.967-2.124-6.155l-.011-.023zm-7.753 18.315c-1.233 0-2.17-.274-2.775-.8-.594-.525-.89-1.415-.89-2.648 0-1.313.445-2.284 1.358-2.97.925-.696 2.581-1.14 4.898-1.346l3.232-.309v4.99c-.434.343-.867.697-1.313 1.05a12.25 12.25 0 01-1.462 1.005 9.879 9.879 0 01-1.53.742 4.157 4.157 0 01-1.518.286z" class="sc-769b8e3a-0 dBldzu"></path><path d="M42.343 28.397l-8.986 1.918.913 8.929-8.415-3.608-4.636 7.753-4.635-7.753-8.416 3.608.914-8.93-8.986-1.917 6.12-6.703-6.12-6.702 8.986-1.918-.914-8.93 8.416 3.609L21.219 0l4.636 7.753 8.415-3.608-.913 8.94 8.986 1.907-6.12 6.702 6.12 6.703z" class="sc-769b8e3a-0 mONEU"></path><path d="M21.219 13.542l-4.636-5.79-8.415-3.607 5.013 6.6 8.038 2.797z" class="sc-769b8e3a-0 jRFdJj"></path><path d="M9.082 13.074L.096 14.992l6.12 6.702 7.193-2.614-4.327-6.006z" class="sc-769b8e3a-0 kFWYpd"></path><path d="M13.18 10.744l-5.012-6.6.913 8.93 4.328 6.006-.228-8.336z" class="sc-769b8e3a-0 cQecPf"></path><path d="M25.856 7.753L21.22 0l-4.636 7.753 4.636 5.789 4.636-5.79z" class="sc-769b8e3a-0 dkjILK"></path><path d="M36.223 21.694l6.12-6.702-8.986-1.918-4.328 6.006 7.194 2.614z" class="sc-769b8e3a-0 isCULA"></path><path d="M29.03 19.08l4.327-6.006.925-8.93-5.024 6.6-.229 8.336z" class="sc-769b8e3a-0 jRFdJj"></path><path d="M29.258 10.744l5.024-6.6-8.426 3.609-4.636 5.789 8.038-2.798z" class="sc-769b8e3a-0 eQOMZU"></path><path d="M34.236 25.69l8.107 2.707-6.12-6.703-7.194-2.614 5.207 6.61z" class="sc-769b8e3a-0 gyaiVl"></path><path d="M13.41 19.08l-7.194 2.614-6.12 6.703 8.107-2.706 5.206-6.611z" class="sc-769b8e3a-0 cYHDTA"></path><path d="M21.22 34.928v8.46l4.636-7.752.194-7.593-4.83 6.885z" class="sc-769b8e3a-0 kCxIqU"></path><path d="M34.237 25.69l-8.187 2.353 7.308 2.272 8.986-1.918-8.107-2.706z" class="sc-769b8e3a-0 fUFcRC"></path><path d="M25.855 35.636l8.416 3.608-.914-8.929-7.307-2.272-.195 7.593z" class="sc-769b8e3a-0 cYHDTA"></path><path d="M8.203 25.69L.096 28.398l8.986 1.907 7.308-2.261-8.187-2.352z" class="sc-769b8e3a-0 cbwiQK"></path><path d="M16.39 28.043l.194 7.593 4.636 7.753v-8.461l-4.83-6.885z" class="sc-769b8e3a-0 hZKnPh"></path><path d="M9.081 30.303l-.913 8.94 8.415-3.607-.194-7.593-7.308 2.26z" class="sc-769b8e3a-0 kCxIqU"></path><path d="M29.03 19.08l.228-8.336-8.038 2.798v8.107l7.81-2.57z" class="sc-769b8e3a-0 hoGXfN"></path><path d="M21.22 13.542l-8.04-2.798.229 8.336 7.81 2.569v-8.107z" class="sc-769b8e3a-0 hCcIpc"></path><path d="M16.39 28.043l4.83 6.885 4.83-6.885-4.83-6.394-4.83 6.394z" class="sc-769b8e3a-0 dkjILK"></path><path d="M21.22 21.649l4.83 6.394 8.187-2.352-5.207-6.611-7.81 2.569z" class="sc-769b8e3a-0 gSWKjc"></path><path d="M13.41 19.08l-5.207 6.61 8.187 2.353 4.83-6.394-7.81-2.57z" class="sc-769b8e3a-0 dRoNkL"></path></svg></a></h1></nav></header><main class="sc-3d5da239-0 cMPKhv sc-23dd3cf1-0 ewOIPz"><div class="sc-21c13e9a-1 dsKfRP sc-7618632e-0 dSIrBv"><div class="sc-21c13e9a-1 eQkcfp sc-b9cbbaae-0 gboyJs"><h1 width="1280" class="sc-b9cbbaae-1 djLtIe">Wolfram|Alpha Pro Terms of Use</h1><a href="/termsofuse" class="_3BQD orange19RedHover _ZJzB sc-c233f61b-2 sc-c233f61b-3 bZJsei lfJXKd sc-b9cbbaae-2 lcqAgv">General Terms of Use »</a></div><div><section class="sc-6f3cc790-0 fLkfwp"><article><p class="sc-db8e37e7-0 elEomH">A Wolfram|Alpha Pro subscription ("Pro") will give you additional functionality and mechanisms for displaying and storing Wolfram|Alpha results. Additionally, you will be eligible for Pro Upload and Pro Download services ("Services") that will expand both the breadth of your access to Wolfram|Alpha data and the ways in which Wolfram|Alpha technology can be a tool for working with your own data. Except as specifically indicated herein, the <a href="/termsofuse" class="_3BQD orange19RedHover inlineLink sc-c233f61b-2 sc-c233f61b-3 bZJsei cosuER"><span class="sc-c233f61b-0 zsCsP">Wolfram|Alpha Terms of Use</span></a> shall apply to your use of Wolfram|Alpha.</p></article></section><section class="sc-6f3cc790-0 fLkfwp"><h4 id="PRO_SUBSCRIPTION" class="sc-21c13e9a-1 eQkcfp sc-6f3cc790-1 hHVOvk">Pro Subscription</h4><article><p class="sc-db8e37e7-0 elEomH">In signing up for Pro, you agree to be bound by the pricing, billing, and purchasing terms as provided to you throughout the purchase process by Wolfram|Alpha** as well as the <a href="https://www.wolfram.com/legal/privacy/wolfram" class="_3BQD orange19RedHover inlineLink sc-c233f61b-2 sc-c233f61b-3 bZJsei cosuER"><span class="sc-c233f61b-0 zsCsP"> Wolfram|Alpha Privacy Policy</span></a>. You are responsible for reviewing the Wolfram|Alpha Terms of Use and Privacy Policy from time to time; however, if Wolfram|Alpha changes the subscription fee or other usage charges at any time, Wolfram|Alpha will give you advance notice of these changes by email. All fees, charges, and unused credits are nonrefundable. Additional Pro usage rules:</p><li class="sc-db8e37e7-0 elEomH sc-db8e37e7-1 cNFBIx">You are required to have a Wolfram ID to sign up for a Pro subscription. You may never use another user's account or share yours with anyone else. When creating your account, you must provide accurate and complete information. You are solely responsible for the activity that occurs on your account, and you must keep your account password secure. You must notify Wolfram|Alpha immediately of any breach of security or unauthorized use of your account.</li><li class="sc-db8e37e7-0 elEomH sc-db8e37e7-1 cNFBIx">Although Wolfram|Alpha will not be liable for your losses caused by any unauthorized use of your account, you may be liable for the losses incurred by Wolfram|Alpha or others due to such unauthorized use.</li><li class="sc-db8e37e7-0 elEomH sc-db8e37e7-1 cNFBIx">Your Pro subscription is for one user accessing the Services from up to five (5) computers or mobile devices owned by you. However, you may only access the Services from one device at a time. If simultaneous or excessive use is detected, you may be blocked from your Pro account until the issue is resolved.</li><li class="sc-db8e37e7-0 elEomH sc-db8e37e7-1 cNFBIx">Billing: By providing a credit card or other payment method accepted by Wolfram Alpha LLC** for your subscription, you are expressly agreeing that we are authorized to charge you a periodic subscription fee on a recurring basis corresponding to the term of your subscription, any other fees for additional services you may purchase, and any applicable taxes in connection with your use of your subscription. You acknowledge that the amount billed each cycle may vary for reasons that may include differing amounts due to promotional offers or changing or adding a plan, and you authorize us to charge your payment method for such varying amounts, which may be billed monthly, annually, or semiannually.</li><li class="sc-db8e37e7-0 elEomH sc-db8e37e7-1 cNFBIx">Price Changes: We reserve the right to adjust pricing for our service or any components thereof in any manner and at any time as we may determine in our sole and absolute discretion. Except as otherwise expressly provided for in these Terms of Use, any price changes to your service will take effect following an email notice to you.</li><li class="sc-db8e37e7-0 elEomH sc-db8e37e7-1 cNFBIx">Cancellation and Refunds: You may cancel your subscription at any time via your account or through your store of purchase. Upon canceling your Pro subscription, you will not receive a refund, but you will continue to have access to your Pro account for the remainder of your current billing cycle.</li><li class="sc-db8e37e7-0 elEomH sc-db8e37e7-1 cNFBIx">Unpaid Amounts: It is important that each subscriber honor the payment obligations to which the subscriber agreed. Accordingly, we reserve the right to retry billing your payment method after failed attempts (e.g. if your payment method is rejected). We also reserve the right to pursue any amounts you fail to pay in connection with your subscription. You will remain liable for all such amounts and all costs incurred in connection with the collection of these amounts, including, without limitation, bank overdraft fees, collection agency fees, reasonable attorneys' fees, and arbitration or court costs.</li></article></section><section class="sc-6f3cc790-0 fLkfwp"><h4 id="PRO_DOWNLOAD_SERVICE" class="sc-21c13e9a-1 eQkcfp sc-6f3cc790-1 hHVOvk">Pro Download Service</h4><article><p class="sc-db8e37e7-0 elEomH">With Pro you can not only read what Wolfram|Alpha computes for you, you can also download it as data ("Pro Data") to use in many desktop formats. This expanded functionality in the Services may not be available for all data in Wolfram|Alpha due to various third-party data licensing restrictions. This expanded functionality in the download options does not modify, expand, or in any way change the limitations of use of data as expressed in the <a href="/termsofuse" class="_3BQD orange19RedHover inlineLink sc-c233f61b-2 sc-c233f61b-3 bZJsei cosuER"><span class="sc-c233f61b-0 zsCsP">Wolfram|Alpha Terms of Use</span></a>.</p><p class="sc-db8e37e7-0 elEomH">You may download Pro Data and results solely to a personal computer owned by you. You may not upload Pro Data to a third-party provider who may have rights to share the data or in any way make it private. You are liable for any damages to Wolfram or any third-party rights holders because of your improper storage or dissemination of Pro Data.</p></article></section><section class="sc-6f3cc790-0 fLkfwp"><h4 id="PRO_UPLOAD_SERVICE" class="sc-21c13e9a-1 eQkcfp sc-6f3cc790-1 hHVOvk">Pro Upload Service</h4><article><p class="sc-db8e37e7-0 elEomH">By using our Pro Upload Services for analysis and computation, you provide us with data, files, and images that you submit to Wolfram (together, "Submissions"). You retain full ownership of these Submissions. These Terms do not grant Wolfram any rights to Submissions except for the limited rights that are needed to run the Services, as explained below. You are solely responsible for your use of the Services and the content of your files and folders. It is your responsibility to ensure that you have the rights or permission to utilize the Pro Data Upload Services and otherwise as needed to comply with these Terms. You acknowledge that Wolfram has no obligation to monitor your content or any other information you upload or otherwise associate with the Services. We are not responsible for the accuracy, completeness, appropriateness, or legality of Submissions, results, analysis, computations, or any other information you may upload, store, receive, or access through or with the Services. Except as identified in our <a href="https://www.wolfram.com/legal/privacy/wolfram" class="_3BQD orange19RedHover inlineLink sc-c233f61b-2 sc-c233f61b-3 bZJsei cosuER"><span class="sc-c233f61b-0 zsCsP">Privacy Policy</span></a>, no matter how the Services change, we won't share your Submission content with others for any purpose. However, we do reserve the right to perpetually store your content.</p></article></section><section class="sc-6f3cc790-0 fLkfwp"><h4 id="APPROPRIATE_CONDUCT_CONTENT" class="sc-21c13e9a-1 eQkcfp sc-6f3cc790-1 hHVOvk">Appropriate Conduct and Content</h4><article><p class="sc-db8e37e7-0 elEomH">While using the Services you will comply with all applicable laws, rules, and regulations. You may not use the Services for any illegal, fraudulent, or unauthorized purpose. You are solely responsible for your conduct and any data, text, information, graphics, photos, profiles, audio clips, links, and other content ("Materials") that you submit, upload, and display via the Services. Wolfram|Alpha may, but shall have no obligation to, remove Materials that we determine in our sole discretion violate these Terms of Use.</p><p class="sc-db8e37e7-0 elEomH">Your use of the Services is conditional based on your compliance with the rules of conduct set forth in this section; any failure to comply may also result in termination of your access to the Service. Examples of illegal or unauthorized uses include, but are not limited to:</p><li class="sc-db8e37e7-0 elEomH sc-db8e37e7-1 cNFBIx">removing any copyright, trademark, or other proprietary rights notices contained in or on the Service or any results generated therefrom;</li><li class="sc-db8e37e7-0 elEomH sc-db8e37e7-1 cNFBIx">distributing results from the Services that express or imply that they are sponsored or endorsed by Wolfram;</li><li class="sc-db8e37e7-0 elEomH sc-db8e37e7-1 cNFBIx">submitting Materials that infringe, misappropriate, or violate the intellectual property, publicity, privacy, or other proprietary rights of any party;</li><li class="sc-db8e37e7-0 elEomH sc-db8e37e7-1 cNFBIx">reproducing, duplicating, copying, selling, reselling, or otherwise exploiting for any commercial purposes any results from Submissions or access to the Services;</li><li class="sc-db8e37e7-0 elEomH sc-db8e37e7-1 cNFBIx">creating a database by systematically downloading and storing all or any Wolfram|Alpha results or other content; and</li><li class="sc-db8e37e7-0 elEomH sc-db8e37e7-1 cNFBIx">submitting Submissions or Materials that are unlawful, would give rise to criminal or civil liability, or promote or encourage dangerous and/or illegal activity in the United States and/or the country from which you are accessing the Services.</li><p class="sc-db8e37e7-0 elEomH">You, and not Wolfram, are responsible for maintaining proper backups and for and protecting all of your Submissions. Wolfram will not be liable or responsible in any way for any loss or corruption of Submissions, or for any costs or expenses associated with backing up or restoring any of your Submissions.</p></article></section><section class="sc-6f3cc790-0 fLkfwp"><h4 id="ACCOUNT_SECURITY" class="sc-21c13e9a-1 eQkcfp sc-6f3cc790-1 hHVOvk">Account Security</h4><article><p class="sc-db8e37e7-0 elEomH">You are responsible for safeguarding the password that you use to access the Services and you agree not to disclose your password to any third party. You are responsible for any activity using your account, whether or not you authorized that activity. You should immediately notify Wolfram of any unauthorized use of your account. You acknowledge that if you wish to protect your transmission of data or files to Wolfram, it is your responsibility to use a secure encrypted connection to communicate with the Services.</p></article></section><section class="sc-6f3cc790-0 fLkfwp"><h4 id="DATA_RETENTION" class="sc-21c13e9a-1 eQkcfp sc-6f3cc790-1 hHVOvk">Data Retention</h4><article><p class="sc-db8e37e7-0 elEomH">Wolfram takes privacy and data protection seriously, and is committed to safeguarding data you share with us. To learn more, please see our <a href="https://www.wolfram.com/legal/privacy/wolfram" class="_3BQD orange19RedHover inlineLink sc-c233f61b-2 sc-c233f61b-3 bZJsei cosuER"><span class="sc-c233f61b-0 zsCsP">Privacy Policy</span></a>.</p></article></section><section class="sc-6f3cc790-0 fLkfwp"><article><p class="sc-db8e37e7-0 elEomH">** Purchases may be made through Wolfram|Alpha, WizAlpha or other applicable stores.</p><p class="sc-db8e37e7-0 elEomH">Effective as of June 29, 2023</p></article></section></div></div></main><footer class="sc-d3c8c5f1-0 hkxlVw sc-3d5da239-0 cMPKhv"><ul class="sc-aea496ab-0 dfMBtc"><li class="sc-87bc1c62-0 ksSXcu"><a href="/pro" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">Pro</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="https://products.wolframalpha.com/mobile" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">Mobile Apps</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="https://products.wolframalpha.com" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">Products</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="https://products.wolframalpha.com/enterprise" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">Business</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="https://products.wolframalpha.com/api" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">API & Developer Solutions</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="https://www.wolfram.com/resources/tools-for-AIs/" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">LLM Solutions</span></a></li></ul><ul class="sc-aea496ab-0 dfMBtc"><li class="sc-87bc1c62-0 ksSXcu"><a href="/resources" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">Resources & Tools</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="/about" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">About</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="/contact-us" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">Contact</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="/social" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">Connect</span><ul class="sc-9be66fc6-0 fvastQ"><li class="sc-9be66fc6-1 jrvlPG"><svg viewBox="0 0 14 14"><path class="mainColor" fill="#777" d="M14 1.5v11a1.5 1.5 0 0 1-1.5 1.5H9.834V8.463h1.894L12 6.35H9.834V5c0-.612.17-1.028 1.047-1.028H12V2.084A15.041 15.041 0 0 0 10.369 2C8.756 2 7.65 2.984 7.65 4.794v1.56h-1.9v2.112h1.903V14H1.5A1.5 1.5 0 0 1 0 12.5v-11A1.5 1.5 0 0 1 1.5 0h11A1.5 1.5 0 0 1 14 1.5z"></path></svg></li><li class="sc-9be66fc6-1 jrvlPG"><svg viewBox="0 0 42 42"><path class="mainColor" d="M37.5 0A4.5 4.5 0 0142 4.5v33a4.5 4.5 0 01-4.5 4.5h-33A4.5 4.5 0 010 37.5v-33A4.5 4.5 0 014.5 0zM15.21 5.727H6.681l11.18 16.452-11.18 13.14h2.526l9.775-11.49 7.808 11.49h8.527L23.724 18.256l10.661-12.53h-2.526l-9.257 10.88-7.393-10.88zM13.998 7.65L31.86 33.483h-3.88L10.117 7.65h3.88z" fill="#777"></path></svg></li><li class="sc-9be66fc6-1 jrvlPG"><svg width="14" height="14" viewBox="0 0 14 14"><g clip-path="url(#clip0_361_2946)"><mask id="mask0_361_2946" maskUnits="userSpaceOnUse" x="0" y="0" width="14" height="14"><path d="M14 0H0V14H14V0Z" class="mainColor"></path></mask><g><path d="M7 5.33313C6.67035 5.33325 6.34814 5.43112 6.07411 5.61435C5.80007 5.79758 5.58652 6.05796 5.46046 6.36255C5.33439 6.66714 5.30147 7.00228 5.36586 7.32558C5.43024 7.64888 5.58905 7.94583 5.82219 8.17888C6.05533 8.41194 6.35234 8.57063 6.67566 8.63489C6.99899 8.69916 7.33411 8.66612 7.63866 8.53993C7.9432 8.41375 8.20349 8.20011 8.38663 7.926C8.56976 7.6519 8.6675 7.32965 8.6675 7C8.66717 6.55791 8.49136 6.13403 8.1787 5.82149C7.86603 5.50894 7.44209 5.33329 7 5.33313ZM10.8972 4.05188C10.8123 3.83683 10.6842 3.64151 10.5207 3.47804C10.3572 3.31456 10.1619 3.18642 9.94688 3.10156C9.29063 2.8425 7.72813 2.90063 7 2.90063C6.27188 2.90063 4.71094 2.84031 4.05281 3.10156C3.83776 3.18642 3.64244 3.31456 3.47897 3.47804C3.3155 3.64151 3.18736 3.83683 3.1025 4.05188C2.84375 4.70813 2.90156 6.27219 2.90156 6.99969C2.90156 7.72719 2.84375 9.28937 3.10375 9.94777C3.18861 10.1629 3.31675 10.3582 3.48022 10.5217C3.64369 10.6851 3.83901 10.8133 4.05406 10.8981C4.71031 11.1572 6.27281 11.0991 7.00125 11.0991C7.72969 11.0991 9.29 11.1594 9.94813 10.8981C10.1632 10.8133 10.3585 10.6851 10.522 10.5217C10.6854 10.3582 10.8136 10.1629 10.8984 9.94777C11.1594 9.29157 11.0994 7.7275 11.0994 7C11.0994 6.2725 11.1594 4.71063 10.8984 4.05219L10.8972 4.05188ZM7 9.56247C6.49319 9.56247 5.99775 9.41217 5.57635 9.13057C5.15495 8.84907 4.82651 8.44886 4.63256 7.98063C4.43861 7.51239 4.38786 6.99716 4.48674 6.50008C4.58561 6.00301 4.82967 5.54641 5.18804 5.18804C5.54641 4.82967 6.00301 4.58561 6.50008 4.48674C6.99716 4.38787 7.51239 4.43861 7.98063 4.63256C8.44886 4.82651 8.84907 5.15495 9.13064 5.57635C9.41221 5.99775 9.5625 6.49319 9.5625 7C9.56291 7.33663 9.49691 7.67003 9.36828 7.98111C9.23965 8.2922 9.05091 8.57485 8.81288 8.81288C8.57485 9.05091 8.2922 9.23957 7.98111 9.36827C7.67003 9.49687 7.33663 9.56287 7 9.56247ZM9.66813 4.92813C9.54982 4.92819 9.43414 4.89316 9.33574 4.82748C9.23734 4.76179 9.16063 4.6684 9.11531 4.55911C9.06999 4.44982 9.0581 4.32955 9.08114 4.21351C9.10419 4.09746 9.16113 3.99086 9.24476 3.90717C9.3284 3.82349 9.43498 3.7665 9.55101 3.74339C9.66704 3.72029 9.78732 3.73212 9.89663 3.77738C10.0059 3.82264 10.0994 3.8993 10.1651 3.99767C10.2309 4.09604 10.2659 4.21169 10.2659 4.33C10.2663 4.40857 10.2511 4.48643 10.2213 4.55911C10.1914 4.6318 10.1475 4.69788 10.0921 4.75356C10.0367 4.80925 9.97082 4.85344 9.89827 4.88362C9.82573 4.91379 9.74794 4.92934 9.66938 4.92938L9.66813 4.92813ZM12.5 0H1.5C1.10218 0 0.720645 0.15804 0.43934 0.43934C0.158036 0.72065 0 1.10218 0 1.5V12.5C0 12.8978 0.158036 13.2794 0.43934 13.5607C0.720645 13.842 1.10218 14 1.5 14H12.5C12.8978 14 13.2794 13.842 13.5607 13.5607C13.842 13.2794 14 12.8978 14 12.5V1.5C14 1.10218 13.842 0.72065 13.5607 0.43934C13.2794 0.15804 12.8978 0 12.5 0ZM11.965 9.06247C11.9247 9.86337 11.7419 10.5731 11.1572 11.1563C10.5725 11.7394 9.86344 11.9259 9.06344 11.9641C8.23813 12.0106 5.76375 12.0106 4.93844 11.9641C4.1375 11.9238 3.43031 11.7406 2.84469 11.1563C2.25906 10.5719 2.075 9.86187 2.03688 9.06247C1.99031 8.23688 1.99031 5.76219 2.03688 4.9375C2.07719 4.13656 2.25781 3.42688 2.84469 2.84375C3.43156 2.26063 4.14063 2.07625 4.93844 2.03813C5.76375 1.99156 8.23813 1.99156 9.06344 2.03813C9.86438 2.07844 10.5738 2.26156 11.1572 2.84594C11.7406 3.43032 11.9269 4.14031 11.965 4.94125C12.0116 5.76375 12.0116 8.23625 11.965 9.06247Z" class="mainColor"></path></g></g><defs><clipPath id="clip0_361_2946"><rect class="mainColor" width="14" height="14" fill="white"></rect></clipPath></defs></svg></li><li class="sc-9be66fc6-1 jrvlPG"><svg viewBox="0 0 14 14"><path class="mainColor" fill="#777" d="M13 0H.997C.447 0 0 .453 0 1.01v11.98C0 13.548.447 14 .997 14H13c.55 0 1-.453 1-1.01V1.01C14 .452 13.55 0 13 0zM4.231 11.994H2.156V5.313h2.078v6.68h-.003zM3.203 4.406A1.204 1.204 0 1 1 3.204 2a1.204 1.204 0 0 1 0 2.407zm8.803 7.597H9.931v-3.25c0-.775-.015-1.772-1.078-1.772-1.081 0-1.247.844-1.247 1.716v3.306H5.531V5.322h1.99v.912h.029c.278-.525.956-1.078 1.966-1.078 2.1 0 2.49 1.385 2.49 3.185v3.662z"></path></svg></li></ul></a></li></ul><ul class="sc-aea496ab-0 LJgzy"><li class="sc-87bc1c62-0 ksSXcu"><span class="sc-105e6ee4-0 ejuFmI"><span class="sc-105e6ee4-1 dhgquj">©2025 </span>Wolfram</span></li><li class="sc-87bc1c62-0 ksSXcu"><a href="/termsofuse" target="_blank" rel="noopener noreferrer" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">Terms</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="https://www.wolfram.com/legal/privacy/wolfram" target="_blank" rel="noopener noreferrer" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">Privacy</span></a></li></ul><ul class="sc-aea496ab-0 cunmhB"><li class="sc-87bc1c62-0 hBBSJU"><a aria-label="wolfram.com" href="https://www.wolfram.com" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><svg class="sc-2983807f-0 bqpxBo" viewBox="0 0 112 25"><path class="sc-70463ee1-0 fExnFO" d="M26.01 8.34h2.962l1.395 7.621L32.42 8.34h2.606l2.439 7.755 1.426-7.755h2.815L39.3 19.744h-3.25l-2.161-7.115-2.211 7.115h-3.41L26.01 8.34zm21.902 9.345c1.842 0 2.574-1.765 2.574-3.643 0-1.98-.732-3.645-2.574-3.645-1.842 0-2.575 1.666-2.575 3.644 0 1.879.733 3.643 2.575 3.643zm0-9.543c3.748 0 5.704 2.24 5.704 5.9 0 3.627-1.988 5.897-5.704 5.897-3.715 0-5.703-2.27-5.703-5.898 0-3.66 1.955-5.899 5.703-5.899zm7.399.196h3.031v9.15h4.693v2.254h-7.724V8.338zm8.98 0h7.607v2.157H67.32v2.5h4.382v2.156H67.32v4.59h-3.03V8.339zm12.222 4.74h.8c.977 0 2.216-.034 2.216-1.325 0-1.061-1.06-1.258-2.216-1.258h-.8v2.583zm-3.03-4.74h5.41c2.02 0 3.667.914 3.667 2.876 0 1.52-.717 2.533-2.184 2.876v.033c.977.262 1.043 1.128 1.613 2.517l1.107 3.102h-3.16l-.651-2.057c-.62-1.96-1.01-2.452-2.135-2.452h-.637v4.509h-3.03V8.338zm16.064 2.354h-.032l-1.467 4.46h2.85l-1.351-4.46zm-1.86-2.354h3.718l4.383 11.404h-3.325l-.847-2.433h-4.269l-.896 2.433H83.37l4.318-11.404zm18.608.001h3.408l2.258 11.404v.001h-2.963l-1.392-7.65-2.057 7.65h-2.606l-2.429-7.753-1.436 7.753h-2.816l2.41-11.405h3.25l2.16 7.122 2.213-7.122z"></path><path class="sc-70463ee1-1 gMmFFj" d="M17.493 16.571l-2.056-.678 2.458-.754 2.302.82-2.704.612zm-3.283 3.02l.071-3.05 2.752.908.344 3.59-3.167-1.449zm-8.405-2.143l2.752-.906.07 3.048-3.167 1.447.345-3.589zm-3.162-1.492l2.3-.817 2.457.754-2.056.677-2.701-.614zm1.57-3.039l1.94-.75-1.508 2.04-2.21.785 1.778-2.075zm-2.434-3.68l3.384-.766 1.626 2.404-2.712 1.047-2.298-2.684zm11.384-4.183L11.42 7.372l-1.743-2.32 1.742-3.105 1.744 3.107zM21.06 9.24l-2.297 2.684-2.713-1.05 1.627-2.402 3.383.768zm-8.878 3.489l2.96-1.038 1.97 2.664-3.103.953-1.827-2.58zm-2.658 4.79l1.424 2.163v2.531L9.575 19.77l-.051-2.25zm1.132-4.79l-1.826 2.58-3.104-.954 1.97-2.664 2.96 1.038zm-4.83-4.984l-.274-2.847 1.391 1.955.07 2.648-1.188-1.756zm6.065.771l3.047-1.128-.09 3.37-2.957 1.037V8.516zm-3.9 2.241L7.9 7.388l3.047 1.128v3.279L7.99 10.757zm3.428 7.905l-1.827-2.776 1.827-2.58 1.827 2.58-1.827 2.776zm5.596-10.916l-1.19 1.756.07-2.648 1.394-1.956-.274 2.848zM14.03 5.494l2.46-1.125-1.355 1.904-2.343.867 1.238-1.646zM10.047 7.14l-2.343-.867-1.356-1.906 2.461 1.126 1.238 1.647zm3.215 12.63l-1.371 2.443v-2.531l1.423-2.162-.052 2.25zm7.14-4.777l-2.209-.786-1.506-2.038 1.94.75 1.775 2.074zm-.87-2.492L22.84 8.64l-4.856-1.102.495-5.149-4.55 2.08L11.418 0 8.913 4.468l-4.55-2.081.494 5.148L0 8.636l3.305 3.863L0 16.362l4.855 1.102-.494 5.148 4.55-2.08L11.42 25l2.507-4.467 4.55 2.08-.494-5.148 4.857-1.1-3.307-3.864z"></path></svg></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="https://www.wolfram.com" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">wolfram.com</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="https://www.wolfram.com/language" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">Wolfram Language</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="https://www.wolfram.com/mathematica" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">Mathematica</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="https://demonstrations.wolfram.com" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">Wolfram Demonstrations</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="https://www.wolfram.com/education" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">Wolfram for Education</span></a></li><li class="sc-87bc1c62-0 ksSXcu"><a href="https://mathworld.wolfram.com" colorInfo="[object Object]" class="_3BQD _dGJe _ZJzB sc-c233f61b-2 sc-c233f61b-3 klpTfJ lfJXKd sc-87bc1c62-1 kqXe"><span class="sc-c233f61b-0 zsCsP">MathWorld</span></a></li></ul></footer><div class="sc-78826ae-0 ECfnZ"></div></div></div><script id="__NEXT_DATA__" type="application/json">{"props":{"staticContext":{"cookies":{},"domain":"www.wolframalpha.com"},"isTouch":false,"userIPInfo":{"isGDPR":false,"country":"SG"},"browserString":"IE","language":"en","pageProps":{}},"page":"/termsofuse/pro","query":{},"buildId":"TArlO3n_zK_862JVBqVpv","isFallback":false,"customServer":true,"appGip":true,"scriptLoader":[]}</script></body></html>