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The simplest coordinate system consists of coordinate axes oriented perpendicularly to each other, known as Cartesian coordinates. Depending on the type of problem under consideration, coordinate systems possessing special properties may allow particularly simple solution. In three dimensions, so-called right-handed coordinate systems (left figure) are usually chosen by convention, although left-handed..." /> <meta name="DC.Subject" scheme="MathWorld" content="Mathematics:Geometry:Coordinate Geometry" /> <meta name="DC.Subject" scheme="MSC_2000" content="51N10" /> <meta name="DC.Rights" content="Copyright 1999-2024 Wolfram Research, Inc. 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The simplest coordinate system consists of coordinate axes oriented perpendicularly to each other, known as Cartesian coordinates. Depending on the type of problem under consideration, coordinate systems possessing special properties may allow particularly simple solution. In three dimensions, so-called right-handed coordinate systems (left figure) are usually chosen by convention, although left-handed..."> <meta name="twitter:card" content="summary_large_image"> <meta name="twitter:site" content="@WolframResearch"> <meta name="twitter:title" content="Coordinate System -- from Wolfram MathWorld"> <meta name="twitter:description" content="A system for specifying points using coordinates measured in some specified way. The simplest coordinate system consists of coordinate axes oriented perpendicularly to each other, known as Cartesian coordinates. Depending on the type of problem under consideration, coordinate systems possessing special properties may allow particularly simple solution. In three dimensions, so-called right-handed coordinate systems (left figure) are usually chosen by convention, although left-handed..."> <meta name="twitter:image:src" content="https://mathworld.wolfram.com/images/socialmedia/share/ogimage_CoordinateSystem.png"> <link rel="canonical" href="https://mathworld.wolfram.com/CoordinateSystem.html" /> <meta http-equiv="x-ua-compatible" content="ie=edge"> <meta name="viewport" content="width=device-width, initial-scale=1"> <meta charset="utf-8"> <script async src="/common/javascript/analytics.js"></script> <script async src="//www.wolframcdn.com/consent/cookie-consent.js"></script> <script async src="/common/javascript/wal/latest/walLoad.js"></script> <link rel="stylesheet" href="/css/styles.css"> <link rel="preload" href="//www.wolframcdn.com/fonts/source-sans-pro/1.0/global.css" as="style" onload="this.onload=null;this.rel='stylesheet'"> <noscript><link rel="stylesheet" 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href="/topics/CoordinateGeometry.html">Coordinate Geometry</a> </li> </ul></nav>   <h1>Coordinate System</h1>  <hr class="margin-t-1-8 margin-b-3-4">   <div class="entry-content"> <p> A system for specifying points using <a href="/Coordinates.html">coordinates</a> measured in some specified way. The simplest coordinate system consists of coordinate axes oriented perpendicularly to each other, known as <a href="/CartesianCoordinates.html">Cartesian coordinates</a>. Depending on the type of problem under consideration, coordinate systems possessing special properties may allow particularly simple solution. </p> <div class="table-responsive-noborders"> <table align="center" border="0"> <tr style=""><td align="center"> <div class="center-image"> <img style="max-width:100%;max-height:100%;" width="169.354" height="120.924" src="images/eps-svg/RightHandedCoordinates_700.svg" class="" alt="RightHandedCoordinates" /> </div> </td><td align="center"> <div class="center-image"> <img style="max-width:100%;max-height:100%;" width="159.979" height="131.143" src="images/eps-svg/LeftHandedCoordinates_700.svg" class="" alt="LeftHandedCoordinates" /> </div> </td></tr> </table> </div> <p> In three dimensions, so-called <a href="/Right-HandedCoordinateSystem.html">right-handed coordinate systems</a> (left figure) are usually chosen by convention, although <a href="/Left-HandedCoordinateSystem.html">left-handed coordinate systems</a> (right figure) are also encountered occasionally. </p> </div>  <hr class="margin-b-1-1-4"> <div class="c-777 entry-secondary-content">  <h2>See also</h2><a href="/Coordinates.html">Coordinates</a>, <a href="/CurvilinearCoordinates.html">Curvilinear Coordinates</a>, <a href="/CyclidicCoordinates.html">Cyclidic Coordinates</a>, <a href="/Left-HandedCoordinateSystem.html">Left-Handed Coordinate System</a>, <a href="/Right-HandedCoordinateSystem.html">Right-Handed Coordinate System</a>, <a href="/SkewCoordinateSystem.html">Skew Coordinate System</a>, <a href="/OrthogonalCoordinateSystem.html">Orthogonal Coordinate System</a>       <h2>Explore with Wolfram|Alpha</h2> <div id="WAwidget"> <div class="WAwidget-wrapper"> <img alt="WolframAlpha" title="WolframAlpha" src="/images/wolframalpha/WA-logo.png" width="136" height="20"> <form name="wolframalpha" action="https://www.wolframalpha.com/input/" target="_blank"> <input type="text" name="i" class="search" placeholder="Solve your math problems and get step-by-step solutions" value=""> <button type="submit" title="Evaluate on WolframAlpha"></button> </form> </div> <div class="WAwidget-wrapper try"> <p class="text-align-r"> More things to try: </p> <ul> <li> <a target="_blank" href="http://www.wolframalpha.com/input/?i=6-sphere+coordinates"> 6-sphere coordinates </a> </li> <li> <a target="_blank" href="http://www.wolframalpha.com/input/?i=polar+coordinates+of+vector+%28-1%2C+-1%29"> polar coordinates of vector (-1, -1) </a> </li> <li> <a target="_blank" href="http://www.wolframalpha.com/input/?i=spherical+coordinates+of+vector+%281%2C+2%2C+3%29"> spherical coordinates of vector (1, 2, 3) </a> </li> </ul> </div> </div>     <h2>Cite this as:</h2> <p> <a href="/about/author.html">Weisstein, Eric W.</a> "Coordinate System." From <a href="/"><i>MathWorld</i></a>--A Wolfram Web Resource. <a href="https://mathworld.wolfram.com/CoordinateSystem.html">https://mathworld.wolfram.com/CoordinateSystem.html</a> </p>  <h2>Subject classifications</h2><nav class="breadcrumbs"><ul class="breadcrumb"> <li> <a href="/topics/Geometry.html">Geometry</a> </li> <li> <a href="/topics/CoordinateGeometry.html">Coordinate Geometry</a> </li> </ul></nav>  </div> </section> </section>  </div> </main> <aside id="bottom"> <style> #bottom { padding-bottom: 65px; } #acknowledgment { display:none; } .attribution { font-size: .75rem; font-style: italic; } footer ul li:not(:last-of-type)::after { background: #a3a3a3; margin-left: .3rem; margin-right: .1rem; } @media all and (max-width: 900px) { .attribution { font-size: 12px; } } @media (max-width: 600px) { footer { max-width: 360px; } footer ul { max-width: 360px; } footer ul:nth-child(1) li:nth-child(2):after { content: ""; height: 11px; } footer ul:nth-child(1) li:nth-child(3):after { content: ""; height: 0px; } } </style> <footer> <ul> <li><a href="/about/">About MathWorld</a></li> <li><a href="/classroom/">MathWorld Classroom</a></li> <li><a href="/contact/">Contribute</a></li> <li><a href="https://www.amazon.com/exec/obidos/ASIN/1420072218/ref=nosim/weisstein-20" target="_blank">MathWorld Book</a></li> <li class="display-n display-ib__600"><a href="https://www.wolfram.com" target="_blank">wolfram.com</a></li> </ul> <ul> <li class="display-n__600"><a href="/whatsnew/">13,208 Entries</a></li> <li class="display-n__600"><a href="/whatsnew/">Last Updated: Thu Nov 21 2024</a></li>  <li><a href="https://www.wolfram.com" target="_blank">©1999–2024 Wolfram Research, Inc.</a></li> <li><a href="https://www.wolfram.com/legal/terms/mathworld.html" target="_blank">Terms of Use</a></li> </ul> <ul class="wolfram"> <li class="display-n__600 display-n__900"><a href="https://www.wolfram.com" target="_blank" aria-label="Wolfram"><img src="/images/footer/wolfram-logo.png" alt="Wolfram" title="Wolfram" width="121" height="28"></a></li> <li class="display-n__600"><a href="https://www.wolfram.com" target="_blank">wolfram.com</a></li> <li class="display-n__600"><a href="https://www.wolfram.com/education/" target="_blank">Wolfram for Education</a></li> <li class="attribution">Created, developed and nurtured by Eric Weisstein at Wolfram Research</li> </ul> </footer> <section id="acknowledgment"> <i>Created, developed and nurtured by Eric Weisstein at Wolfram Research</i> </section> </aside> <script type="text/javascript" src="/scripts/scripts.js"></script> <script src="/common/js/c2c/1.0/WolframC2C.js"></script> <script src="/common/js/c2c/1.0/WolframC2CGui.js"></script> <script src="/common/js/c2c/1.0/WolframC2CDefault.js"></script> <link rel="stylesheet" href="/common/js/c2c/1.0/WolframC2CGui.css.en"> <style> .wolfram-c2c-wrapper { padding: 0px !important; border: 0px; } .wolfram-c2c-wrapper:active { border: 0px; } .wolfram-c2c-wrapper:hover { border: 0px; } </style> <script> let c2cWrittings = new WolframC2CDefault({'triggerClass':'mathworld-c2c_above', 'uniqueIdPrefix': 'mathworld-c2c_above-'}); </script> <style> #IPstripe-outer { background: #47a2af; } #IPstripe-outer:hover { background: #0095aa; } </style> <div id="IPstripe-wrap"></div> <script src="/common/stripe/stripe.en.js"></script> </body> </html>