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<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Spheroid - Geometry Calculator</title> <meta name="description" content="Calculations of geometric shapes and solids: Spheroid."> <meta name="robots" content="index,follow"> <script type="text/plain" async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-9435517763545530" crossorigin="anonymous" data-cmp-custom-vendor="492" data-cmp-script></script> <link rel="stylesheet" href="pi.css" type="text/css"> <link rel="alternate" hreflang="de" href="https://rechneronline.de/pi/sphaeroid.php"> <link rel="alternate" hreflang="en" href="https://rechneronline.de/pi/spheroid.php"> <link rel="canonical" href="https://rechneronline.de/pi/spheroid.php"> <script type="text/javascript"> function docalc() { var a=parseFloat(document.getElementById("v0").value.replace(",",".")); var c=parseFloat(document.getElementById("v1").value.replace(",",".")); if(!a||!c) { alert("Please enter both semi axes."); return false; } if(a==c) { alert("a=c is a sphere, please calculate there."); return false; } if(a<0) { a=-a; document.getElementById("v0").value=a; } if(c<0) { c=-c; document.getElementById("v1").value=c; } var ro=document.getElementById("r").selectedIndex; var e=0; var area=2*Math.PI*a; if(a>c) { e=Math.sqrt((a*a-c*c)/(a*a)); area*=(a+c*c/Math.sqrt(a*a-c*c)*ash(Math.sqrt(a*a-c*c)/c)); } else { e=Math.sqrt((c*c-a*a)/(c*c)); area*=(a+c*c/Math.sqrt(c*c-a*a)*Math.asin(Math.sqrt(c*c-a*a)/c)); } var v=4/3*Math.PI*a*a*c; document.getElementById("v2").value=rounddig(area,ro); document.getElementById("v3").value=rounddig(v,ro); document.getElementById("v4").value=rounddig(area/v,ro); document.getElementById("v5").value=rounddig(e,ro); } function ash(x) { return Math.log(x+Math.sqrt(x*x+1)); } function rounddig(i,j) { return Math.round(Math.pow(10,j)*i)/Math.pow(10,j); } </script> <script type="text/javascript"> function res() { for(var i=0;i<20;++i) { if(document.getElementById("v"+i)) document.getElementById("v"+i).value=""; } } </script> <script type="text/javascript" src="https://cdn.opencmp.net/tcf-v2/cmp-stub-latest.js" id="open-cmp-stub" data-domain="rechneronline.de"></script> <script type="text/javascript" id="trfAdSetup" async data-traffectiveConf='{ "targeting": [{"key":"zone","values":null,"value":"sonstiges"}] ,"dfpAdUrl" : "/307308315,73333489/Rechneronline" }' src="//cdntrf.com/trf-rechneronline.js"></script></head> <body><a id="top"></a> <center> <div class="outer"> <br><br> <table border="0" cellspacing="0" cellpadding="0" class="all"><tr> <td style="text-align:left;width:40%;line-height:25px"><a href="geometry.php">Geometry</a> | <a href="forms.php">Forms</a> | <a href="https://rechneronline.de/impressum.php" class="n">Contact & Privacy</a></td> <td style="text-align:center;width:20%"><b>Geometric Calculators</b></td> <td style="text-align:right;width:40%">German: <a href="./" hreflang="de">Geometrierechner</a>, <a href="formen.php" hreflang="de">Formen</a></td></tr></table><br> <table border="0" cellspacing="0" cellpadding="0" class="all"><tr><td style="text-align:left"> <fieldset style="width:200px;line-height:20px"> <legend>1D</legend><a href="line.php" class="n">Line</a>, <a href="circular-arc.php" class="n">Circular Arc</a>, <a href="parabola.php" class="n">Parabola</a>, <a href="helix-e.php" class="n">Helix</a>, <a href="koch-curve.php" class="n">Koch Curve</a> </fieldset> <fieldset style="width:200px;line-height:20px"> <legend>2D</legend> <b>Regular Polygons:</b><br><a href="equilateral-triangle.php" class="n">Equilateral Triangle</a>, <a href="square-calculator.php">Square</a>, <a href="pentagon.php">Pentagon</a>, <a href="hexagon.php">Hexagon</a>, <a href="heptagon.php">Heptagon</a>, <a href="octagon.php">Octagon</a>, <a href="nonagon.php">Nonagon</a>, <a href="decagon.php">Decagon</a>, <a href="hendecagon.php">Hendecagon</a>, <a href="dodecagon.php">Dodecagon</a>, <a href="hexadecagon.php">Hexadecagon</a>, <a href="n-gon.php" class="n">N-gon</a>, <a href="polygon-ring.php" class="n">Polygon Ring</a><br><br> <b>Other Polygons:</b><br><a href="triangle.php">Triangle</a>, <a href="right-triangle.php" class="n">Right Triangle</a>, <a href="isosceles-triangle.php" class="n">Isosceles Triangle</a>, <a href="ir-triangle.php" class="n">IR Triangle</a>, <a href="half-equilateral-triangle.php" class="n">1/2 EL Triangle</a>, <a href="golden-triangle.php" class="n">Golden Triangle</a>, <a href="quadrilateral.php">Quadrilateral</a>, <a href="rectangle.php">Rectangle</a>, <a href="golden-rectangle.php" class="n">Golden Rectangle</a>, <a href="rhombus.php">Rhombus</a>, <a href="equidiagonal-rhombus.php" class="n">Equidiagonal Rhombus</a>, <a href="parallelogram.php">Parallelogram</a>, <a href="kite.php">Kite</a>, <a href="60-90-120-kite.php">60-90-120 Kite</a>, <a href="half-square-kite.php" class="n">Half Square Kite</a>, <a href="right-kite.php" class="n">Right Kite</a>, <a href="trapezoid.php">Trapezoid</a>, <a href="right-trapezoid.php" class="n">Right Trapezoid</a>, <a href="isosceles-trapezoid.php" class="n">Isosceles Trapezoid</a>, <a href="tri-equilateral-trapezoid.php" class="n">Tri-equilateral Trapezoid</a>, <a href="obtuse-trapezoid.php" class="n">Obtuse Trapezoid</a>, <a href="cyclic-quadrilateral.php" class="n">Cyclic Quadrilateral</a>, <a href="tangential-quadrilateral.php" class="n">Tangential Quadrilateral</a>, <a href="arrowhead-quadrilateral.php">Arrowhead</a>, <a href="concave-quadrilateral.php" class="n">Concave Quadrilateral</a>, <a href="crossed-rectangle.php" class="n">Crossed Rectangle</a>, <a href="antiparallelogram.php">Antiparallelogram</a>, <a href="house-shape.php" class="n">House-Shape</a>, <a href="axial-symmetric-pentagon.php" class="n">Symmetric Pentagon</a>, <a href="diagonally-bisected-octagon.php" class="n">Diagonally Bisected Octagon</a>, <a href="cut-rectangle.php" class="n">Cut Rectangle</a>, <a href="concave-pentagon.php" class="n">Concave Pentagon</a>, <a href="concave-regular-pentagon.php" class="n">Concave Regular Pentagon</a>, <a href="stretched-pentagon.php" class="n">Stretched Pentagon</a>, <a href="straight-bisected-octagon.php" class="n">Straight Bisected Octagon</a>, <a href="stretched-hexagon.php" class="n">Stretched Hexagon</a>, <a href="symmetric-hexagon.php" class="n">Symmetric Hexagon</a>, <a href="semiregular-hexagon.php" class="n">Semi-regular Hexagon</a>, <a href="parallelogon-e.php">Parallelogon</a>, <a href="concave-hexagon.php" class="n">Concave Hexagon</a>, <a href="arrow-hexagon.php" class="n">Arrow-Hexagon</a>, <a href="rectangular-hexagon.php" class="n">Rectangular Hexagon</a>, <a href="L-shape.php" class="n">L-Shape</a>, <a href="sharp-kink.php" class="n">Sharp Kink</a>, <a href="T-shape.php" class="n">T-Shape</a>, <a href="square-heptagon.php" class="n">Square Heptagon</a>, <a href="truncated-square.php" class="n">Truncated Square</a>, <a href="stretched-octagon.php" class="n">Stretched Octagon</a>, <a href="frame.php">Frame</a>, <a href="open-frame.php" class="n">Open Frame</a>, <a href="grid.php">Grid</a>, <a href="cross.php">Cross</a>, <a href="X-shape.php" class="n">X-Shape</a>, <a href="H-shape.php" class="n">H-Shape</a>, <a href="threestar.php">Threestar</a>, <a href="fourstar.php">Fourstar</a>, <a href="pentagram.php">Pentagram</a>, <a href="hexagram.php">Hexagram</a>, <a href="unicursal-hexagram.php" class="n">Unicursal Hexagram</a>, <a href="octagram.php">Oktagram</a>, <a href="star-of-lakshmi.php" class="n">Star of Lakshmi</a>, <a href="double-star-polygon.php" class="n">Double Star Polygon</a>, <a href="polygram.php">Polygram</a>, <a href="the-hat.php" class="n">The Hat</a>, <a href="simple-polygon.php">Polygon</a><br><br> <b>Round Forms:</b><br><a href="circle-calculator.php">Circle</a>, <a href="semicircle.php">Semicircle</a>, <a href="circular-sector.php" class="n">Circular Sector</a>, <a href="circular-segment.php" class="n">Circular Segment</a>, <a href="circular-layer.php" class="n">Circular Layer</a>, <a href="circular-central-segment.php" class="n">Circular Central Segment</a>, <a href="round-corner.php" class="n">Round Corner</a>, <a href="circular-corner.php" class="n">Circular Corner</a>, <a href="circle-tangent-arrow.php" class="n">Circle Tangent Arrow</a>, <a href="drop-shape.php" class="n">Drop Shape</a>, <a href="crescent.php">Crescent</a>, <a href="pointed-oval.php" class="n">Pointed Oval</a>, <a href="two-circles.php" class="n">Two Circles</a>, <a href="lancet-arch.php" class="n">Lancet Arch</a>, <a href="knoll.php">Knoll</a>, <a href="elongated-semicircle.php" class="n">Elongated Semicircle</a>, <a href="annulus.php">Annulus</a>, <a href="semi-annulus.php" class="n">Semi-Annulus</a>, <a href="annulus-sector.php" class="n">Annulus Sector</a>, <a href="annulus-segment.php" class="n">Annulus Segment</a>, <a href="cash.php">Cash</a>, <a href="curved-rectangle.php" class="n">Curved Rectangle</a>, <a href="rounded-polygon.php" class="n">Rounded Polygon</a>, <a href="rounded-rectangle.php" class="n">Rounded Rectangle</a>, <a href="ellipse-e.php">Ellipse</a>, <a href="semi-ellipse.php" class="n">Semi-Ellipse</a>, <a href="elliptical-segment.php" class="n">Elliptical Segment</a>, <a href="elliptical-sector.php" class="n">Elliptical Sector</a>, <a href="elliptical-ring.php" class="n">Elliptical Ring</a>, <a href="stadium.php">Stadium</a>, <a href="half-stadium.php" class="n">Half Stadium</a>, <a href="stadium-segment.php" class="n">Stadium Segment</a>, <a href="spiral.php">Spiral</a>, <a href="logarithmic-spiral.php" class="n">Log. Spiral</a>, <a href="reuleaux-triangle.php" class="n">Reuleaux Triangle</a>, <a href="cycloid.php">Cycloid</a>, <a href="double-cycloid.php" class="n">Double Cycloid</a>, <a href="astroid.php">Astroid</a>, <a href="hypocycloid.php">Hypocycloid</a>, <a href="cardioid.php">Cardioid</a>, <a href="epicycloid.php">Epicycloid</a>, <a href="parabolic-segment.php" class="n">Parabolic Segment</a>, <a href="heart.php">Heart</a>, <a href="tricorn.php">Tricorn</a>, <a href="pointed-semicircle.php" class="n">Pointed Semicircle</a>, <a href="interarc-triangle.php" class="n">Interarc Triangle</a>, <a href="circular-arc-triangle.php" class="n">Circular Arc Triangle</a>, <a href="interarc-quadrangle.php" class="n">Interarc Quadrangle</a>, <a href="intercircle-quadrangle.php" class="n">Intercircle Quadrangle</a>, <a href="circular-arc-quadrangle.php" class="n">Circular Arc Quadrangle</a>, <a href="circular-arc-polygon.php" class="n">Circular Arc Polygon</a>, <a href="claw.php">Claw</a>, <a href="half-yin-yang.php" class="n">Half Yin-Yang</a>, <a href="arbelos-e.php">Arbelos</a>, <a href="salinon-e.php">Salinon</a>, <a href="bulge.php">Bulge</a>, <a href="lune.php">Lune</a>, <a href="three-circles.php" class="n">Three Circles</a>, <a href="polycircle.php">Polycircle</a>, <a href="round-edged-polygon.php" class="n">Round-Edged Polygon</a>, <a href="rose.php">Rose</a>, <a href="gear.php">Gear</a>, <a href="oval-e.php">Oval</a>, <a href="egg-profile.php" class="n">Egg-Profile</a>, <a href="lemniscate.php">Lemniscate</a>, <a href="squircle.php">Squircle</a>, <a href="circular-square.php" class="n">Circular Square</a>, <a href="digon.php">Digon</a>, <a href="spherical-triangle.php" class="n">Spherical Triangle</a><br> </fieldset> <fieldset style="width:200px;line-height:20px"> <legend>3D</legend> <b>Platonic Solids:</b><br><a href="tetrahedron.php">Tetrahedron</a>, <a href="cube-calculator.php">Cube</a>, <a href="octahedron.php">Octahedron</a>, <a href="dodecahedron.php">Dodecahedron</a>, <a href="icosahedron.php">Icosahedron</a><br><br> <b>Archimedean Solids:</b><br><a href="truncated-tetrahedron.php" class="n">Truncated Tetrahedron</a>, <a href="cuboctahedron.php">Cuboctahedron</a>, <a href="truncated-cube.php" class="n">Truncated Cube</a>, <a href="truncated-octahedron.php" class="n">Truncated Octahedron</a>, <a href="rhombicuboctahedron.php">Rhombicuboctahedron</a>, <a href="truncated-cuboctahedron.php" class="n">Truncated Cuboctahedron</a>, <a href="icosidodecahedron.php">Icosidodecahedron</a>, <a href="truncated-dodecahedron.php" class="n">Truncated Dodecahedron</a>, <a href="truncated-icosahedron.php" class="n">Truncated Icosahedron</a>, <a href="snub-cube.php" class="n">Snub Cube</a>, <a href="rhombicosidodecahedron.php">Rhombicosidodecahedron</a>, <a href="truncated-icosidodecahedron.php" class="n">Truncated Icosidodecahedron</a>, <a href="snub-dodecahedron.php" class="n">Snub Dodecahedron</a><br><br> <b>Catalan Solids:</b><br><a href="triakis-tetrahedron.php" class="n">Triakis Tetrahedron</a>, <a href="rhombic-dodecahedron.php" class="n">Rhombic Dodecahedron</a>, <a href="triakis-octahedron.php" class="n">Triakis Octahedron</a>, <a href="tetrakis-hexahedron.php" class="n">Tetrakis Hexahedron</a>, <a href="deltoidal-icositetrahedron.php" class="n">Deltoidal Icositetrahedron</a>, <a href="hexakis-octahedron.php" class="n">Hexakis Octahedron</a>, <a href="rhombic-triacontahedron.php" class="n">Rhombic Triacontahedron</a>, <a href="triakis-icosahedron.php" class="n">Triakis Icosahedron</a>, <a href="pentakis-dodecahedron.php" class="n">Pentakis Dodecahedron</a>, <a href="pentagonal-icositetrahedron.php" class="n">Pentagonal Icositetrahedron</a>, <a href="deltoidal-hexecontahedron.php" class="n">Deltoidal Hexecontahedron</a>, <a href="hexakis-icosahedron.php" class="n">Hexakis Icosahedron</a>, <a href="pentagonal-hexecontahedron.php" class="n">Pentagonal Hexecontahedron</a><br><br> <b>Johnson Solids:</b><br><a href="johnson-pyramid.php">Pyramids</a>, <a href="cupola.php">Cupolae</a>, <a href="rotunda.php">Rotunda</a>, <a href="elongated-pyramid.php" class="n">Elongated Pyramids</a>, <a href="gyroelongated-pyramid.php" class="n">Gyroelongated Pyramids</a>, <a href="johnson-bipyramid.php">Bipyramids</a>, <a href="elongated-bipyramid.php" class="n">Elongated Bipyramids</a>, <a href="gyroelongated-square-dipyramid.php" class="n">Gyroelongated Square Dipyramid</a>, <a href="gyrobifastigium.php">Gyrobifastigium</a>, <a href="disheptahedron.php">Disheptahedron</a>, <a href="snub-disphenoid.php" class="n">Snub Disphenoid</a>, <a href="sphenocorona-e.php">Sphenocorona</a>, <a href="disphenocingulum-e.php">Disphenocingulum</a><br><br> <b>Other Polyhedrons:</b><br><a href="cuboid.php">Cuboid</a>, <a href="square-pillar.php" class="n">Square Pillar</a>, <a href="triangular-pyramid.php" class="n">Triangular Pyramid</a>, <a href="pyramid.php" class="n">Square Pyramid</a>, <a href="regular-pyramid.php" class="n">Regular Pyramid</a>, <a href="pyramid-2.php">Pyramid</a>, <a href="square-frustum.php" class="n">Square Frustum</a>, <a href="regular-frustum.php" class="n">Regular Frustum</a>, <a href="frustum.php">Frustum</a>, <a href="bent-pyramid.php" class="n">Bent Pyramid</a>, <a href="regular-bipyramid.php" class="n">Regular Bipyramid</a>, <a href="bipyramid.php">Bipyramid</a>, <a href="regular-bifrustum.php">Bifrustum</a>, <a href="frustum-pyramid.php" class="n">Frustum-Pyramid</a>, <a href="ramp.php">Ramp</a>, <a href="right-wedge.php" class="n">Right Wedge</a>, <a href="wedge.php">Wedge</a>, <a href="half-tetrahedron.php" class="n">Half Tetrahedron</a>, <a href="rhombohedron.php">Rhombohedron</a>, <a href="parallelepiped-e.php">Parallelepiped</a>, <a href="regular-prism.php" class="n">Regular Prism</a>, <a href="prism.php">Prism</a>, <a href="oblique-prism.php" class="n">Oblique Prism</a>, <a href="anticube.php">Anticube</a>, <a href="antiprism.php">Antiprism</a>, <a href="prismatoid-e.php">Prismatoid</a>, <a href="trapezohedron.php">Trapezohedron</a>, <a href="disphenoid-e.php">Disphenoid</a>, <a href="corner.php">Corner</a>, <a href="general-tetrahedron.php" class="n">General Tetrahedron</a>, <a href="wedge-cuboid.php" class="n">Wedge-Cuboid</a>, <a href="half-cuboid.php" class="n">Half Cuboid</a>, <a href="skewed-cuboid.php" class="n">Skewed Cuboid</a>, <a href="ingot.php">Ingot</a>, <a href="skewed-three-edged-prism.php" class="n">Skewed Three-Edged Prism</a>, <a href="cut-cuboid.php" class="n">Cut Cuboid</a>, <a href="truncated-cuboid.php" class="n">Truncated Cuboid</a>, <a href="obtuse-edged-cuboid.php" class="n">Obtuse Edged Cuboid</a>, <a href="elongated-dodecahedron.php" class="n">Elongated Dodecahedron</a>, <a href="truncated-rhombohedron.php" class="n">Truncated Rhombohedron</a>, <a href="obelisk-e.php">Obelisk</a>, <a href="bent-cuboid.php" class="n">Bent Cuboid</a>, <a href="hollow-cuboid.php" class="n">Hollow Cuboid</a>, <a href="hollow-pyramid.php" class="n">Hollow Pyramid</a>, <a href="hollow-frustum.php" class="n">Hollow Frustum</a>, <a href="star-pyramid.php" class="n">Star Pyramid</a>, <a href="stellated-octahedron.php" class="n">Stellated Octahedron</a>, <a href="small-stellated-dodecahedron.php" class="n">Small Stellated Dodecahedron</a>, <a href="great-stellated-dodecahedron.php" class="n">Great Stellated Dodecahedron</a>, <a href="great-dodecahedron.php" class="n">Great Dodecahedron</a>, <a href="great-icosahedron.php" class="n">Great Icosahedron</a><br><br> <b>Round Forms:</b><br><a href="sphere-calculator.php">Sphere</a>, <a href="hemisphere.php">Hemisphere</a>, <a href="quarter-sphere.php" class="n">Quarter Sphere</a>, <a href="spherical-corner.php" class="n">Spherical Corner</a>, <a href="cylinder.php">Cylinder</a>, <a href="cut-cylinder.php" class="n">Cut Cylinder</a>, <a href="oblique-cylinder.php" class="n">Oblique Cylinder</a>, <a href="bent-cylinder.php" class="n">Bent Cylinder</a>, <a href="elliptic-cylinder.php" class="n">Elliptic Cylinder</a>, <a href="generalized-cylinder.php" class="n">Generalized Cylinder</a>, <a href="cone.php">Cone</a>, <a href="truncated-cone.php" class="n">Truncated Cone</a>, <a href="oblique-circular-cone.php" class="n">Oblique Circular Cone</a>, <a href="elliptic-cone.php" class="n">Elliptic Cone</a>, <a href="truncated-elliptic-cone.php" class="n">Truncated Elliptic Cone</a>, <a href="general-cone.php" class="n">General Cone</a>, <a href="general-truncated-cone.php" class="n">General Truncated Cone</a>, <a href="bicone.php">Bicone</a>, <a href="truncated-bicone.php" class="n">Truncated Bicone</a>, <a href="pointed-pillar.php" class="n">Pointed Pillar</a>, <a href="rounded-cone.php" class="n">Rounded Cone</a>, <a href="elongated-hemisphere.php" class="n">Elongated Hemisphere</a>, <a href="drop.php">Drop</a>, <a href="spheroid.php">Spheroid</a>, <a href="ellipsoid-e.php">Ellipsoid</a>, <a href="semi-ellipsoid.php" class="n">Semi-Ellipsoid</a>, <a href="spherical-sector.php" class="n">Spherical Sector</a>, <a href="spherical-cap.php" class="n">Spherical Cap</a>, <a href="spherical-segment.php" class="n">Spherical Segment</a>, <a href="spherical-central-segment.php" class="n">Spherical Central Segment</a>, <a href="double-calotte.php" class="n">Double Calotte</a>, <a href="rounded-disc.php" class="n">Rounded Disc</a>, <a href="double-sphere.php" class="n">Double Sphere</a>, <a href="spherical-wedge.php" class="n">Spherical Wedge</a>, <a href="half-cylinder.php" class="n">Half Cylinder</a>, <a href="diagonally-halved-cylinder.php" class="n">Diagonally Halved Cylinder</a>, <a href="cylindrical-wedge.php" class="n">Cylindrical Wedge</a>, <a href="cylindrical-sector.php" class="n">Cylindrical Sector</a>, <a href="cylindrical-segment.php" class="n">Cylindrical Segment</a>, <a href="flat-end-cylinder.php" class="n">Flat End Cylinder</a>, <a href="half-cone.php" class="n">Half Cone</a>, <a href="conical-sector.php" class="n">Conical Sector</a>, <a href="conical-wedge.php" class="n">Conical Wedge</a>, <a href="spherical-shell.php" class="n">Spherical Shell</a>, <a href="half-spherical-shell.php" class="n">Half Spherical Shell</a>, <a href="spherical-shell-cap.php" class="n">Spherical Shell Cap</a>, <a href="cylindrical-shell.php" class="n">Cylindrical Shell</a>, <a href="cut-cylindrical-shell.php" class="n">Cut Cylindrical Shell</a>, <a href="oblique-cylindrical-shell.php" class="n">Oblique Cylindrical Shell</a>, <a href="hollow-cone.php" class="n">Hollow Cone</a>, <a href="truncated-hollow-cone.php" class="n">Truncated Hollow Cone</a>, <a href="spherical-ring.php" class="n">Spherical Ring</a>, <a href="torus-e.php">Torus</a>, <a href="spindle-torus.php" class="n">Spindle Torus</a>, <a href="toroid-e.php">Toroid</a>, <a href="torus-sector.php" class="n">Torus Sector</a>, <a href="toroid-sector.php" class="n">Toroid Sector</a>, <a href="arch.php">Arch</a>, <a href="reuleaux-tetrahedron.php" class="n">Reuleaux-Tetrahedron</a>, <a href="capsule.php">Capsule</a>, <a href="half-capsule.php" class="n">Half Capsule</a>, <a href="capsule-segment.php" class="n">Capsule Segment</a>, <a href="double-point.php" class="n">Double Point</a>, <a href="anticone.php">Anticone</a>, <a href="truncated-anticone.php" class="n">Truncated Anticone</a>, <a href="sphere-cylinder-intersection.php" class="n">Sphere-Cylinder</a>, <a href="lens.php">Lens</a>, <a href="concave-lens.php" class="n">Concave Lens</a>, <a href="barrel.php">Barrel</a>, <a href="egg-shape.php" class="n">Egg Shape</a>, <a href="paraboloid-e.php">Paraboloid</a>, <a href="hyperboloid-e.php">Hyperboloid</a>, <a href="oloid-e.php">Oloid</a>, <a href="steinmetz-solids.php" class="n">Steinmetz Solids</a>, <a href="solid-of-revolution.php" class="n">Solid of Revolution</a><br> </fieldset> <fieldset style="width:200px;line-height:20px"> <legend>4D</legend> <a href="tesseract.php" class="n">Tesseract</a>, <a href="hypersphere.php" class="n">Hypersphere</a><br> </fieldset> </td><td style="padding-left:5px"> <br> <script type="text/plain" async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-9435517763545530" crossorigin="anonymous" data-cmp-custom-vendor="492" data-cmp-script></script>  <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-9435517763545530" data-ad-slot="9191691689" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> <br><div style="font-size:10px;margin-top:1px">Anzeige</div><br> <br> <div class="content"> <h1>Spheroid Calculator</h1> <p>Calculations at a spheroid (ellipsoid of revolution). A spheroid is an <a href="ellipsoid-e.php">ellipsoid</a> with two semi axes of equal length. There are two forms: the oblate or flattened spheroid with a>c, this is the form of stars and planets. With a<c, it is a prolate or elongated spheroid, like an American football or rugby ball. With a=c, it is a <a href="sphere-calculator.php">sphere</a>.<br>Enter the semi axes a and c, choose the number of decimal places and click Calculate.</p><br> <form> <center> <table border="0" cellspacing="2" cellpadding="0"> <tr><td rowspan="10" class="imr"><img src="img/euclid.jpg" width="150" height="150" alt="Euclid" title="Euclid, 'Artes liberales Geometria'"></td> <td class="r">Equatorial semi axes (a): </td><td class="r"><input type="number" step="any" id="v0" class="l"></td><td class="lc"><input type="button" value=" C " onclick="document.getElementById('v0').value=''"></td> <td rowspan="10" class="iml"><img src="img/oblate-spheroid.png" width="150" height="150" alt="Oblate spheroid"><br> Oblate spheroid<br> <img src="img/prolate-spheroid.png" width="150" height="150" alt="Prolate spheroid"><br> Prolate spheroid</td></tr> <tr><td class="r">Polar semi axis (c): </td><td class="r"><input type="number" step="any" id="v1" class="l"></td><td class="lc"><input type="button" value=" C " onclick="document.getElementById('v1').value=''"></td></tr> <tr><td class="r">Ellipticity (e): </td><td class="r"><input id="v5" class="l" readonly></td><td></td></tr> <tr><td class="r">Surface area (A): </td><td class="r"><input id="v2" class="l" readonly></td><td></td></tr> <tr><td class="r">Volume (V): </td><td class="r"><input id="v3" class="l" readonly></td><td></td></tr> <tr><td class="r">Surface-to-volume ratio (A/V): </td><td class="r"><input id="v4" class="l" readonly></td><td></td></tr> <tr><td colspan="2">Round to  <select id="r"> <option> 0 </option> <option> 1 </option> <option> 2 </option> <option selected> 3 </option> <option> 4 </option> <option> 5 </option> <option> 6 </option> <option> 7 </option> <option> 8 </option> <option> 9 </option> <option> 10 </option> <option> 11 </option> <option> 12 </option> <option> 13 </option> <option> 14 </option> <option> 15 </option> </select>  decimal places.</td><td></td></tr> <tr><td class="r"><br><input type="button" class="l" value="Calculate" onclick="docalc()"></td><td class="r"><br><input type="button" class="l" value="Delete" onclick="res()"></td><td></td></tr> <tr><td class="fm" colspan="3"> <br><br> <b>Formulas:</b><br><br> Oblate spheroid, a>c:<br> e = √<span style="border-top:1px solid #000"> ( a² - c² ) / a² </span><br> A = 2πa * [ a + c² / √<span style="border-top:1px solid #000"> a² - c² </span> * arsinh( √<span style="border-top:1px solid #000"> a² - c² </span> / c ) ]<br><br> Prolate spheroid, a<c:<br> e = √<span style="border-top:1px solid #000"> ( c² - a² ) / c² </span><br> A = 2πa * [ a + c² / √<span style="border-top:1px solid #000"> c² - a² </span> * arcsin( √<span style="border-top:1px solid #000"> c² - a² </span> / c ) ]<br><br> V = 4/3 * π * a² * c<br> <br> pi:<br> π = 3.141592653589793... </td></tr><br> </table> </center> </form> <br> <div class="fm"> <p>The semi axes have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit <sup>-1</sup>. Ellipticity is dimensionless.</p> <p>The ellipticity of celestial bodies is caused by the conflict between two forces. The gravitational force pulls everything towards the center of mass, so it wants to form a sphere. The centrifugal force, which is caused by rotation, pushes outwards into a plane, so if it were only up to it, a <a href="circle-calculator.php">circle</a> would be formed. The faster a celestial body rotates around itself, the flatter it becomes. The oblate spheroid can be seen as an intermediate stage between a sphere and a circle. The smaller the ellipticity, the more spherical the spheroid is. The ellipticity of the earth is 0.081, so it is already very close to a sphere.</p> <p>The ellipticity does not provide any information about whether it is a oblate or a prolate spheroid. To distinguish between them, you have to compare the lengths of the semi-axes. If you swap the values of the two different semi-axes, the oblate spheroid has a larger surface area and a larger volume than the prolate. This is because the longer axis a is present twice there and is therefore included in the weighting twice as often.</p> <br><br> © <a href="https://jumk.de/indexengl.html">Jumk.de Webprojects</a> | <a href="https://rechneronline.de/english.php">Online Calculators</a> <br><br><hr><br><br> <script type="text/plain" async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-9435517763545530" crossorigin="anonymous" data-cmp-custom-vendor="492" data-cmp-script></script>  <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-9435517763545530" data-ad-slot="4742624485" data-ad-format="auto"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> <br><div style="font-size:10px;margin-top:1px">Anzeige</div> </div> </td></tr> </table> <br><br> <script type="text/plain" async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-9435517763545530" crossorigin="anonymous" data-cmp-custom-vendor="492" data-cmp-script></script>  <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-9435517763545530" data-ad-slot="2579545285" data-ad-format="auto"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> <br><div style="font-size:10px;margin-top:1px">Anzeige</div> <br><br> </div> <br> <a href="#top">↑ up</a> </center><br><br><br><br> <div class="trr"><div id="traffective-ad-WpSkyscraper" style='display:none' class='WpSkyscraper'></div></div> <div class="trr2"><div id="traffective-ad-HalfpageAd" style='display:none' class="HalfpageAd"></div></div> <script type="text/javascript"> if(document.getElementById('v0')) document.getElementById('v0').focus(); </script> </body> </html>