How it works
Calculate total and component surface areas for nine common three-dimensional shapes. Inputs are calculated locally in the browser, and valid values are retained in the page URL for bookmarking.
Input query strings and outputs
Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.
Input query strings
20-
?shape=SolidChoice · Required · Default: sphere · Accepted values: sphere, cone, cube, cylinder, box, capsule, spherical-cap, frustum, ellipsoid
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?sphereRadius=Sphere radiusNumber · Required · Default: 5 · Used when shape = sphere
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?coneRadius=Cone radiusNumber · Required · Default: 3 · Used when shape = cone
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?coneHeight=Cone heightNumber · Required · Default: 4 · Used when shape = cone
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?cubeEdge=Cube edgeNumber · Required · Default: 5 · Used when shape = cube
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?cylinderRadius=Cylinder radiusNumber · Required · Default: 3 · Used when shape = cylinder
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?cylinderHeight=Cylinder heightNumber · Required · Default: 5 · Used when shape = cylinder
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?boxLength=Tank lengthNumber · Required · Default: 10 · Used when shape = box
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?boxWidth=Tank widthNumber · Required · Default: 6 · Used when shape = box
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?boxHeight=Tank heightNumber · Required · Default: 4 · Used when shape = box
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?capsuleRadius=Capsule radiusNumber · Required · Default: 2 · Used when shape = capsule
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?capsuleHeight=Cylinder-section heightNumber · Required · Default: 6 · Used when shape = capsule
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?capBallRadius=Ball radiusNumber · Required · Default: 5 · Used when shape = spherical-cap
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?capHeight=Cap heightNumber · Required · Default: 2 · Used when shape = spherical-cap
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?frustumTopRadius=Top radiusNumber · Required · Default: 2 · Used when shape = frustum
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?frustumBottomRadius=Bottom radiusNumber · Required · Default: 4 · Used when shape = frustum
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?frustumHeight=Frustum heightNumber · Required · Default: 6 · Used when shape = frustum
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?ellipsoidA=Ellipsoid axis aNumber · Required · Default: 3 · Used when shape = ellipsoid
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?ellipsoidB=Ellipsoid axis bNumber · Required · Default: 4 · Used when shape = ellipsoid
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?ellipsoidC=Ellipsoid axis cNumber · Required · Default: 5 · Used when shape = ellipsoid
Outputs
5-
surfaceAreaTotal surface areaNumber · Primary output
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lateralAreaLateral or curved areaNumber
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baseAreaBase areaNumber
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volumeVolumeNumber
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shapeNameSolidText
Formula notes
Examples: sphere 4πr²; cone πr(r+√(r²+h²)); cylinder 2πr(r+h); box 2(lw+lh+wh).
Input guidance
Use consistent units for every length or measurement in the same calculation. Results are educational mathematical estimates and should be checked before high-stakes use.