# Surface Area Calculator

> Calculate total and component surface areas for nine common three-dimensional shapes.

Page: https://askcalculators.com/calculator/surface-area-calculator/
Definition: https://askcalculators.com/calculator/surface-area-calculator/definition.json
JSON Schema: https://askcalculators.com/calculator/surface-area-calculator/schema.json
Version: 2.0.0
Maintained by: AskCalculators (software project; not a credentialed reviewer)
Qualified review: pending. Automated checks do not establish professional approval.
Page status: Live
Review status: Pending

## Use
Open the calculator page and enter values. Query-string parameters can restore and bookmark a calculation.
Example: https://askcalculators.com/calculator/surface-area-calculator/?shape=sphere&sphereRadius=5

## Inputs
- shape: Solid; type=select; required; default=sphere; values=sphere|cone|cube|cylinder|box|capsule|spherical-cap|frustum|ellipsoid
- sphereRadius: Sphere radius; type=number; required; default=5; min=0.000001; showWhen=shape:sphere
- coneRadius: Cone radius; type=number; required; default=3; min=0.000001; showWhen=shape:cone
- coneHeight: Cone height; type=number; required; default=4; min=0.000001; showWhen=shape:cone
- cubeEdge: Cube edge; type=number; required; default=5; min=0.000001; showWhen=shape:cube
- cylinderRadius: Cylinder radius; type=number; required; default=3; min=0.000001; showWhen=shape:cylinder
- cylinderHeight: Cylinder height; type=number; required; default=5; min=0.000001; showWhen=shape:cylinder
- boxLength: Tank length; type=number; required; default=10; min=0.000001; showWhen=shape:box
- boxWidth: Tank width; type=number; required; default=6; min=0.000001; showWhen=shape:box
- boxHeight: Tank height; type=number; required; default=4; min=0.000001; showWhen=shape:box
- capsuleRadius: Capsule radius; type=number; required; default=2; min=0.000001; showWhen=shape:capsule
- capsuleHeight: Cylinder-section height; type=number; required; default=6; min=0.000001; showWhen=shape:capsule
- capBallRadius: Ball radius; type=number; required; default=5; min=0.000001; showWhen=shape:spherical-cap
- capHeight: Cap height; type=number; required; default=2; min=0.000001; showWhen=shape:spherical-cap
- frustumTopRadius: Top radius; type=number; required; default=2; min=0.000001; showWhen=shape:frustum
- frustumBottomRadius: Bottom radius; type=number; required; default=4; min=0.000001; showWhen=shape:frustum
- frustumHeight: Frustum height; type=number; required; default=6; min=0.000001; showWhen=shape:frustum
- ellipsoidA: Ellipsoid axis a; type=number; required; default=3; min=0.000001; showWhen=shape:ellipsoid
- ellipsoidB: Ellipsoid axis b; type=number; required; default=4; min=0.000001; showWhen=shape:ellipsoid
- ellipsoidC: Ellipsoid axis c; type=number; required; default=5; min=0.000001; showWhen=shape:ellipsoid

## Outputs
- surfaceArea: Total surface area; format=number; primary
- lateralArea: Lateral or curved area; format=number
- baseArea: Base area; format=number
- volume: Volume; format=number
- shapeName: Solid; format=text

## Formula
Examples: sphere 4πr²; cone πr(r+√(r²+h²)); cylinder 2πr(r+h); box 2(lw+lh+wh).

## Rules
- Empty optional inputs are undefined, not zero.
- Hidden conditional inputs are ignored.
- Do not invent missing required inputs.