Surface Area Calculator

How it works

Checking which surfaces are included

Surface area adds the modeled exposed faces of a solid, rather than measuring the space inside it. Review the selected shape's formula to see whether bases, ends, or inner surfaces are included. This matters for tasks such as covering a container or comparing an open and closed shape. The output uses squared units, even though the object itself has volume.

Sphere: formula and assumptions

A = 4πr².

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Cone: formula and assumptions

A = πr(r + √(r²+h²)).

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Cube: formula and assumptions

A = 6a².

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Cylinder: formula and assumptions

A = 2πr(r+h).

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Rectangular prism: formula and assumptions

A = 2(ab+ah+bh).

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Capsule: formula and assumptions

A = 2πrh + 4πr².

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Spherical cap: formula and assumptions

Total area = 2πrh + π(2rh−h²), including the flat base.

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Conical frustum: formula and assumptions

A = π(r+r₂)√((r−r₂)²+h²)+π(r²+r₂²).

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Ellipsoid: formula and assumptions

Surface area uses the Knud Thomsen approximation with p = 1.6075.

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Rectangular pyramid: formula and assumptions

A = ab + a√((b/2)²+h²) + b√((a/2)²+h²).

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Hollow cylinder: formula and assumptions

A = 2π(r+r₂)h + 2π(r²−r₂²).

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Spherical cap alternate dimensions: formula and assumptions

Curved surface=2πRh; base=π×base radius²; total=curved+base.

Surface area includes the flat base, with curved and base areas also shown separately. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Worked example

Using the Sphere example:

Radius

5

Radius unit

Meters

Result length unit (squared for area, cubed for volume)

Meters

A = 4πr².

Example result

These are illustrative inputs. Change the values to explore a different scenario.

Formula references

• OpenStax: Algebra and Trigonometry (opens in a new tab)

References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.

Common questions