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Geometry · Solids

Geometric Solids Volume & Surface Area Calculator

Calculate volume, lateral or curved area, and total surface area for prisms, cylinders, pyramids, cones, and spheres.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

Standard right solids whose dimensions share one positive length unit

Prisms and cylinders

V=Bh

Pyramids and cones

V=Bh/3

Sphere

V=4πr³/3S=4πr²
Geometry · Solids

Compare volume and surface area

Inputs and displayed decimal results use at most three decimal places. Exact internal values are retained during calculation.

V = Bh

Choose a standard solid and enter every visible dimension.

r = 3h = 5

Using the model

Symbols, assumptions and limitations

Interpretation notes

The supported presets are a rectangular prism, right circular cylinder, right square pyramid, right circular cone, and sphere. All entered dimensions must be positive and expressed in one common length unit. Slant heights for right cones and square pyramids are derived from vertical height.

Worked examples

See the method in practice

01

Cylinder

A cylinder with radius 2 and height 3 has volume 12π, curved area 12π, and total area 20π.

02

Sphere

A sphere of radius 3 has surface area 36π and volume 36π.

Questions

Frequently asked

What is lateral area?

It excludes the bases. For a sphere, which has no bases, curved and total surface area are identical.

Why distinguish vertical and slant height?

Volume uses perpendicular height, while lateral area of a cone or pyramid uses the derived slant height.

Can dimensions use different units?

No. Convert all dimensions to the same unit before calculating.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax Contemporary Mathematics — Volume and Surface Area

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology