Volume Calculator (cube, cylinder, cone, sphere, pyramid & more)

Understanding the volume calculator — concept and principle

This calculator finds the volume and surface area of common solids: cube, box, cylinder, cone, sphere, hemisphere, pyramid, triangular prism, capsule, frustum, ellipsoid and torus. With cm, m, inches or feet it also converts the volume to litres and US gallons. Use it for tanks, containers, concrete, soil, aquariums, packaging and geometry homework.

Stack the 28.27 cm² circle ten times: 90π ≈ 282.74 cm³, about 0.28 litres.

How it is calculated

Cube a³; box abc; cylinder πa²b; cone πa²b ÷ 3.
Sphere (4/3)πa³; hemisphere (2/3)πa³; rectangular pyramid abc ÷ 3; triangular prism ½·abc.
Capsule πa²b + (4/3)πa³; frustum πc ÷ 3 × (a² + ab + b²); ellipsoid (4/3)πabc; torus 2π²ab².
1 L = 1,000 cm³; 1 US gallon = 3.785411784 L.

The ellipsoid surface uses Knud Thomsen's approximation (within about 1%).

The principle

Volume measures the space inside a solid in cubic units. For prisms and cylinders, volume = base area × height, because the solid is a stack of identical slices. Cones and pyramids taper to a point, and their volume is exactly one third of the matching prism or cylinder, a result known since ancient Greece and proved with integration today. Spheres and tori come from rotating shapes; Pappus's theorem gives the torus volume as the area of the tube's circle times the distance its centre travels.

Worked example

Default inputs: cylinder, radius a = 3 cm, height b = 10 cm.

Volume = π × 3² × 10 = 90π ≈ 282.7433388 cm³.
Surface area = 2π × 3 × 10 + 2π × 3² = 78π ≈ 245.044227 cm².
In litres: 282.7433388 ÷ 1,000 ≈ 0.2827433388 L.
In US gallons: 0.2827433388 ÷ 3.785411784 ≈ 0.0746928881 gal.

Each point is the calculator re-run with only “a” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

a	Volume
0.75	17.67145868
1.5	70.68583471
2.25	159.0431281
3	282.7433388
3.75	441.7864669
4.5	636.1725124
6	1,130.973355

How to read the result

Volume is in the input unit cubed, and capacity in litres helps for liquids. For a tank, the inside dimensions give the capacity; the outside dimensions include the walls. For concrete or soil, add a margin for waste and settling.

Common mistakes

Using the diameter instead of the radius.
Forgetting the ÷ 3 for cones and pyramids.
Mixing units, such as cm for the radius and m for the height.
Confusing US and imperial gallons; an imperial gallon is about 4.546 L.

Keep in mind: For ordering concrete, fuel tanks or structural work, use manufacturer data and allow for waste; real designs need local codes and a qualified professional.

Frequently asked questions

How many litres is 1 cubic metre?

1,000 litres.

Why is a cone one third of a cylinder?

A cone with the same base and height holds exactly one third of the cylinder's volume, which can be shown with integration or by filling experiments.

How do I find the volume of an irregular object?

Submerge it in water and measure the volume of water displaced.

Sources: OpenStax, Calculus Volume 1, §6.2–6.3 (volumes of solids) · NIST Special Publication 811 (2008), Appendix B (litre and gallon factors)

Checked 9 Nov 2026. Standard solid-geometry formulas (e.g. OpenStax Calculus Volume 1, §6.2–6.3 and Precalculus); surface area of an ellipsoid by Knud Thomsen’s formula (p = 1.6075); NIST SP 811 for litre and gallon factors.

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