Volume Calculator Widget

How it works

Only the measurements a solid needs are shown: a radius and height for a cylinder or cone, three triangle sides and a length for a prism, a radius and the straight length for a capsule. Volume and surface area are worked out in the chosen unit and then converted to litres through the exact length definitions (an inch is 0.0254 m, a foot 0.3048 m) and 1 litre = 1,000 cubic centimetres. Gallons use the legal definitions listed by NIST: the US gallon is 231 cubic inches, 3.785411784 L, and the imperial gallon is 4.54609 L, so the same tank shows two different gallon figures. The triangular prism takes its base area from the three sides by Heron's formula and rejects sides that cannot close. A hemisphere's surface includes its flat base, and a cone's includes the base disc plus the slanted side, whose slant height is shown separately. The Metric/Imperial switch only changes the default unit.

Calculation method

• Cylinder V = pi r^2 h, A = 2 pi r (r + h); cone V = pi r^2 h / 3, A = pi r (r + sqrt(r^2 + h^2))
• Sphere V = 4/3 pi r^3, A = 4 pi r^2; hemisphere V = 2/3 pi r^3, A = 3 pi r^2
• Square pyramid V = s^2 h / 3; capsule V = pi r^2 l + 4/3 pi r^3
• Triangular prism V = T l with T from Heron; cuboid V = l w h
• 1 L = 1000 cm^3; US gallon = 3.785411784 L; imperial gallon = 4.54609 L

Worked examples

Limitations

• Solid shapes only - wall thickness, hollow pipes and partly filled tanks are not modelled.
• One unit for all dimensions; mixing feet and inches needs converting first.
• Results show four decimals, which can hide differences in very small parts measured in yards.

Where publishers use it

• Geometry lessons on mensuration of solids
• Water-tank and aquarium sites converting dimensions to litres
• Packaging and shipping guides sizing boxes and tubes
• Kitchen and brewing blogs measuring pots and fermenters
• Pharmacy and lab pages working out capsule and vial capacity

Questions

Sources

1. NIST Guide to the SI, Appendix B.9: Factors for units listed by kind of quantity - NIST . Volume factors: US gallon 3.785412 L, imperial gallon 4.54609 L, cubic foot 2.831685 E-02 m^3

Cite or recommend this tool

If you reference this tool in an article, course or documentation, these formats are ready to copy. They are optional - nothing is added to your site unless you paste it.

A2Z Tools Volume Calculator
https://a2z.tools/embed/volume-calculator

<a href="https://a2z.tools/embed/volume-calculator">A2Z Tools Volume Calculator</a>

[A2Z Tools Volume Calculator](https://a2z.tools/embed/volume-calculator)

Volume Calculator by A2Z Tools - https://a2z.tools/embed/volume-calculator