Volume Calculator

Choose a 3D shape, enter its dimensions and get the volume, with optional liquid capacity conversions.

For a capsule, the length of the straight middle section

How to use the Volume Calculator

  1. Choose the shape.
  2. Enter the edge length.
  3. Enter the length.
  4. Enter the width.
  5. Enter the radius.
  6. Enter the height – For a capsule, the length of the straight middle section.
  7. Enter the triangle base.
  8. Enter the triangle height.
  9. Enter the semi-axis a.
  10. Enter the semi-axis b.
  11. Enter the semi-axis c.
  12. Choose the unit of the dimensions.
  13. Press Calculate. The result updates automatically as you type.

About the Volume Calculator

Volume is the amount of space a solid occupies, measured in cubic units. It tells you how much water fills a tank, how much soil fills a planter or how much air is in a room. Most volume formulas follow one pattern: a prism or cylinder is base area × height, and a pointed shape such as a cone or pyramid holds exactly one third of the matching prism.

Enter every dimension in the same unit. If you tell the calculator which unit you used, it also converts the result to US gallons and liters, which is handy for aquariums, tanks and containers. Remember that a radius is half the diameter; using the diameter by mistake makes a cylinder's volume four times too large.

Formula

  • Cube: s³  |  Box: l × w × h  |  Triangular prism: ½ b h × length
  • Cylinder: πr²h  |  Cone: ⅓ πr²h  |  Pyramid: ⅓ × base area × h
  • Sphere: 4/3 πr³  |  Hemisphere: 2/3 πr³  |  Ellipsoid: 4/3 πabc
  • Capsule: πr²h + 4/3 πr³

1 ft³ ≈ 7.48 US gallons ≈ 28.32 liters; 1 in³ ≈ 16.39 mL.

Example calculation

Using the default values:

  • Shape = Rectangular box (prism)
  • Length = 4
  • Width = 3
  • Height = 2
  • Unit of the dimensions = Any / not specified

the calculator returns:

  • Volume: 24 cubic units
  • Formula used: V = l × w × h

Frequently asked questions

How do I calculate the volume of a cylinder?

Multiply π by the radius squared and by the height. A cylinder with radius 2 ft and height 2 ft holds π × 4 × 2 ≈ 25.13 ft³, about 188 gallons.

Why is a cone one third of a cylinder?

Calculus (or a water-pouring experiment) shows that a cone with the same base and height as a cylinder holds exactly one third as much.

How many gallons are in a cubic foot?

About 7.48 US gallons.

Last updated: · Category: Math calculators

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