Volume Calculator

What volume measures

Volume is the amount of three-dimensional space a solid occupies. It is written in cubic units: a cube that measures 1 cm along each edge has a volume of 1 cm³. For containers, volume is also the capacity, the quantity of liquid or material the container can hold when full.

Every formula on this page follows one idea: the area of a cross-section multiplied by the distance it extends. That is a rectangle times a height for a box, a circle times a height for a cylinder, a triangle times a length for a prism. Cones and spheres need a small correction factor because their cross-section changes along the way.

Choosing the solid, the unit and each dimension

1. Choose the solid under Volume of.
2. Select the Metric: the length unit whose cube you want the answer in.
3. Enter each dimension that appears. Every field has its own unit selector, so a width in meters and a height in inches can be entered as measured.
4. Press Calculate Volume. The answer is written with its unit, for example cm³ (cubic centimeters).

Labels change with the shape. The cube asks for a single Side, the triangular prism for a Base (one side of its triangular end), a Length and a Height, and the round shapes ask for a Diameter rather than a radius, since that is the measurement you can take with a ruler.

Volume formulas at a glance

Box and cube

V = width × length × height

V = side³a cube is a box whose three edges are equal

Example: a storage bin is 2 m long, 1.5 m wide and 0.8 m tall: 2 × 1.5 × 0.8 = 2.4 m³, which is 2,400 liters. A cube with a 12 cm edge holds 12 × 12 × 12 = 1,728 cm³, about 1.7 liters. Doubling the edge of a cube multiplies its volume by 8.

You can mix units freely. A box 2 m wide, 150 cm long and 30 in high, calculated in meters, gives 2 × 1.5 × 0.762 = 2.286 m³.

Cylinder

V = π × r² × h

The base is a circle of area πr², and the cylinder stacks that circle up to height h. Example: a barrel is 20 cm across and 30 cm tall, so r = 10 cm and V = π × 100 × 30 ≈ 9,424.78 cm³, close to 9.4 liters.

Cone

V = ⅓ × π × r² × h

A cone fills exactly one third of the cylinder that has the same base and height. Use the vertical height from tip to base, not the slanted side. Example: a paper cup shaped like a cone is 8 cm across and 12 cm tall: ⅓ × π × 16 × 12 ≈ 201.06 cm³, a little over 200 mL.

Sphere

V = ⁴⁄₃ × π × r³

Example: a ball with a 30 cm diameter has r = 15 cm, so V = ⁴⁄₃ × π × 3,375 = 4,500π ≈ 14,137.17 cm³, or 14.1 liters.

Triangular prism

V = ½ × base × height × length

Take the area of the triangular end, ½ × base × height, and multiply by the length of the prism. Example: a tent-shaped shed has a triangular end 5 m wide and 3 m high, and it is 10 m long: ½ × 5 × 3 × 10 = 75 m³ of air inside.

Units, mistakes and everyday uses

Cubic units grow quickly: one cubic meter is 1,000,000 cm³ and 1,000 liters, one cubic foot is 1,728 in³, and one cubic yard is 27 ft³. A cubic meter is about 35.3147 ft³. Use the volume converter when you need a different unit than the ones offered here.

• Using the diameter as the radius. In a round solid that error makes the volume 4 times too large for cylinders and cones and 8 times too large for spheres.
• Mixing units without converting. The calculator converts for you; if you do it by hand, convert all lengths before multiplying.
• Forgetting the cone's one third. A cone is a third of the matching cylinder.
• Using the slant height for a cone. Only the straight-up height belongs in the formula.

Volumes decide how much concrete a slab needs, how much soil fills a raised bed, how much water a tank holds and how much cargo fits in a crate.

Worked examples with the Volume Calculator

Example 1. Volume of: Rectangular Box; Metric: cm; Width: 2 cm; Length: 3 cm; Height: 4 cm.

Result: Volume 24 cm³ (cubic centimeters).

Example 2. Volume of: Rectangular Box; Metric: m; Width: 2 m; Length: 300 cm; Height: 4000 mm.

Result: Volume 24 m³ (cubic meters).

Example 3. Volume of: Rectangular Box; Metric: ft; Width: 2.5 in; Length: 1.5 yd; Height: 7 cm.

Result: Volume 0.215305 ft³ (cubic feet).