Volume Calculator
Pick a solid — cube, box, cylinder, sphere, cone, square pyramid or triangular prism — enter its dimensions and instantly get the volume, plus the same volume restated in every other unit. Works in mm, cm, m, inches or feet.
Calculator
The same volume in other units
- mm³
- 282,743.3388 mm³
- m³
- 0.0003 m³
- in³
- 17.2541 in³
- ft³
- 0.01 ft³
About this calculator
Volume is the amount of space a solid occupies. This calculator covers the seven shapes you meet most often — the cube, the rectangular box (cuboid), the cylinder, the sphere, the cone, the square pyramid and the triangular prism. Pick a shape, type its dimensions in millimetres, centimetres, metres, inches or feet, and the volume appears at once, expressed in that unit cubed. Because everything is computed from one unit, the answer is also restated in every other length unit so a tank measured in inches can be read off in litres-equivalent cubic metres without retyping.
How to read your results
The large figure is the volume in the unit you chose, raised to the third power (cm becomes cm³, ft becomes ft³). Beneath it, the “same volume in other units” panel converts that figure into every other length unit. The conversion is NOT the linear factor — a volume is a length cubed, so the factor is the linear conversion cubed: 1 cm³ is 1,000 mm³ (because 10 mm to a centimetre, and 10³ = 1,000), and 1 ft³ is about 0.0283 m³.
How it's calculated
Each shape uses its standard solid-geometry formula, with V in the cube of the chosen length unit. Cube: V = s³. Rectangular box: V = l × w × h. Cylinder: V = π × r² × h. Sphere: V = 4⁄3 × π × r³. Cone: V = 1⁄3 × π × r² × h. Square pyramid: V = 1⁄3 × b² × h, where b is the base edge. Triangular prism: V = (½ × base × triangle height) × length. To restate the volume in another unit, the linear conversion factor between the two units is cubed and multiplied through.
Worked example
A sphere with a radius of 5 cm.
The volume is 4⁄3 × π × 5³ ≈ 523.60 cm³. Restated in other units that is 523,598.78 mm³, about 0.000524 m³, roughly 31.95 in³ and about 0.0185 ft³.
Frequently asked questions
How do I find the volume of a cylinder?
A cylinder’s volume is π × radius² × height. For a radius of 3 cm and a height of 10 cm that is π × 9 × 10 ≈ 282.74 cm³. Choose “Cylinder”, enter the radius and height in the same unit, and the volume is returned instantly.
What is the formula for the volume of a sphere?
The volume of a sphere is 4⁄3 × π × radius³. With a radius of 5 cm that is 4⁄3 × π × 125 ≈ 523.60 cm³. A cone of the same base radius and a height equal to the radius holds exactly one quarter of that.
Why is 1 cm³ equal to 1,000 mm³ and not 10 mm³?
Volume scales with the cube of length. There are 10 millimetres in a centimetre, so a 1 cm cube measures 10 mm on every side: 10 × 10 × 10 = 1,000 mm³. That is why the “other units” panel cubes the linear conversion factor instead of using it directly.
Which shapes and units are supported?
Seven solids — cube, rectangular box, cylinder, sphere, cone, square pyramid and triangular prism — in five length units: millimetres, centimetres, metres, inches and feet. Inches and feet use the exact international definitions (1 in = 2.54 cm, 1 ft = 0.3048 m).
Sources
Reviewed by the YouCalc Team · Last reviewed
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