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About this tool
Find the volume of a cube, box, cylinder, cone, sphere, pyramid, prism, capsule, frustum or pipe in m³, litres or gallons, with a sketch, steps and weight.
This Volume Calculator handles eleven solids: cube, cuboid (box), cylinder, cone, sphere, hemisphere, rectangular pyramid, triangular prism, capsule, conical frustum and tube or pipe. Pick a solid, enter its dimensions in mm, cm, m, in, ft or yd, and switch round sizes between radius and diameter if that is what you measured. The volume is worked out with the standard formula, shown step by step, and converted to the unit you choose and to thirteen units at once, including litres, millilitres, cubic feet, cubic yards, and US and UK gallons. Choose a material such as water or concrete to estimate weight. All maths runs in your browser.
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Under Solid, choose a shape such as Cylinder, Cone, Sphere, Cuboid / box or Tube / pipe.
Pick Radius or Diameter for round solids, type each dimension (for example a diameter of 30 and a height of 50) and set the Length unit to cm, m, in or ft.
Read the Volume card in your chosen Volume unit, plus litres, US gallons and cubic feet, and check the Sketch and Steps.
Choose a material under Weight if filled with / made of, such as Water or Concrete, to see the mass in kg and lb.
Everyday shapes plus less common ones such as capsules, frustums and pipes, each with its own labelled inputs and formula.
Measure across the top of a tank or pipe and enter the diameter directly; the calculator halves it and shows that step.
Cubic metres, cm³, mm³, litres, mL, ft³, in³, yd³, US and UK gallons, US quarts, cups and fluid ounces in one table, each copyable.
Pick water, concrete, steel, wood or a custom density to see the mass in kilograms, tonnes and pounds.
| Solid | Volume formula | Variables |
|---|---|---|
| Cube | V = a³ | a = edge |
| Cuboid / box | V = l × w × h | length, width, height |
| Cylinder | V = πr²h | r = radius, h = height |
| Cone | V = ⅓πr²h | r = base radius, h = height |
| Sphere | V = ⁴⁄₃πr³ | r = radius |
| Hemisphere | V = ⅔πr³ | r = radius |
| Rectangular pyramid | V = ⅓ × l × w × h | base l × w, height h |
| Triangular prism | V = ½ × b × h × L | triangle base b and height h, length L |
| Capsule | V = πr²a + ⁴⁄₃πr³ | r = radius, a = straight length |
| Conical frustum | V = ⅓πh(R² + Rr + r²) | R, r = end radii, h = height |
| Tube / pipe | V = π(R² − r²)L | R = outer, r = inner radius, L = length |
1 m³ = 1,000 L; 1 L = 1,000 cm³; 1 US gal = 231 in³ ≈ 3.785 L; 1 UK gal = 4.54609 L; 1 ft³ ≈ 28.317 L.
Multiply the area of the circular base by the height: V = πr²h. A cylinder with a radius of 3 cm and a height of 10 cm has a volume of π × 9 × 10 ≈ 282.74 cm³. If you measured the diameter, halve it first to get the radius.
Multiply length × width × height. A box 40 cm long, 30 cm wide and 20 cm high holds 24,000 cm³, which is 24 litres. Make sure all three measurements use the same unit; the answer is in that unit cubed.
V = (4/3)πr³. A ball with a radius of 5 cm has a volume of about 523.6 cm³. Because the radius is cubed, doubling the radius makes the volume eight times larger. A hemisphere is exactly half: (2/3)πr³. Use the inside radius when you want to know how much a hollow ball or bowl can hold.
A cone holds one third of the cylinder with the same base and height: V = (1/3)πr²h. A cone with a base radius of 3 and a height of 8 has a volume of 24π ≈ 75.40 cubic units. The height is measured straight up from the base, not along the slanted side.
One cubic metre equals exactly 1,000 litres, and one litre is 1,000 cubic centimetres (cm³), so 1 mL = 1 cm³. A tank measuring 1 m × 1 m × 1 m holds 1,000 litres, which weighs about one tonne when filled with fresh water.
A cubic foot holds about 7.48 US gallons or about 6.23 imperial (UK) gallons. The US gallon is exactly 231 cubic inches, about 3.785 litres, while the UK gallon is exactly 4.54609 litres, so the two are not interchangeable. Check which gallon a recipe, pool chemical or fuel figure uses.
For the material of the pipe wall, use V = π(R² − r²)L with outer radius R, inner radius r and length L. For the liquid the pipe can hold, use only the inner radius: πr²L. The calculator shows both, so you can size a pipe run or estimate its weight.
A frustum is a cone with the top cut off parallel to the base, like a bucket or a lampshade. Its volume is V = (1/3)πh(R² + Rr + r²), where R and r are the bottom and top radii. A bucket with radii 15 and 12 cm and a height of 30 cm holds about 17.25 litres.
Multiply length × width × thickness in the same unit. A slab 3 m × 4 m × 0.1 m needs 1.2 m³, or about 1.57 cubic yards. Suppliers usually recommend adding 5–10% extra for spillage and uneven ground. At about 2,400 kg/m³, 1.2 m³ of concrete weighs roughly 2.9 tonnes.
Volume is the space a solid object takes up; capacity is how much a container can hold inside it. For a thin-walled tank they are nearly the same. For a thick pipe or mug, the capacity uses the inner dimensions and is smaller than the volume of the material.
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