Volume calculator for 10 common solids
This volume calculator finds the volume of cubes, cuboids, cylinders, cones, spheres, hemispheres, square pyramids, triangular prisms, capsules and frustums. Enter the dimensions and you instantly get the volume in cubic units, its capacity in litres, millilitres and gallons, and — where it is straightforward — the surface area too.
Every result shows the formula and the working with your numbers, next to a labelled 3D diagram so you know exactly which length is the radius, the height or the slant. Use it for maths and physics homework, or for practical jobs such as working out how many litres a water tank holds, how much concrete a slab needs, or the capacity of a fish tank or planter in US or imperial gallons.
How to use the Volume Calculator
- Choose the solid from the list.
- Pick the unit your measurements are in — millimetres, centimetres, metres, inches, feet or yards.
- Enter the dimensions shown on the diagram. Use the radius, not the diameter, for round shapes (half the width across).
- Read the volume in the result panel, with its value in litres and US gallons underneath.
- Check the working, the surface area and the conversion table for cubic feet, cubic metres, imperial gallons and more.
Volume Calculator features
Ten solids
From simple boxes to frustums (truncated cones, like buckets) and capsules (cylinders with rounded ends, like many tanks and pills).
Litres and gallons
Capacity in litres, millilitres, US gallons, imperial gallons and US fluid ounces alongside cubic units.
Surface area included
Total and curved surface area, slant heights and diagonals where they follow directly from your inputs.
Formulas with working
The general formula and your substituted calculation, ready to check or copy.
Labelled 3D diagrams
Hidden edges are dashed and every label matches an input box.
Volume formulas for common solids
Volume is the amount of space a solid occupies, measured in cubic units. A useful pattern: any prism or cylinder has volume = base area × height, while any pyramid or cone holds exactly one third of the prism or cylinder with the same base and height.
| Solid | Volume | Surface area |
|---|---|---|
| Cube | V = a³ | 6a² |
| Cuboid | V = l × w × h | 2(lw + lh + wh) |
| Cylinder | V = πr²h | 2πr(r + h) |
| Cone | V = ⅓πr²h | πr(r + s), s = √(r² + h²) |
| Sphere | V = (4/3)πr³ | 4πr² |
| Hemisphere | V = (2/3)πr³ | 3πr² (with flat base) |
| Square pyramid | V = ⅓a²h | a² + 2as |
| Triangular prism | V = ½bhl | depends on all three sides |
| Capsule | V = πr²a + (4/3)πr³ | 2πr(2r + a) |
| Frustum | V = ⅓πh(R² + Rr + r²) | π(R + r)s + πR² + πr² |
Worked example: how many litres does a tank hold?
A cylindrical water tank is 1.2 m across and 1.5 m tall. Its radius is half the diameter, 0.6 m, so V = π × 0.6² × 1.5 = π × 0.54 ≈ 1.696 m³. Because 1 m³ = 1,000 litres, the tank holds about 1,696 litres, roughly 448 US gallons or 373 imperial gallons.
For a rectangular aquarium measuring 60 cm × 30 cm × 36 cm, V = 64,800 cm³. Since 1,000 cm³ = 1 litre, that is 64.8 litres — about 17.1 US gallons. In practice, subtract a few centimetres of height for the gap at the top and the space taken by gravel and decorations.
Units and common mistakes
To convert a volume you already know, use the volume converter; for kitchen measures such as cups and tablespoons, try the cooking converter. Flat shapes are covered by the area calculator. For specific jobs there are dedicated calculators: water tank capacity (with sump and overhead sizing), aquarium volume, CBM for cartons and the grain bin calculator.
- Cubic units scale by the cube. 1 m = 100 cm, but 1 m³ = 1,000,000 cm³. Likewise 1 ft³ = 1,728 in³ and 1 yd³ = 27 ft³.
- Capacity shortcuts: 1 cm³ = 1 mL, 1 litre = 1,000 cm³, 1 m³ = 1,000 litres, 1 ft³ ≈ 28.32 litres ≈ 7.48 US gallons.
- US and imperial gallons differ. A US gallon is 3.785 litres; an imperial (UK) gallon is 4.546 litres — about 20% more.
- Radius, not diameter. Using the full diameter in πr²h makes the answer four times too big.
- Slant height is not height. For cones and pyramids, the height is the vertical distance from the base to the tip, measured straight down the middle.
Volume Calculator FAQ
How do I use the volume calculator?
Choose a solid, pick your unit, and enter the dimensions shown in the diagram. The volume calculator shows the volume, the formula with your numbers, the surface area where simple, and the capacity in litres and gallons.
How do I calculate the volume of a cylinder?
Multiply π by the radius squared and by the height: V = πr²h. A can with a 3.5 cm radius and 12 cm height holds π × 12.25 × 12 ≈ 461.8 cm³, or about 462 mL.
How do I convert cubic metres or cubic feet to litres?
One cubic metre is exactly 1,000 litres, and one cubic foot is about 28.317 litres. The calculator lists the litre value for every result automatically.
What is the volume of a sphere?
V = (4/3)πr³. A ball with a radius of 10 cm has a volume of about 4,188.8 cm³, or 4.19 litres.
Why is a cone one third of a cylinder?
A cone with the same base and height as a cylinder holds exactly one third of its volume. This can be shown with calculus, or by filling a cone three times to fill the matching cylinder.
What is a frustum?
A frustum is a cone with its top sliced off parallel to the base — the shape of a bucket, lampshade or flowerpot. Its volume is ⅓πh(R² + Rr + r²), where R and r are the bottom and top radii.