Volume Calculator
Pick a shape, enter the dimensions, read the volume in any unit.
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- Cubic metres—
- Litres—
- Cubic feet—
- US gallons—
- UK gallons—
- Weight if filled with water—
How to use this volume calculator
- Choose your shape from the dropdown. The input boxes change to match it, and the diagram shows which measurement goes where.
- Enter the dimensions and tell it which unit you measured in. You can mix nothing up here, because every box uses the same unit.
- Pick the unit you want the answer in. Litres for tanks and containers, cubic metres for rooms and concrete, cubic feet for shipping, gallons for fuel and water.
- Check the working. The formula is shown with your own numbers substituted in, so you can follow the calculation rather than just trusting the result.
The conversions underneath update at the same time, along with the weight of that volume of water, which is a quick sanity check when you are sizing a tank or a floor that has to carry it.
What is volume?
Volume is the amount of three dimensional space an object occupies, or the amount a container can hold. Area is measured in square units because it has two dimensions; volume is measured in cubic units because it has three. A box one metre on every side holds one cubic metre, which is exactly 1,000 litres.
That relationship between cubic measure and liquid measure is the one worth committing to memory, because it links the two systems people actually use:
Volume formulas for every shape
All eleven shapes in the calculator, with the formula each one uses:
| Shape | Formula | What to measure |
|---|---|---|
| Cube | V = a³ | One edge |
| Rectangular box | V = l × w × h | Length, width, height |
| Cylinder | V = πr²h | Radius and height |
| Sphere | V = (4/3)πr³ | Radius |
| Hemisphere | V = (2/3)πr³ | Radius |
| Cone | V = (1/3)πr²h | Base radius and height |
| Capsule | V = πr²h + (4/3)πr³ | Radius and straight section |
| Square pyramid | V = (1/3)a²h | Base edge and height |
| Triangular prism | V = (1/2)bh × l | Triangle base, triangle height, length |
| Tube or pipe | V = π(R² − r²)l | Outer radius, inner radius, length |
| Ellipsoid | V = (4/3)πabc | Three semi-axes |
Two patterns run through that table. Anything that tapers to a point holds exactly one third of the prism or cylinder it would fit inside, which is why the cone and pyramid both carry a 1/3. And anything built on a circle carries a πr², because that is the area of the circle it is standing on.
How to calculate volume by hand
The method is the same for every prism shape: find the area of the base, then multiply by the height. Take a cylindrical water tank 0.6 m across and 1.2 m tall.
- Halve the diameter to get the radius. 0.6 ÷ 2 = 0.3 m
- Find the area of the base. π × 0.3² = π × 0.09 = 0.2827 m²
- Multiply by the height. 0.2827 × 1.2 = 0.3393 m³
- Convert to litres. 0.3393 × 1,000 = 339 litres
The most common mistake by a wide margin is using the diameter where the formula wants the radius. Because the radius is squared, that single slip makes the answer four times too big.
Keep your units consistent
Measure everything in the same unit before you start. Mixing centimetres and metres in one calculation is the second most common error, and unlike the radius mistake it produces answers that are wrong by a factor of a hundred or a million, which at least makes it easier to spot.
Volume and capacity are not quite the same thing
In everyday use the words are interchangeable, but there is a distinction worth knowing when it matters:
- Volume is the space an object takes up, measured from its outside.
- Capacity is how much it can hold, measured from its inside.
For a thin plastic bottle the difference is negligible. For a concrete tank with 150 mm walls it is substantial, and using the external measurements will have you ordering far more water, fuel or grain than will actually fit. Measure the inside when you want capacity.
Volume units and how they convert
| Unit | In cubic metres | In litres | Typically used for |
|---|---|---|---|
| 1 cm³ (ml) | 0.000001 | 0.001 | Medicine, small parts |
| 1 litre | 0.001 | 1 | Drinks, fuel, paint |
| 1 cubic foot | 0.0283 | 28.32 | Shipping, appliances |
| 1 US gallon | 0.003785 | 3.785 | US fuel and water |
| 1 UK gallon | 0.004546 | 4.546 | UK fuel and water |
| 1 cubic metre | 1 | 1,000 | Concrete, rooms, freight |
| 1 cubic yard | 0.7646 | 764.6 | Soil, aggregate, concrete |
Note that a US gallon and a UK gallon are not the same measure. The UK gallon is about twenty percent larger, which is why fuel economy figures never translate directly between the two.
Where volume calculations come up in tech
- PC cases and cooling. Internal case volume sets how much air a build can move, and loop capacity decides how much coolant a water-cooled system needs.
- 3D printing. Slicers price a print from the volume of filament or resin it consumes, so model volume is what the job actually costs.
- Data centres. Rack space is sold by volume as much as by floor area, and airflow per cubic metre is what caps the density you can run.
- Shipping hardware. Couriers charge on volumetric weight, which is the parcel’s volume divided by a fixed factor, not what it weighs on the scales.
- Battery design. Energy density is quoted per litre as well as per kilogram, which is why cell volume drives the size of every phone and EV.
Frequently asked questions
What is the formula for volume?
There is no single formula; it depends on the shape. For any prism or cylinder it is the area of the base multiplied by the height. For a rectangular box that gives length times width times height. For a cylinder it gives pi times the radius squared, times the height.
How do I calculate the volume of a tank in litres?
Work out the volume in cubic metres from the internal measurements, then multiply by 1,000. A cylindrical tank 0.6 m across and 1.2 m tall holds about 339 litres. Use the inside dimensions, not the outside, or you will overestimate.
How many litres are in a cubic metre?
Exactly 1,000. A cubic metre is a box one metre on each side, and it holds 1,000 litres of water weighing one tonne. One litre is 1,000 cubic centimetres, and one cubic centimetre is one millilitre.
What is the difference between volume and capacity?
Volume is the space an object occupies, measured from the outside. Capacity is how much it can hold, measured from the inside. For a thick-walled container the two differ considerably, so measure internally whenever you need to know what will fit.
Why do cones and pyramids have a one third in the formula?
Because a cone holds exactly one third of the cylinder it fits inside, and a pyramid one third of the matching prism. Fill a cone with water and pour it into a cylinder of the same base and height, and it takes three cone-fulls to fill it.
Do I use the radius or the diameter?
Every formula here uses the radius, which is half the diameter. This is the most common mistake in volume calculations: because the radius is squared or cubed, using the diameter by accident makes the answer four or eight times too large.
How do I find the volume of an irregular object?
Use displacement. Fill a container with water, lower the object in, and measure how much the water rises. The increase in volume equals the volume of the object. For anything too large to submerge, break the shape into simpler parts and add them together.
How much does a volume of water weigh?
One litre of fresh water weighs one kilogram, so a cubic metre weighs 1,000 kg, or one tonne. The calculator shows this figure for whatever volume you enter. Seawater is around two and a half percent heavier.