Volume Calculator
Find the volume of seven common 3D solids, with the formula and the substituted numbers shown for every result.
Details
Volume
27
in cubic units
This works out how much space a shape holds. Pick the shape, enter its measurements, and it returns the volume in cubic units.
It covers boxes, cubes, cylinders, cones, spheres, hemispheres and capsules, and shows which formula it used so you can check it by hand.
What is volume?
Volume is how much space something takes up, or how much it can hold. Length tells you how far, area tells you how much surface, volume tells you how much inside.
Because it measures three directions at once, volume is always in cubic units: cubic metres, cubic feet, or litres and gallons when you are filling something.
Nearly every shape follows the same idea: work out the area of one flat face, then multiply by how tall or long the shape is. Curved shapes like spheres and cones have their own formulas, but they come from the same principle.
Length × width gives the area of the base (15 squares). Stacking that base 2 high gives 30 cubes. Every straight-sided shape works this way: base area × height.
What to enter
- Shape
- Pick the shape you are measuring. The boxes below change to match it.
- Radius
- For round shapes, the distance from the centre to the edge. That is half the width across, so measure across and halve it.
- Height / length
- How tall or how long the shape runs.
- Units
- Use the same unit for every measurement. Mixing feet and inches in one shape is the most common cause of a wrong answer.
The formulas behind each shape
- Box
- length × width × height
- Cube
- side × side × side
- Cylinder
- π × radius² × height
- Sphere
- ⁴⁄₃ × π × radius³
- Cone
- ⅓ × π × radius² × height — exactly a third of the cylinder that would contain it
What this assumes
Shapes are perfectly regular. A real pond or an uneven excavation will differ from the maths.
Wall thickness is ignored. For a container, the answer is the outside volume unless you measure the inside.
How to calculate volume
For anything with straight sides, one rule covers it: find the area of the base, then multiply by the height.
- area of the base
- The flat face the shape stands on
- height
- How far it extends straight up
Check your units match. Convert everything to one unit before you start. This catches more errors than any other step.
Find the base area. A rectangle is length × width. A circle is π × radius².
Multiply by the height. That gives the volume in cubic units.
Convert if you are filling it. One cubic metre is 1,000 litres. One cubic foot is about 7.48 US gallons, and the unit converter handles the rest.
See a worked example: a cylinder 3 units across the radius and 10 tall
- Radius
- 3
- Height
- 10
Base area first: π × 3² = π × 9 = 28.27 square units.
Then multiply by the height: 28.27 × 10.
That gives 282.74 cubic units.
If those were metres, it would hold about 282,740 litres.
282.74 cubic units
Frequently asked questions
Volume is what fits inside. Surface area is how much skin is on the outside.
You want volume to know how much water a tank holds, and surface area to know how much paint covers it.
Work out the volume in cubic units first, then convert. 1 cubic metre = 1,000 litres. 1 cubic foot ≈ 7.48 US gallons.
Measure the inside of the tank, not the outside, or the walls will be counted as capacity.
Because that is what the geometry works out to: a cone and a cylinder with the same base and the same height always have a 1 : 3 relationship.
It is worth remembering, because it means you can work out any cone by finding the cylinder around it and dividing by three.
Because doubling affects all three directions at once: 2 × 2 × 2 = 8.
This surprises people constantly. A tank twice as big in every direction holds eight times as much, and a pizza twice the diameter has four times the area.
Problems people actually run into
Mixing units halfway through
Measuring a tank as 6 feet long, 30 inches wide and 4 feet deep, then multiplying those numbers straight together, gives an answer that is wrong by a factor of twelve.
Convert everything to a single unit before any multiplying. In practical jobs, this single mistake causes more wrong concrete and water orders than any other.
Measuring the diameter and using it as the radius
It is far easier to measure across a circular tank than to find its exact centre, so people measure the full width and put that straight into the formula.
Because the radius is squared, using the diameter makes the answer four times too big. Always halve the measurement across before using it.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: August 29, 2026