Volume Size Calculator
Choose a shape, enter its sizes and the unit. The calculator gives the volume in cubic units, litres, US gallons and cubic metres, plus the surface area and how much of its surrounding box or cylinder it fills.
- Volume of shapes
- Litres and gallons
- Surface area
For a cone, cylinder or frustum enter the radius, which is half the diameter. For a pyramid enter the base side, and for a prism the triangle base and height.
Each shape has its own formula, but they are related. A cone holds one third of the cylinder it fits in, and a sphere two thirds. A cylinder 10 cm in radius and 20 cm tall holds 6.28 litres, the sphere inside it 4.19 litres and the cone 2.09 litres.
Volume formulas
Common shapes. Search for a shape.
| Shape | Formula | Example (litres) |
|---|---|---|
| Cylinder | π r² h | 6.28 |
| Cone | π r² h ÷ 3 | 2.09 |
| Sphere | 4/3 π r³ | 4.19 |
| Hemisphere | 2/3 π r³ | 2.09 |
| Frustum, top radius 5 | π h (R² + Rr + r²) ÷ 3 | 3.67 |
| Square pyramid, side 20 | a² h ÷ 3 | 2.67 |
Volume with radius 10 cm and height 20 cm where used.
Radius and volume
Height equal to two radii. Slide the radius.
The cylinder, sphere and cone share the same radius, so you can see the one third and two thirds rule.
How to work out volume
Any shape. Step through it.
Pick the shape
Closest match.
Measure inside for capacity and outside for the material a solid shape contains.
Cylinder, cone or sphere
Round shapes. Compare them.
Straight sides.
Round.
Pointed.
Many real containers combine shapes, such as a cylinder with a cone at the bottom. Work out each part and add them.
Before you calculate
Measuring checks. Tick each item.
Tick each item as you go.
One cubic metre is one thousand litres, and one cubic foot is about 28.3 litres.
What you get
Shape volume. Each tile explains one result.
Cubic units.
Capacity.
US.
Surface.
Of the box.
Surface area tells you how much paint, sheet or label a shape needs.
Frequently Asked Questions
No question matches that search.
How do I calculate the volume of a cylinder?
Multiply pi by the radius squared and by the height.
How do I find the volume of a cone?
Work out the cylinder volume with the same radius and height, then divide by three.
What is the volume of a sphere?
Four thirds times pi times the radius cubed.
How do I convert cubic centimetres to litres?
Divide by one thousand. One litre is one thousand cubic centimetres.
What is a frustum?
A cone with its top cut off flat, like a bucket or lampshade.
Should I use the slant height?
No. Volume formulas use the straight up height. Only the surface area uses the slant.
How do I find volume from diameter?
Halve the diameter to get the radius first.
Any shape, any unit
Pick the shape, measure carefully and get the volume in the units you need, whether it is a tank, a funnel or a garden pot.
More size calculators
Each one has its own calculator, worked examples and answers to common questions.