Math & Science · Guide
Volume Formulas for Every Common Shape
Most volume formulas are just “area of the base × height” — with a third for anything that comes to a point.
Want the answer for your own numbers? Use the free Volume Calculator — it does every step below for you.
The big idea
For any shape with straight sides running up from its base — boxes, cylinders, prisms — volume is base area × height. Shapes that taper to a point — cones and pyramids — hold exactly one third of that.
All the formulas
| Shape | Volume formula | Example |
|---|---|---|
| Rectangular prism (box) | V = l × w × h | 5 × 3 × 2 = 30 |
| Cube | V = s³ | 4³ = 64 |
| Cylinder | V = πr²h | r 3, h 10: 282.7 |
| Cone | V = ⅓πr²h | r 3, h 4: 37.7 |
| Sphere | V = (4/3)πr³ | r 3: 113.1 |
| Hemisphere | V = ⅔πr³ | r 3: 56.5 |
| Pyramid | V = ⅓ × base area × h | base 6 × 6, h 5: 60 |
| Triangular prism | V = ½ × b × h△ × length | b 4, h 3, length 10: 60 |
"Volume of a rectangle"
A flat rectangle has no volume — only area. What people usually mean is a rectangular prism, a box shape. Multiply length, width and height. A shipping box 40 cm × 30 cm × 25 cm holds 30,000 cm³, or 30 litres.
How to find the volume of a rectangular prism, step by step
- Measure length, width and height in the same unit.
- Multiply them together.
- Write the answer in cubic units (cm³, m³, ft³).
Volume of a right circular cone
A "right circular" cone has a round base and a tip directly above its centre. Use V = ⅓πr²h with the vertical height, not the slant height. An ice-cream cone with a 3 cm radius and 10 cm height holds ⅓ × 3.1416 × 9 × 10 = 94.2 cm³.
Hemisphere volume formula
A hemisphere is half a sphere, so V = ½ × (4/3)πr³ = ⅔πr³. A bowl with an inside radius of 10 cm holds ⅔ × 3.1416 × 1,000 = 2,094 cm³, about 2.1 litres.
Volume of prisms and cylinders together
A cylinder is really a prism with a circular base. That is why both use the same rule: base area × height. Find the area of the end shape — triangle, hexagon, circle — and multiply by the length.
Frustum: a cone with the top cut off
Buckets, flower pots and lampshades are frustums — cones with the tip sliced off. Use the radius of both ends:
V = ⅓πh(R² + Rr + r²)
R = radius of the wide end, r = radius of the narrow end, h = height between them
A bucket: top radius 15 cm, bottom radius 12 cm, height 30 cm
R² + Rr + r² = 225 + 180 + 144 = 549.
⅓ × π × 30 × 549 = 17,247 cm³.
About 17.2 litres
Two more shapes
- Ellipsoid (a stretched sphere, like a rugby ball): V = (4/3)πabc, using the three half-widths. With 3, 4 and 5: about 251.3.
- Pipe or tube: it is a cylinder, so V = πr² × length. A 10 m pipe with a 50 mm inside diameter holds π × 0.025² × 10 = 0.0196 m³, about 19.6 litres.
Irregular objects: use water
For a stone, a key or any odd shape, use displacement. Half-fill a measuring jug, note the level, drop the object in, and read the new level. The rise is the object’s volume — 1 ml of rise equals 1 cm³.
Units: cubic to litres and gallons
- 1,000 cm³ = 1 litre
- 1 m³ = 1,000 litres
- 1 ft³ = 7.48 US gallons = 28.3 litres
- 1 in³ = 16.39 cm³
Mixing units is the most common mistake. Convert everything to one unit before you multiply. The volume calculator handles seven shapes and shows the result in litres and gallons too. For pools specifically, see how to calculate pool volume.
Frequently asked questions
Multiply length × width × height, all in the same unit. A box 5 × 3 × 2 cm has a volume of 30 cm³.
V = ⅔πr³, which is half the volume of a sphere. A hemisphere with a radius of 3 has a volume of about 56.5 cubic units.
V = ⅓πr²h, one third of a cylinder with the same base and height. A cone with radius 3 and height 4 has a volume of about 37.7.
Measure in centimetres, work out πr²h to get cm³, then divide by 1,000. A cylinder with a 10 cm radius and 30 cm height holds π × 100 × 30 = 9,425 cm³, which is about 9.4 litres.
V = (4/3)πr³ = (4/3) × π × 125, which is about 523.6 cubic units. If the radius is in centimetres, that is 523.6 cm³, or about half a litre.