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About the volume calculator
Volume is how much space a solid takes up — how much water a tank holds, how much air is in a ball, how much sand fills a box. It is measured in cubic units: cm³, m³, in³, ft³, and also in liters and gallons.
This calculator knows nine shapes: cube, box (cuboid or rectangular prism), cylinder, cone, sphere, hemisphere, pyramid, triangular prism and capsule. Pick the shape, type the sizes, and you get the volume with the formula and the steps filled in with your own numbers — the way a teacher writes it on the board. A drawing of the shape shows which size is which.
Features
- Nine shapes — cube, box, cylinder, cone, sphere, hemisphere, pyramid, triangular prism and capsule
- Formula and steps — your numbers put into the formula, one line at a time
- Exact answers with π — a cylinder with r = 3 and h = 10 shows 90π as well as 282.7433
- Radius or diameter — type the one you know; the other is worked out
- 11 units at once — mm³, cm³ (mL), liters, m³, in³, ft³, yd³, US and UK gallons, US fl oz and US cups
- Surface area too — the total surface area, and extras such as the slant height of a cone
- A drawing — the shape is drawn with your sizes on it
- Saved on your device — your shape and sizes are still there next time
Volume formulas
r = radius, h = height, π ≈ 3.14159.
| Shape | Formula | Example | Volume |
|---|---|---|---|
| Cube | V = a³ | a = 5 | 125 |
| Box (cuboid) | V = l × w × h | 10 × 4 × 6 | 240 |
| Cylinder | V = π × r² × h | r = 3, h = 10 | 90π ≈ 282.74 |
| Cone | V = 1/3 × π × r² × h | r = 3, h = 4 | 12π ≈ 37.70 |
| Sphere | V = 4/3 × π × r³ | r = 5 | ≈ 523.60 |
| Hemisphere | V = 2/3 × π × r³ | r = 3 | 18π ≈ 56.55 |
| Pyramid | V = 1/3 × l × w × h | 6 × 4 × 5 | 40 |
| Triangular prism | V = 1/2 × b × h × L | b = 6, h = 4, L = 10 | 120 |
| Capsule | V = π × r² × a + 4/3 × π × r³ | r = 3, a = 8 | 108π ≈ 339.29 |
A cone holds one third of the cylinder with the same base and height. A pyramid holds one third of the box with the same base and height.
Worked examples
A can (cylinder). r = 3 in, h = 10 in.
V = π × 3² × 10 = π × 9 × 10 = 90π ≈ 282.74 in³. That is about 1.22 US gallons.
A ball (sphere). The diameter is 24 cm, so r = 24 ÷ 2 = 12 cm.
V = 4/3 × π × 12³ = 4/3 × π × 1,728 ≈ 7,238.23 cm³, or about 7.24 liters.
An ice cream cone. r = 3 cm, h = 4 cm.
V = 1/3 × π × 3² × 4 = 12π ≈ 37.70 cm³. The slant height is √(3² + 4²) = 5 cm.
A fish tank (box). 24 in × 12 in × 16 in.
V = 24 × 12 × 16 = 4,608 in³. One US gallon is 231 in³, so the tank holds 4,608 ÷ 231 ≈ 19.95 gallons.
Volume units
| From | Equals |
|---|---|
| 1 liter | 1,000 cm³ (mL) |
| 1 m³ | 1,000 liters |
| 1 US gallon | 231 in³ ≈ 3.785 liters |
| 1 UK gallon | ≈ 4.546 liters |
| 1 ft³ | 1,728 in³ ≈ 28.32 liters ≈ 7.48 US gallons |
| 1 yd³ | 27 ft³ ≈ 0.7646 m³ |
| 1 in³ | ≈ 16.39 cm³ |
Frequently asked questions
What is the volume of a cylinder?
V = π × r² × h. Square the radius, multiply by π, then by the height. With r = 3 and h = 10 you get 90π, about 282.74 cubic units.
Why is a cone one third of a cylinder?
A cone with the same base and height as a cylinder holds exactly one third as much. You can test it with water: three full cones fill the cylinder. The same is true for a pyramid and a box.
I only know the diameter. What do I do?
Choose I know the: diameter under the sizes. The calculator halves it for you (r = d ÷ 2) and shows that step too.
Can I mix units, like feet and inches?
No. Type every size in the same unit, then pick that unit. The answer comes in that unit cubed, and in the other units in the table.
What does "in terms of π" mean?
The answer is written with π left as a symbol, for example 90π. Teachers often ask for it because it is exact. 90π ≈ 282.7433.
How is the triangular prism measured?
b and h are the base and the height of the triangle at the end, and L is the length of the prism. Any triangle works, because the area of the triangle is always 1/2 × b × h.
Related tools
- Circle Calculator — radius, diameter, circumference and area of a circle
- Square Footage Calculator — the area of a room or a floor
- Concrete Calculator — cubic yards or bags of concrete for a slab
- Unit Converter — liters, gallons, cubic feet and more
- Scientific Calculator — powers, roots and π for your own sums
How to use it
- Tap a shape
- Type its sizes — all in the same unit
- Pick the unit of length (and radius or diameter for round shapes)
- Read the volume in the result box, with liters or gallons under it
- See the formula and the steps under the form, and the volume in 11 units in the table
