Volume is the space a solid occupies – how much water fits in a tank, concrete in a footing or sand in a box. Choose the matching shape and enter its dimensions.
How to use the Volume Calculator
- Solid
- Side a (semi-axis a for an ellipsoid; base for a prism)
- Side b (semi-axis b; triangle height for a prism; top side for a truncated pyramid)
- Semi-axis c
- Radius r (outer radius, bottom radius, or sphere radius for a cap)
- Inner radius / top radius
- Height h (length for a prism)
Results update as you type, and everything is calculated in your browser.
How it works
Choose the solid; only its fields appear. Results can be shown in cubic units or litres and gallons.
Inputs explained
| Field | What to enter |
|---|---|
| Solid | Choose one: Cube, Rectangular box, Sphere, Hemisphere … |
| Side a (semi-axis a for an ellipsoid; base for a prism) | Units: cm, m, mm, in, ft, yd … |
| Side b (semi-axis b; triangle height for a prism; top side for a truncated pyramid) | Units: cm, m, mm, in, ft, yd … |
| Semi-axis c | Units: cm, m, mm, in, ft, yd … |
| Radius r (outer radius, bottom radius, or sphere radius for a cap) | Units: cm, m, mm, in, ft, yd … |
| Inner radius / top radius | Units: cm, m, mm, in, ft, yd … |
| Height h (length for a prism) | Units: cm, m, mm, in, ft, yd … |
Example values
How the main result changes when Side a changes and everything else stays at the example values above:
| Side a (semi-axis a for an ellipsoid; base for a prism) (cm) | Volume (cm³) |
|---|---|
| 2 | 785.3982 |
| 3 | 785.3982 |
| 4 | 785.3982 |
| 5 | 785.3982 |
| 6 | 785.3982 |
| 8 | 785.3982 |
Formula
Cube a³ · Box abh · Sphere 4/3πr³ · Cap πh²(3r − h)/3 · Cylinder πr²h · Cone πr²h/3
Frustum πh(R² + Rr + r²)/3 · Pyramid a²h/3 · Truncated pyramid h(a² + ab + b²)/3
Worked example
Inputs — Solid: Cylinder; Radius r (outer radius, bottom radius, or sphere radius for a cap): 5 cm; Height h (length for a prism): 10 cm.
Results — Volume = 785.398163 cm³.
Key terms
- Volume
- The amount of 3D space enclosed.
Frequently asked questions
How do I convert cm³ to litres?
Divide by 1,000 – or pick L in the unit menu.
What is the volume of a cylindrical tank 1 m across and 2 m tall?
π·0.5²·2 ≈ 1.571 m³.
What is a frustum?
A cone with its top cut off parallel to the base.
Which has more volume: a sphere or the cube around it?
The cube – the sphere fills about 52.4%.