# Volume Calculator

URL: https://speedycalculator.com/calculators/math/volume/
Last updated: 2026-10-30

> The volume calculator finds the volume of 14 solids: cube, box, sphere, hemisphere, spherical cap, ellipsoid, cylinder, tube, capsule, cone, conical frustum, triangular prism, square pyramid and truncated pyramid – in any unit.

## Inputs

- Solid
- Side a (semi-axis a for an ellipsoid; base for a prism) (cm, m, mm, in, ft, yd, km, mi)
- Side b (semi-axis b; triangle height for a prism; top side for a truncated pyramid) (cm, m, mm, in, ft, yd, km, mi)
- Semi-axis c (cm, m, mm, in, ft, yd, km, mi)
- Radius r (outer radius, bottom radius, or sphere radius for a cap) (cm, m, mm, in, ft, yd, km, mi)
- Inner radius / top radius (cm, m, mm, in, ft, yd, km, mi)
- Height h (length for a prism) (cm, m, mm, in, ft, yd, km, mi)

## Results

- Volume

## 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
```

## Explanation

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

FieldWhat to enterSolidChoose 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 cUnits: 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 radiusUnits: 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)2785.39823785.39824785.39825785.39826785.39828785.3982

## 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.

## FAQ

**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%.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Solid geometry](https://mathworld.wolfram.com/SolidGeometry.html)