# Torus Calculator

URL: https://speedycalculator.com/calculators/math/torus/
Last updated: 2026-10-25

> The torus calculator finds the volume and surface area of a torus (doughnut or ring shape) from its major radius, the distance from the centre to the tube’s centre, and its minor radius, the tube radius.

## Inputs

- Major radius (R) (m, cm, mm, km, in, ft, yd, mi)
- Minor radius (r) (m, cm, mm, km, in, ft, yd, mi)

## Results

- Volume
- Surface area

## Formula

```
V = 2π² R r²
Surface area = 4π² R r
```

## Explanation

Tori appear in inner tubes, O-rings, doughnuts and some reactor designs.

### How to use the Torus Calculator

- **Major radius (R)**
- **Minor radius (r)**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

The volume equals the tube’s cross-sectional area times the distance travelled by its centre around the ring.

### Inputs explained

FieldWhat to enterMajor radius (R)Units: m, cm, mm, km, in, ft …Minor radius (r)Units: m, cm, mm, km, in, ft …

### What each result means

- **Volume** = 2×pi^2×[Major radius (R)]×[Minor radius (r)]^2
- **Surface area** = 4×pi^2×[Major radius (R)]×[Minor radius (r)]

### Example values

How the main result changes when **Major radius** changes and everything else stays at the example values above:

Major radius (R) (m)Volume (m³)5888.267.51,332.4101,776.5312.52,220.66152,664.79203,553.06

## Worked example

Inputs — Major radius (R): 10 m; Minor radius (r): 3 m.

Results — **Volume = 1,776.53 m³**; Surface area = 1,184.35 m².

## FAQ

**What if r is larger than R?**
The torus self-intersects (a spindle torus); the formulas then overestimate.

**How do I measure R?**
From the centre of the hole to the centre of the tube.

**What formula does the Torus Calculator use?**
V = 2π² R r².