# Angular Velocity Calculator

URL: https://speedycalculator.com/calculators/physics/angular-velocity/
Last updated: 2026-10-30

> The angular velocity calculator finds how fast something rotates from the angle turned in a time, or from the linear speed of a point and its distance from the axis – in rad/s, rpm, Hz and °/s.

## Inputs

- Method
- Angle change Δα (°, rad, rev)
- Time t (s, ms, min, h, days)
- Velocity v (m/s, km/h, mph, ft/s, knots, km/s)
- Radius r (m, cm, mm, km, in, ft, yd, mi)

## Results

- Angular velocity ω
- In rpm
- Period of one turn

## Formula

```
ω = Δα/t · ω = v/r
```

## Explanation

Angular velocity measures rotation rate. A car wheel at 100 km/h turns at about 85 rad/s (800 rpm); the Earth turns at 7.29 × 10⁻⁵ rad/s. Linear speed grows with distance from the axis: v = ω·r.

### How to use the Angular Velocity Calculator

- **Method**
- **Angle change Δα**
- **Time t**
- **Velocity v**
- **Radius r**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the method and enter your values. Use the unit menu to show the result in rpm or Hz.

### Inputs explained

FieldWhat to enterMethodChoose one: Angle difference and time, Linear (tangential) velocity and radiusAngle change ΔαUnits: °, rad, revTime tUnits: s, ms, min, h, daysVelocity vUnits: m/s, km/h, mph, ft/s, knots, km/sRadius rUnits: m, cm, mm, km, in, ft …

### What each result means

- **In rpm** = [Angular velocity ω]
- **Period of one turn** = 2×pi÷[Angular velocity ω]

### Example values

How the main result changes when **Angle change Δα** changes and everything else stays at the example values above:

Angle change Δα (°)Angular velocity ω (rad/s)1801.57082702.35623603.14164503.9275404.71247206.2832

## Worked example

Inputs — Method: Angle difference and time; Angle change Δα: 360 °; Time t: 2 s.

Results — **Angular velocity ω = 3.14159 rad/s**; In rpm = 30 rpm; Period of one turn = 2 s.

## Key terms

- **Angular velocity**: Rate of change of angle.

## FAQ

**How fast does the Earth rotate?**
7.29 × 10⁻⁵ rad/s – one turn per sidereal day.

**How do I convert rpm to rad/s?**
Multiply by π/30.

**Do all points of a rigid wheel have the same ω?**
Yes – but points farther out move faster.

**Is angular velocity a vector?**
Yes, pointing along the rotation axis.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)