Angular Velocity Calculator (rpm to rad/s & Linear Speed)
By Santaji GadepatilinUpdated October 29, 2026
Rotating machines are rated in revolutions per minute, but physics formulas use angular velocity in radians per second. This angular velocity calculator converts between rpm, rad/s and Hz and gives the tangential speed at any radius, v = ωr — handy for motor shafts, wheels, grinding discs and fans.
How to use the angular velocity calculator
Enter the speed in rpm and a radius. You get the angular velocity in rad/s, the rotational frequency in Hz, the tangential speed at that radius and the time for one revolution. Enter rad/s or a rim speed instead and clear rpm to convert the other way.
Angular velocity formulas
ω = 2π × N ÷ 60 · f = N ÷ 60 · v = ω × r
Example
A 4-pole motor at 1,450 rpm driving a 200 mm diameter disc (r = 100 mm):
- ω = 2π × 1450 ÷ 60 = 151.84 rad/s
- f = 24.17 Hz (one turn every 41.4 ms)
- Rim speed = 151.84 × 0.1 = 15.18 m/s
rpm conversion table
| Speed | Angular velocity | Frequency |
|---|---|---|
| 1 rpm | 0.10 rad/s | 0.02 Hz |
| 60 rpm | 6.28 rad/s | 1.00 Hz |
| 750 rpm | 78.54 rad/s | 12.50 Hz |
| 1,000 rpm | 104.72 rad/s | 16.67 Hz |
| 1,500 rpm | 157.08 rad/s | 25.00 Hz |
| 3,000 rpm | 314.16 rad/s | 50.00 Hz |
| 3,600 rpm | 376.99 rad/s | 60.00 Hz |
| 10,000 rpm | 1047.20 rad/s | 166.67 Hz |
Frequently asked questions
How do I convert rpm to rad/s?
Multiply by 2π and divide by 60, so ω = rpm × 0.10472. 1,450 rpm is about 151.8 rad/s.
How do I find linear speed from rpm?
v = ω × r = 2π r × rpm ÷ 60. A 200 mm diameter disc at 1,450 rpm has a rim speed of about 15.2 m/s.
What is the difference between angular velocity and frequency?
Frequency counts revolutions per second (Hz); angular velocity counts radians per second. One revolution is 2π radians, so ω = 2πf.
Why does rim speed matter?
Grinding wheels, saw blades and fans have a maximum safe peripheral speed, and belt and conveyor speeds are set by pulley rim speed.