Rotational Speed Converter

Convert rotational speed with the factor behind each answer. Motors are rated in rpm, and the equations of motion use radians per second.

Common conversions

• 1 rpm = 0.1047197551 rad/s
• 1 rad/s = 9.549296586 rpm
• 1 rpm = 0.01666666667 rev/s
• 1 rev/s = 60 rpm
• 1 rpm = 6 °/s

Synchronous speed

The synchronous speed of an AC machine is n = 120 f / p in rpm, where f is the supply frequency in Hz and p is the number of poles. At 50 Hz, a 4-pole motor has a synchronous speed of 1,500 rpm. The rated speed on the nameplate is lower, by the slip.

Radians per second

Mechanical power is torque times angular speed: P = T × ω, with ω in rad/s. To find the power of a motor from its torque and rpm, convert rpm to rad/s first.

Unit factors

Every unit in terms of the base unit shown. To convert, multiply by the factor of the unit you have and divide by the factor of the unit you want.

Conversion pages

rpm to rad/srad/s to rpm

Frequently asked questions

What is the formula to convert rpm to rad/s?

rad/s = rpm × 0.1047197551. For example, 1,500 rpm is 157.0796327 rad/s.

How do I convert rad/s back to rpm?

rpm = rad/s × 9.549296586. The Swap button above reverses the direction for any pair of units.

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