Rotational Speed Calculator (rpm, Angular Velocity, Linear Speed)

Convert between rpm, angular velocity, linear speed, and period. From a radius, also get linear speed and centripetal acceleration.

Input

Enter the rotational speed (rpm) and the radius to compute angular velocity, linear speed, period, and more.

Rotational speed N

rpm

Radius r

Distance from the center of rotation. Used to compute the linear speed.

Formulas: omega = 2 pi f and v = r omega, where f is revolutions per second.

Angular velocity omega

104.719755

rad/s

Linear speed v

10.471976

m/s

Period T

0.06 s

Frequency (per second)

16.666667 Hz

Rotational speed (per minute)

1,000 rpm

Angular velocity (deg/s)

6,000 deg/s

Linear speed (km/h)

37.699112 km/h

Centripetal acceleration a

1,096.622711 m/s²

f = N / 60, omega = 2 pi f, T = 1 / f, v = r omega, and a = r omega^2 = v^2 / r. The radius r is in meters and N is in rpm.

Convert revolutions per minute N (rpm) to revolutions per second with f = N / 60 (unit Hz).
Angular velocity is omega = 2 pi f (unit rad/s). One revolution equals 2 pi radians.
Period is T = 1 / f (unit s). When the rotational speed is zero, the period is undefined.
Linear (tangential) speed is v = r omega (unit m/s). A larger radius r gives a higher linear speed.
Centripetal acceleration is a = r omega^2 = v^2 / r (unit m/s^2), directed toward the center of the circle.

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