CalcKit
Angular Velocity Converter
Angular velocity (ω) is how fast something turns: the angle it sweeps each second, ω = Δθ / Δt. Its SI unit is the radian per second (rad/s). Engines and motors are rated in revolutions per minute (rpm, r/min), and gyroscopes and telescopes in degrees per second or per hour.
One revolution is 360°, or 2π radians, so ω = rpm × 2π / 60.
How to convert angular velocity
Type a value into any field, and every other unit is calculated at once. For example, an engine at 3,000 rpm:
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In rad/s: multiply by 2π, then divide by 60.
3,000 × 2π / 60 = 314.2 rad/s -
In degrees per second: multiply by 6, since one revolution per minute is 360° in 60 seconds.
3,000 × 6 = 18,000 °/s
A point at radius r moves at the speed v = ω * r, with ω in rad/s: on a 0.3 m wheel at 314.2 rad/s, that is about 94 m/s.
Common conversions
| Value | Equals |
|---|---|
| 1 rpm | 0.10472 rad/s |
| 1 rad/s | 9.5493 rpm |
| 1 rpm | 6 °/s |
| 1 °/s | 0.166667 rpm |
| 1 rad/s | 57.2958 °/s |
| 1 °/s | 0.0174533 rad/s |
| 1 r/s | 6.28319 rad/s |
Angular velocity units
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Radian/second (rad/s): Radian/second is the standard unit for measuring angular velocity. It represents the change in angular position of an object in radians per second.
Conversion factor: 1 rad/s = 57.2958 °/s = 0.1592 r/s -
Radian/minute (rad/min): Radian/minute measures angular velocity in radians per minute, indicating the change in angular position over a minute.
Conversion factor: 1 rad/min = 1/60 rad/s -
Radian/hour (rad/h): Radian/hour measures angular velocity in radians per hour, indicating the change in angular position over an hour.
Conversion factor: 1 rad/h = 1/3600 rad/s -
Radian/day (rad/d): Radian/day measures angular velocity in radians per day, indicating the change in angular position over a day.
Conversion factor: 1 rad/d = 1/86400 rad/s -
Degree/second (°/s): Degree/second represents angular velocity in degrees per second, indicating the change in angular position in degrees over a second.
Conversion factor: 1 °/s = 0.0175 rad/s -
Degree/minute (°/min): Degree/minute measures angular velocity in degrees per minute, indicating the change in angular position in degrees over a minute.
Conversion factor: 1 °/min = 1/60 °/s = 0.0175 rad/min -
Degree/hour (°/h): Degree/hour represents angular velocity in degrees per hour, indicating the change in angular position in degrees over an hour.
Conversion factor: 1 °/h = 1/3600 °/s = 0.0175 rad/h -
Degree/day (°/d): Degree/day measures angular velocity in degrees per day, indicating the change in angular position in degrees over a day.
Conversion factor: 1 °/d = 1/86400 °/s = 0.0175 rad/d -
Revolution/second (r/s): Revolution/second represents angular velocity in complete revolutions per second, indicating the number of full rotations per second.
Conversion factor: 1 r/s = 6.2832 rad/s -
Revolution/minute (r/min): Revolution/minute measures angular velocity in complete revolutions per minute, indicating the number of full rotations per minute.
Conversion factor: 1 r/min = 1/60 r/s = 6.2832 rad/min -
Revolution/hour (r/h): Revolution/hour represents angular velocity in complete revolutions per hour, indicating the number of full rotations per hour.
Conversion factor: 1 r/h = 1/3600 r/s = 6.2832 rad/h -
Revolution/day (r/d): Revolution/day measures angular velocity in complete revolutions per day, indicating the number of full rotations per day.
Conversion factor: 1 r/d = 1/86400 r/s = 6.2832 rad/d
Frequently asked questions
What is the difference between angular velocity and speed?
Angular velocity is how fast the angle changes, the same for every point of a turning wheel. Speed is how fast a point moves along its path, and it grows with the distance from the center: v = ω * r.