Quick reference table
Common angular velocity conversions
| From | To |
|---|---|
| 1 rpm | 0.1047197551 rad/s |
| 1 rad/s | 9.549296586 rpm |
| 1 °/s | 0.1666666667 rpm |
| 1 rpm | 6.000000000 °/s |
| 1 rev/s | 60.00000000 rpm |
How to convert angular velocity
Angular velocity is how fast something rotates. Motors and engines are rated in rpm, physics uses radians per second, and cameras and robotics often use degrees per second.
Every angular velocity unit is a fixed multiple of one base unit, the rad/s. To convert a value, multiply it by the size of the starting unit and divide by the size of the target unit. For example, to convert rpm to rad/s, multiply by 0.1047197551. To go the other way, divide by 0.1047197551.
The converter above does this for you and shows the exact formula under the result.
Worked examples
Revolutions per minute to Radians per second
| Revolutions per minute (rpm) | Radians per second (rad/s) |
|---|---|
| 1 rpm | 0.1047197551 rad/s |
| 2 rpm | 0.2094395102 rad/s |
| 5 rpm | 0.5235987756 rad/s |
| 10 rpm | 1.047197551 rad/s |
| 25 rpm | 2.617993878 rad/s |
| 50 rpm | 5.235987756 rad/s |
| 100 rpm | 10.47197551 rad/s |
| 1,000 rpm | 104.7197551 rad/s |
Radians per second to Revolutions per minute
| Radians per second (rad/s) | Revolutions per minute (rpm) |
|---|---|
| 1 rad/s | 9.549296586 rpm |
| 2 rad/s | 19.09859317 rpm |
| 5 rad/s | 47.74648293 rpm |
| 10 rad/s | 95.49296586 rpm |
| 25 rad/s | 238.7324146 rpm |
| 50 rad/s | 477.4648293 rpm |
| 100 rad/s | 954.9296586 rpm |
| 1,000 rad/s | 9,549.296586 rpm |
Angular velocity units explained
| Unit | Symbol | Equals |
|---|---|---|
| Radians per second | rad/s | 1 rad/s = 1 rad/s |
| Milliradians per second | mrad/s | 1 mrad/s = 0.001 rad/s |
| Radians per minute | rad/min | 1 rad/min = 0.0166666666667 rad/s |
| Degrees per second | °/s | 1 °/s = 0.0174532925199 rad/s |
| Degrees per minute | °/min | 1 °/min = 0.000290888208666 rad/s |
| Revolutions per minute | rpm | 1 rpm = 0.104719755120 rad/s |
| Revolutions per second | rev/s | 1 rev/s = 6.28318530718 rad/s |
| Revolutions per hour | rev/h | 1 rev/h = 0.00174532925199 rad/s |
Popular conversions: rpm to rad/s, rad/s to rpm, deg/s to rpm.
Frequently asked questions
How many rad/s is 1 rpm?
One revolution per minute is 2π/60 rad/s, about 0.10472 rad/s.
How many degrees per second is 1 rpm?
One rpm is 6 degrees per second.
How do I convert rpm to rad/s?
Multiply the value in rpm by 0.1047197551 to get rad/s. For example, 10 rpm = 1.047197551 rad/s.
How many rad/s is 1 rpm?
1 rpm = 0.1047197551 rad/s, and 1 rad/s = 9.549296586 rpm.
Does this angular velocity converter work offline?
Yes. After the page has loaded once, all calculations run in your browser, so it keeps working without an internet connection.