RPM to rad/s Converter
Convert revolutions per minute (RPM) to radians per second (rad/s) instantly. Type a value — the result updates as you type, and the swap button converts the other way.
RPM to rad/s formula
rad/s = RPM × 0.10471975512
1 revolution per minute = 0.1047 radians per second · 1 radian per second = 9.55 revolutions per minute
To convert revolutions per minute to radians per second, multiply the value by 0.10471975512. For example, 1000 RPM:
rad/s = 1000 × 0.10471975512rad/s = 104.719755
So 1000 RPM = 104.72 rad/s.
Mental math shortcut
Quick mental estimate: divide by 10 (multiply by 0.105). For 1000 RPM that gives about 100 rad/s — off by 4.72 rad/s (4.5%). Use the exact formula when precision matters.
RPM to rad/s conversion table
rad/s back to RPM
The same values converted the other way, rounded for everyday use:
| Radians per second | Revolutions per minute |
|---|---|
| 0.1047 rad/s | 0.9998 RPM |
| 6.28 rad/s | 59.97 RPM |
| 10.47 rad/s | 99.98 RPM |
| 104.72 rad/s | 1000 RPM |
| 188.5 rad/s | 1800.04 RPM |
| 314.16 rad/s | 3000.01 RPM |
| 376.99 rad/s | 3599.99 RPM |
About the units
Revolutions per minute (RPM)
Revolutions per minute measure rotational speed for engines, motors and record players.
Radians per second (rad/s)
Radians per second is the SI unit of angular velocity. One revolution is 2π radians.
Frequently asked questions
How many radians per second are in a revolution per minute?
One revolution per minute equals 0.1047 radians per second.
What is 1000 RPM in rad/s?
1000 RPM = 104.72 rad/s.
How do I convert rad/s back to RPM?
Divide the radians per second by 0.10471975512.