Unit converter
Angular velocity.
Convert rpm to rad/s, or pick any of the 4 units in the menus. Type in either box and the other follows. Rotation rate in radians per second, the ω of physics, alongside the revolutions per minute that machinery is actually labelled with.
| rpm | rad/s |
|---|---|
| 1 rpm | 0.10472 rad/s |
| 2 rpm | 0.20944 rad/s |
| 3 rpm | 0.314159 rad/s |
| 4 rpm | 0.418879 rad/s |
| 5 rpm | 0.523599 rad/s |
| 10 rpm | 1.0472 rad/s |
| 15 rpm | 1.5708 rad/s |
| 20 rpm | 2.0944 rad/s |
| 25 rpm | 2.61799 rad/s |
| 50 rpm | 5.23599 rad/s |
| 75 rpm | 7.85398 rad/s |
| 100 rpm | 10.472 rad/s |
| 250 rpm | 26.1799 rad/s |
| 500 rpm | 52.3599 rad/s |
| 1000 rpm | 104.72 rad/s |
- Every unit in the menus is defined against rad/s, so any pairing converts by the same single route.
Definitions
- Revolutions per minute counts whole turns. One rpm is 2π/60 rad/s, so 1000 rpm is about 104.7 rad/s.
- Radians per second is the SI measure of rotation rate, and the ω that appears in physics equations.
- Angular velocity measures angle swept per second. Revolutions per minute become rad/s using 2π radians per revolution; ordinary frequency in hertz is kept separate.
- Every unit in the menus is exact by definition, so the only rounding on this page is the one you choose for the display.
How it works
Every value is converted into radians per second and then back out into the unit you asked for. One route covers every pairing in the menus, so an unusual combination is no less accurate than a common one, and adding a unit affects only that unit.
Both boxes are live. Whichever one you last typed in is the source, changing either menu recalculates straight away, and Swap exchanges the units and the values so the number you are reading stays where you are looking.
Display precision sets a maximum number of significant figures and trims trailing zeroes, so it changes what you see and never what was calculated. The editable box always holds a plain number at full working precision, so you can carry on from either side.
Common questions this answers: how many radians per second in a revolution per minute (0.10472), how many revolutions per minute in a radian per second (9.5493), and what 1000 rpm is in radians per second (104.72 rad/s).
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