RPM, rim speed and rad/s come from the same turn
RPM counts full turns per minute. To get the speed of a point on the edge, you also need its distance from the center. To get angular speed in physics units (rad/s), you convert one turn to 2 pi radians and one minute to 60 seconds.
Running it the other way, RPM = v × 60 ÷ (2π × r) gives you the spin rate from a measured surface speed. The shortcut for the first formula: RPM × 0.1047 ≈ rad/s, so 1000 RPM is roughly 104.7 rad/s.
Radius decides the surface speed
Same shaft, same RPM — but the rim of a wider part covers more ground per turn, so it moves faster. This is why RPM by itself is not a speed.
Double the radius, double the rim speed at the same RPM. A wind turbine turning at just 12 RPM can still have a blade tip moving near 300 km/h, purely because the tip is so far out.
Quick reference — RPM to angular speed
| RPM | rad/s | Turns per second |
|---|---|---|
| 60 | 6.28 | 1.0 |
| 300 | 31.4 | 5.0 |
| 1,000 | 104.7 | 16.7 |
| 3,000 | 314.2 | 50.0 |
| 5,400 | 565.5 | 90.0 |
| 7,200 | 754.0 | 120.0 |
5,400 and 7,200 are the common hard-drive platter speeds; a car engine cruises near 1,500–3,000 RPM on the highway.
The three things people mix up
- Radius vs diameter. The surface-speed formula uses the radius. If you have the diameter, halve it first.
- RPM vs surface speed. Two parts at the same RPM move at different edge speeds if their radii differ — same rotation, different distance covered.
- Gear ratio direction. Ratio = driven teeth ÷ driver teeth. A ratio above 1 (e.g. 3.5) slows the output and raises torque: 3000 RPM in becomes about 857 RPM out.
Common questions
How do you convert RPM to rad/s?
Multiply RPM by 2 pi divided by 60, which is about 0.10472. So 3000 RPM is 3000 x 0.10472 = 314.2 radians per second.
How do I get surface speed from RPM?
Surface speed at the rim equals angular speed times radius: v = RPM x 2 pi x radius divided by 60. Use the radius, not the diameter. A 3000 RPM shaft with a 0.1 m radius has a rim speed of about 31.4 m/s.
Does a bigger wheel spin faster at the same RPM?
No. The RPM is identical, but the edge of the bigger wheel travels farther each turn, so its surface speed is higher. RPM alone tells you nothing about speed until you fix the radius.
