rad/s to RPM Converter
Convert angular speed between radians per second (rad/s) and revolutions per minute (RPM)
Quick answer
To convert rad/s to RPM, multiply by 60 and divide by 2π, which is about 9.549 times the rad/s value. To convert RPM to rad/s, multiply by 2π and divide by 60, which is about 0.1047 times the RPM value.
Unfamiliar with a term? Check the electric motor glossary.
| Rotations per Minute (RPM) | Radians per Second (rad/s) |
|---|---|
| 1000 | 104.72 |
| 1500 | 157.08 |
| 2000 | 209.44 |
| 2500 | 261.80 |
| 3000 | 314.16 |
| 3500 | 366.52 |
| 4000 | 418.88 |
| 4500 | 471.24 |
| 5000 | 523.60 |
| 5500 | 575.96 |
Angular Speed Conversion Chart
Formula
RPM = rad/s × 60 ÷ 2π ≈ rad/s × 9.549
rad/s = RPM × 2π ÷ 60 ≈ RPM × 0.1047
One revolution is 2π radians and one minute is 60 seconds, so 1 RPM = 2π ÷ 60 rad/s ≈ 0.10472 rad/s, and 1 rad/s = 60 ÷ 2π RPM ≈ 9.5493 RPM.
Table of Common Speeds
| rad/s | RPM | Typical context |
|---|---|---|
| 1 | 9.549 | Very slow positioning axis |
| 6.283 | 60 | One revolution per second |
| 20.94 | 200 | Direct-drive robot joint |
| 52.36 | 500 | Low-speed actuator or wheel motor |
| 104.7 | 1,000 | Mid-speed drive |
| 314.2 | 3,000 | Typical rated speed of an industrial servo motor |
| 628.3 | 6,000 | High-speed motor |
| 1,047 | 10,000 | Small high-speed spindle or fan motor |
Worked Examples
- 100 rad/s × 9.549 = 954.9 RPM
- 300 rad/s × 9.549 = 2,864.8 RPM
- 3,000 RPM × 0.1047 = 314.2 rad/s
- A robot joint at 200 RPM: 200 × 2π ÷ 60 = 20.94 rad/s. At 20 Nm, that is 20 × 20.94 ≈ 419 W of mechanical power.
Why Two Units Exist
Physics and control work use rad/s because the equations stay simple: mechanical power is torque times angular speed, P = T × ω, only when ω is in rad/s. Datasheets, drive parameters and tachometers use RPM because whole revolutions are easy to picture and measure. Most unit errors in motor specifications come from mixing the two. The power from torque calculator handles the conversion inside the power formula for you.
Common Mistakes
- Using RPM in P = T × ω without converting. Power is torque × rad/s, not torque × RPM; the result would be 9.55 times too large.
- Forgetting the factor of 60. A value that is 60 times off is the sign of this error.
- Mixing rad/s with revolutions per second (rps). 1 rps = 2π rad/s ≈ 6.283 rad/s = 60 RPM.
- Confusing mechanical and electrical speed. In a motor with p pole pairs, the electrical angular frequency is p times the mechanical one.
Frequently Asked Questions
How many RPM is 1 rad/s?
About 9.549 RPM (60 ÷ 2π).
How do I convert RPM to rad/s?
Multiply the RPM value by 2π and divide by 60, or multiply by about 0.1047. For example, 3,000 RPM is about 314.2 rad/s.
How do I convert rad/s to RPM?
Multiply the rad/s value by 60 and divide by 2π, or multiply by about 9.549. For example, 100 rad/s is about 954.9 RPM.
Why do motor equations use rad/s?
Because power equals torque times angular speed only when the speed is in rad/s. With RPM, a conversion factor of 2π ÷ 60 has to be added.
What is a radian per second?
An angular speed of one radian each second. A full rotation is 2π radians, so 1 rad/s is about 0.159 revolutions per second, or 9.549 RPM.