Convert Radians per Second to RPM (rad/s to rpm)
1 radian per second (rad/s) = 9.549296586 revolutions per minute (rpm). 1 rpm = 0.1047197551 rad/s. Example: 100 rad/s = 100 × 9.549296586 = 954.9296586 rpm.
Also searched as rad/s to rpm, radians per second to rpm and angular velocity to rpm.
1 rad/s = 9.549296586 rpm
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk radian per second to revolution per minute converter to paste a column from Excel.
How to Convert Radian per Second to RPM
- 1 rad/s = 9.549296586 rpm
- 1 rpm = 0.1047197551 rad/s
- Example: convert 100 rad/s to rpm: 100 rad/s = 100 × 9.549296586 rpm = 954.9296586 rpm
Formula
rpm = rad/s × 9.549296585514
Derivation from SI units:
- ω = 2πf, so 1 rad/s = 1/(2π) Hz ≈ 0.159155 Hz.
- 1 rpm = 1/60 revolution per second = 1/60 Hz.
- 1 rad/s = 0.1591549430919 Hz ÷ 0.01666666666667 Hz per rpm = 9.549296585514 rpm
Both units are defined exactly, so the factor is exact. Radian per Second definition: radian per second; RPM definition: revolution per minute.
Worked examples
- An angular velocity of 100 rad/s is 954.9296586 rpm.
100 rad/s × 9.549296586 = 954.9296586 rpm - A rotor at 314.159 rad/s turns at 2999.997466 rpm.
314.159 rad/s × 9.549296586 = 2999.997466 rpm
Radian per Second to RPM conversion table
| Radians per Second (rad/s) | RPM |
|---|---|
| 1 rad/s | 9.549296586 rpm |
| 2 rad/s | 19.09859317 rpm |
| 3.14159 rad/s | 29.99997466 rpm |
| 6.28318 rad/s | 59.99994932 rpm |
| 10 rad/s | 95.49296586 rpm |
| 50 rad/s | 477.4648293 rpm |
| 100 rad/s | 954.9296586 rpm |
| 314.159 rad/s | 2999.997466 rpm |
| 376.991 rad/s | 3599.998869 rpm |
| 1000 rad/s | 9549.296586 rpm |
Where it's used
Angular velocities in rad/s from physics problems and simulations are converted to rpm to compare with motor nameplates and machine speeds. Multiply by 60/(2π), about 9.5493.
Radian per Second to other frequency units
| Conversion | 1 rad/s equals |
|---|---|
| radian per second to revolution per minute | 9.549296586 rpm |
| radian per second to hertz | 0.1591549431 Hz |
| radian per second to megahertz | 1.591549431 × 10⁻⁷ MHz |
| radian per second to gigahertz | 1.591549431 × 10⁻¹⁰ GHz |
| radian per second to kilohertz | 0.0001591549431 kHz |
| radian per second to revolution per second | 0.1591549431 rps |
| radian per second to degree per second | 57.29577951 °/s |
| radian per second to beat per minute | 9.549296586 bpm |
Show 1 more units
| radian per second to terahertz | 1.591549431 × 10⁻¹³ THz |
|---|
Frequently asked questions
How many rpm is 1 rad/s?
1 rad/s = 9.549296586 rpm.
How many revolutions per minute are in 1 radian per second?
1 rad/s = 9.549296586 rpm.
How do I convert radians per second to revolutions per minute?
Multiply the value in rad/s by 9.549296586. For example, 100 rad/s × 9.549296586 = 954.9296586 rpm.
Is the rad/s to rpm conversion exact?
Yes. Both units are defined exactly, so the ratio is exact; its decimal form does not terminate and is shown here to 10 significant figures (more with the precision selector).
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures , Table 7 (SI prefixes); hertz, Table 4.
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Convert Radians per Second to RPM (rad/s to rpm). Retrieved October 25, 2026, from https://scientificconverters.com/frequency/radians-per-second-to-rpm/
IEEE
Scientific Converters, "Convert Radians per Second to RPM (rad/s to rpm)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/frequency/radians-per-second-to-rpm/