Convert RPM to Radians per Second (rpm to rad/s)
1 revolution per minute (rpm) = 0.1047197551 radians per second (rad/s). 1 rad/s = 9.549296586 rpm. Example: 1000 rpm = 1000 × 0.1047197551 = 104.7197551 rad/s.
Also searched as rpm to rad/s, rpm to radians per second, rev/min to rad/s and rpm to angular velocity.
1 rpm = 0.1047197551 rad/s
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk revolution per minute to radian per second converter to paste a column from Excel.
How to Convert RPM to Radian per Second
- 1 rpm = 0.1047197551 rad/s
- 1 rad/s = 9.549296586 rpm
- Example: convert 1000 rpm to rad/s: 1000 rpm = 1000 × 0.1047197551 rad/s = 104.7197551 rad/s
Formula
rad/s = rpm × 0.1047197551197
or rad/s = rpm ÷ 9.549296585514
Derivation from SI units:
- 1 rpm = 1/60 revolution per second = 1/60 Hz.
- ω = 2πf, so 1 rad/s = 1/(2π) Hz ≈ 0.159155 Hz.
- 1 rpm = 0.01666666666667 Hz ÷ 0.1591549430919 Hz per rad/s = 0.1047197551197 rad/s
Both units are defined exactly, so the factor is exact. RPM definition: revolution per minute; Radian per Second definition: radian per second.
Worked examples
- A shaft at 1000 rpm has ω = 104.7197551 rad/s.
1000 rpm × 0.1047197551 = 104.7197551 rad/s - A motor at 3000 rpm turns at 314.1592654 rad/s.
3000 rpm × 0.1047197551 = 314.1592654 rad/s
RPM to Radian per Second conversion table
| RPM | Radians per Second (rad/s) |
|---|---|
| 60 rpm | 6.283185307 rad/s |
| 100 rpm | 10.47197551 rad/s |
| 600 rpm | 62.83185307 rad/s |
| 750 rpm | 78.53981634 rad/s |
| 1000 rpm | 104.7197551 rad/s |
| 1450 rpm | 151.8436449 rad/s |
| 1500 rpm | 157.0796327 rad/s |
| 3000 rpm | 314.1592654 rad/s |
| 3600 rpm | 376.9911184 rad/s |
| 7200 rpm | 753.9822369 rad/s |
Where it's used
Rotational speeds in rpm are converted to angular velocity in rad/s for torque–power calculations (P = Tω), dynamics and control. Multiply by 2π/60, about 0.10472.
RPM to other frequency units
| Conversion | 1 rpm equals |
|---|---|
| revolution per minute to radian per second | 0.1047197551 rad/s |
| revolution per minute to hertz | 0.01666666667 Hz |
| revolution per minute to megahertz | 1.666666667 × 10⁻⁸ MHz |
| revolution per minute to gigahertz | 1.666666667 × 10⁻¹¹ GHz |
| revolution per minute to kilohertz | 0.00001666666667 kHz |
| revolution per minute to revolution per second | 0.01666666667 rps |
| revolution per minute to degree per second | 6 °/s |
| revolution per minute to beat per minute | 1 bpm |
Show 1 more units
| revolution per minute to terahertz | 1.666666667 × 10⁻¹⁴ THz |
|---|
Frequently asked questions
How do I convert rpm to rad/s?
Multiply by 2π/60: 1000 rpm = 104.7197551 rad/s.
How many radians per second are in 1 revolution per minute?
1 rpm = 0.1047197551 rad/s.
How do I convert revolutions per minute to radians per second?
Multiply the value in rpm by 0.1047197551, or divide it by 9.549296586. For example, 1000 rpm × 0.1047197551 = 104.7197551 rad/s.
Is the rpm to rad/s 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 RPM to Radians per Second (rpm to rad/s). Retrieved October 25, 2026, from https://scientificconverters.com/frequency/rpm-to-radians-per-second/
IEEE
Scientific Converters, "Convert RPM to Radians per Second (rpm to rad/s)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/frequency/rpm-to-radians-per-second/