The revolution per minute
Revolutions per minute (RPM) equals 1/60 Hz — one full rotation every 60 seconds' worth of a cycle. It is the standard unit for engine, motor, and turntable rotational speed in mechanical and automotive engineering.
Revolutions per minute to Radians per second
1 rpm = 0.10472 rad/s (revolution per minute → radian per second)
1 rpm = 0.10472 rad/s
1 revolution per minute equals 0.10472 radians per second. To convert revolutions per minute to radians per second, multiply the revolution per minute value by 0.10472. For quick reference: 1 rpm = 0.10472 rad/s, 5 rpm = 0.523599 rad/s, 10 rpm = 1.0472 rad/s, 100 rpm = 10.472 rad/s.
Formula
Radians per second = Revolutions per minute × 0.10472Quick
How to convert revolutions per minute to radians per second
Take your value
Start with your value in revolutions per minute.
Multiply by 0.10472
Multiply the revolution per minute value by 0.10472. This is the exact conversion factor from revolutions per minute to radians per second.
Read the result
The product is your value in radians per second. For example, 5 rpm × 0.10472 = 0.523599 rad/s.
Conversion formula
The exact factor from revolutions per minute to radians per second is 0.10472.
Radians per second = Revolutions per minute × 0.10472
Revolutions per minute to Radians per second conversion table
Fifty common reference values, hand-picked for skim utility. Use the calculator above for any value not listed.
| Revolutions per minute (rpm) | Radians per second (rad/s) |
|---|---|
| 0.1 rpm | 0.010472 rad/s |
| 0.25 rpm | 0.02618 rad/s |
| 0.5 rpm | 0.05236 rad/s |
| 1 rpm | 0.10472 rad/s |
| 2 rpm | 0.20944 rad/s |
| 3 rpm | 0.31416 rad/s |
| 4 rpm | 0.41888 rad/s |
| 5 rpm | 0.5236 rad/s |
| 6 rpm | 0.62832 rad/s |
| 7 rpm | 0.73304 rad/s |
| 8 rpm | 0.83776 rad/s |
| 9 rpm | 0.94248 rad/s |
| 10 rpm | 1.0472 rad/s |
| 11 rpm | 1.1519 rad/s |
| 12 rpm | 1.2566 rad/s |
| 13 rpm | 1.3614 rad/s |
| 14 rpm | 1.4661 rad/s |
| 15 rpm | 1.5708 rad/s |
| 16 rpm | 1.6755 rad/s |
| 18 rpm | 1.885 rad/s |
| 20 rpm | 2.0944 rad/s |
| 22 rpm | 2.3038 rad/s |
| 24 rpm | 2.5133 rad/s |
| 25 rpm | 2.618 rad/s |
| 28 rpm | 2.9322 rad/s |
| 30 rpm | 3.1416 rad/s |
| 32 rpm | 3.351 rad/s |
| 36 rpm | 3.7699 rad/s |
| 40 rpm | 4.1888 rad/s |
| 45 rpm | 4.7124 rad/s |
| 48 rpm | 5.0265 rad/s |
| 50 rpm | 5.236 rad/s |
| 60 rpm | 6.2832 rad/s |
| 70 rpm | 7.3304 rad/s |
| 75 rpm | 7.854 rad/s |
| 80 rpm | 8.3776 rad/s |
| 90 rpm | 9.4248 rad/s |
| 100 rpm | 10.472 rad/s |
| 125 rpm | 13.09 rad/s |
| 150 rpm | 15.708 rad/s |
| 200 rpm | 20.944 rad/s |
| 250 rpm | 26.18 rad/s |
| 300 rpm | 31.416 rad/s |
| 400 rpm | 41.888 rad/s |
| 500 rpm | 52.36 rad/s |
| 600 rpm | 62.832 rad/s |
| 750 rpm | 78.54 rad/s |
| 800 rpm | 83.776 rad/s |
| 900 rpm | 94.248 rad/s |
| 1000 rpm | 104.72 rad/s |
Real-world reference
A car engine idles at around 600–1,000 RPM. A standard vinyl record turntable spins at 33⅓ or 45 RPM. In radians per second, that gives you: 1 rpm = 0.10472 rad/s, 10 rpm = 1.0472 rad/s, 100 rpm = 10.472 rad/s.
Frequently asked questions
- How many radians per second are in 1 revolution per minute?
- 1 revolution per minute equals 0.10472 radians per second.
- How do I convert revolutions per minute to radians per second?
- Multiply the revolution per minute value by 0.10472. So x rpm × 0.10472 = the equivalent in rad/s.
- What is 5 revolutions per minute in radians per second?
- 5 revolutions per minute equals 0.523599 radians per second.
- What is 10 revolutions per minute in radians per second?
- 10 revolutions per minute equals 1.0472 radians per second.
- What is 100 revolutions per minute in radians per second?
- 100 revolutions per minute equals 10.472 radians per second.
- How do I convert back from radians per second to revolutions per minute?
- Multiply the radian per second value by 9.5493. For example, 1 rad/s = 9.5493 rpm.
- Is the revolution per minute bigger than the radian per second?
- No. 1 revolution per minute is smaller than 1 radian per second. It takes 9.5493 revolutions per minute to equal 1 radian per second.
- Are these conversion factors exact?
- The factor is derived directly from the SI definitions of revolution per minute and radian per second; the displayed value is rounded for readability, and the browser computes using IEEE 754 double-precision arithmetic.
About the revolution per minute and the radian per second
The radian per second
The radian per second (rad/s) equals 1/(2π) Hz, since one full cycle sweeps out 2π radians. It is the standard unit for angular velocity in physics and control-systems engineering, distinct from RPM's mechanical-engineering convention.