RPM to Radians per Second Converter (RPM to rad/s)
Convert revolutions per minute to radians per second (RPM to rad/s). See results in rad/s, degrees/second, Hertz, and linear velocity. Includes a quick reference table.
ANGULAR VELOCITY
376.991 rad/s
21600.0 ยฐ/s
60.00 Hz
37.70 m/s
3600ร2ฯ/60
RPM to Radians/Second โ Quick Reference
| RPM | rad/s | ยฐ/s | Hz |
|---|---|---|---|
| 1 RPM | 0.105 rad/s | 6 ยฐ/s | 0.02 Hz |
| 10 RPM | 1.047 rad/s | 60 ยฐ/s | 0.17 Hz |
| 60 RPM | 6.283 rad/s | 360 ยฐ/s | 1.00 Hz |
| 100 RPM | 10.472 rad/s | 600 ยฐ/s | 1.67 Hz |
| 300 RPM | 31.416 rad/s | 1,800 ยฐ/s | 5.00 Hz |
| 600 RPM | 62.832 rad/s | 3,600 ยฐ/s | 10.00 Hz |
| 1,000 RPM | 104.720 rad/s | 6,000 ยฐ/s | 16.67 Hz |
| 1,800 RPM | 188.496 rad/s | 10,800 ยฐ/s | 30.00 Hz |
| 3,600 RPM | 376.991 rad/s | 21,600 ยฐ/s | 60.00 Hz |
| 7,200 RPM | 753.982 rad/s | 43,200 ยฐ/s | 120.00 Hz |
| 10,000 RPM | 1047.198 rad/s | 60,000 ยฐ/s | 166.67 Hz |
| 15,000 RPM | 1570.796 rad/s | 90,000 ยฐ/s | 250.00 Hz |
How to Convert RPM to Radians per Second
One revolution = 2ฯ radians, and one minute = 60 seconds. So:
rad/s = RPM ร 0.10472
Example: 3,600 RPM
= 3,600 ร 0.10472 = 376.99 rad/s
Example: 1,800 RPM (standard US motor)
= 1,800 ร 0.10472 = 188.50 rad/s
Example: 60 RPM (1 revolution per second)
= 60 ร 0.10472 = 6.283 rad/s (= 2ฯ)
Angular Velocity Units Compared
| Unit | Symbol | 1 RPM = | Used In |
|---|---|---|---|
| Revolutions/minute | RPM | 1 RPM | Motors, engines, tools |
| Radians/second | rad/s | 0.10472 rad/s | Physics, engineering |
| Degrees/second | ยฐ/s | 6 ยฐ/s | Gyroscopes, robotics |
| Hertz (rev/second) | Hz | 0.01667 Hz | Frequency measurement |
RPM to rad/s โ Conversion Table
| RPM | rad/s | ยฐ/s | Hz | Common Example |
|---|---|---|---|---|
| 1 RPM | 0.105 | 6 | 0.017 | Rotisserie motor |
| 33 RPM | 3.456 | 198 | 0.550 | Vinyl record (LP) |
| 60 RPM | 6.283 | 360 | 1.000 | Clock second hand |
| 300 RPM | 31.42 | 1,800 | 5.000 | Washing machine spin |
| 900 RPM | 94.25 | 5,400 | 15.00 | US ceiling fan (high) |
| 1,800 RPM | 188.5 | 10,800 | 30.00 | US 4-pole motor (60Hz) |
| 3,600 RPM | 377.0 | 21,600 | 60.00 | US 2-pole motor (60Hz) |
| 5,400 RPM | 565.5 | 32,400 | 90.00 | Laptop hard drive |
| 7,200 RPM | 753.9 | 43,200 | 120.0 | Desktop hard drive |
| 10,000 RPM | 1,047 | 60,000 | 166.7 | High-perf hard drive |
| 15,000 RPM | 1,571 | 90,000 | 250.0 | Dental drill |
| 20,000 RPM | 2,094 | 120,000 | 333.3 | Turbocharger |
Linear Velocity from RPM (v = ฯ ร r)
If an object rotates at ฯ rad/s and has radius r meters, the edge moves at:
Example: A 26" bicycle wheel at 300 RPM
ฯ = 300 ร 0.10472 = 31.42 rad/s
r = 26" ร 0.0254 รท 2 = 0.3302 m
v = 31.42 ร 0.3302 = 10.37 m/s โ 23.2 mph
Common Motors & Engines โ RPM in the US
| Device | Typical RPM | rad/s |
|---|---|---|
| Ceiling fan (low) | 100โ200 RPM | 10.5โ20.9 |
| Washing machine (spin) | 800โ1,600 RPM | 83.8โ167.5 |
| Car engine (idle) | 600โ1,000 RPM | 62.8โ104.7 |
| Car engine (highway) | 2,000โ3,000 RPM | 209.4โ314.2 |
| Power drill | 500โ3,000 RPM | 52.4โ314.2 |
| Circular saw | 3,000โ5,000 RPM | 314.2โ523.6 |
| Blender | 6,000โ20,000 RPM | 628.3โ2,094 |
| Jet engine turbine | 10,000โ25,000 RPM | 1,047โ2,618 |
What Are Revolutions per Minute (RPM)?
RPM is a unit of rotational speed indicating how many full 360ยฐ turns an object completes in one minute. It is the most commonly used unit for expressing motor speed, engine speed, and tool speed in the United States. Tachometers in cars, spec sheets for power tools, and hard drive speeds all use RPM.
What Are Radians per Second (rad/s)?
A radian per second (rad/s) is the SI unit of angular velocity. One radian is approximately 57.3ยฐ โ the angle where the arc length equals the radius. Radians are dimensionless, making rad/s the preferred unit in physics and engineering calculations involving torque, angular momentum, and rotational kinetic energy.