Radians/sec to RPM Converter
Enter angular velocity in rad/s and instantly convert to revolutions per minute (rpm).
What this rad/sec to rpm calculator does
This tool converts angular velocity from radians per second (rad/s) into revolutions per minute (rpm). If you work with motors, rotating shafts, wheels, fans, robotics, CNC systems, or physics problems, this is one of the most common unit conversions you will use.
Radians per second is a standard SI unit for angular speed. RPM is often used in engineering specs, motor labels, and practical machine settings. The calculator bridges both units quickly so you can move from formulas to real-world equipment values without manual math mistakes.
rad/s to rpm formula
Use this conversion equation:
Equivalent constant form: rpm = (rad/s) × 9.549296586
Why this works:
- One full revolution equals 2π radians.
- One minute equals 60 seconds.
- So you convert radians to revolutions, then seconds to minutes.
Reverse conversion (rpm to rad/s)
If you need the opposite direction, use:
How to use the calculator
- Enter your angular speed in rad/s.
- Set your desired decimal precision.
- Click Convert to RPM.
- Read the result instantly, including the exact formula used.
You can also tap one of the quick examples (1, 2π, 10, or 100 rad/s) to auto-fill a common value.
Examples
Example 1: 1 rad/s
rpm = 1 × 60 / (2π) = 9.5493 rpm
Example 2: 2π rad/s
rpm = 2π × 60 / (2π) = 60 rpm
Example 3: 25 rad/s
rpm = 25 × 9.549296586 ≈ 238.7324 rpm
Quick conversion chart
| rad/s | rpm |
|---|---|
| 0.1 | 0.9549 |
| 0.5 | 4.7746 |
| 1 | 9.5493 |
| 5 | 47.7465 |
| 10 | 95.4930 |
| 20 | 190.9859 |
| 50 | 477.4648 |
| 100 | 954.9297 |
Where this conversion is used
- Electric motors: Compare simulation output in rad/s with motor specs in rpm.
- Robotics: Convert joint angular velocity to actuator rpm requirements.
- Mechanical design: Match pulley, gear, and shaft speed ratings.
- Automotive and aerospace: Translate rotational dynamics equations into practical speed limits.
- Education: Solve physics and engineering homework accurately.
Common mistakes to avoid
- Forgetting the 2π factor when converting radians to revolutions.
- Confusing rad/s with deg/s (degrees per second).
- Rounding too early in multi-step calculations.
- Ignoring sign: negative rad/s means reverse rotational direction.
FAQ
Is rad/s bigger or smaller than rpm?
Numerically, 1 rad/s is about 9.5493 rpm, so rpm values are usually larger for the same physical speed.
Can this calculator handle negative values?
Yes. A negative result indicates opposite rotation direction. Magnitude still represents speed.
How many decimals should I use?
For rough engineering estimates, 2 to 3 decimals is usually enough. For simulations or precision work, use 4 to 6 decimals.
What is the exact conversion constant?
60 / (2π), which is approximately 9.54929658551372.
Final note
If you regularly convert radians per second to revolutions per minute, this angular velocity converter can save time and prevent unit errors. Keep the formula handy, use consistent units, and always sanity-check your results against expected machine speed ranges.