RPM to rad/s Calculator
Convert rotational speed instantly from revolutions per minute (RPM) to radians per second (rad/s) with accuracy.
Rotational Speed Converter
How to Use RPM to Rad s Calculator
Follow these simple steps:
- 1Enter RPM Value: Input the rotational speed in revolutions per minute (RPM).
- 2Click Calculate: Press the “Calculate Rad/s” button to process the conversion.
- 3View Result: The result will instantly appear in radians per second (rad/s).
- 4Apply Result: Use the precise value for your engineering analysis, design, or motor testing.
Tips for Best Use: Always enter numeric values only. Double-check units before calculating. Use decimals for precise results.
How to Convert RPM to Rad s
You can convert RPM to radians per second using this standard engineering formula:
Or simplified:
Step-by-Step Example
Convert 120 RPM to rad/s:
1. Formula: rad/s = RPM × (2π / 60)
2. Substitute: rad/s = 120 × (2 × 3.14159 / 60)
3. Simplify: rad/s = 120 × (0.10472)
4. Result: rad/s ≈ 12.57
Final Answer: 120 RPM = 12.57 rad/s
RPM to Rad s Conversion Chart
| RPM | Rad/s |
|---|---|
| 10 | 1.05 |
| 50 | 5.24 |
| 100 | 10.47 |
| 200 | 20.94 |
| 300 | 31.42 |
| 500 | 52.36 |
| 1000 | 104.72 |
| 2000 | 209.44 |
| 3000 | 314.16 |
Frequently Asked Questions (FAQs)
To convert RPM to radians per second (rad/s), multiply the RPM value by π (pi) and then divide the result by 30. Alternatively, you can multiply by the conversion factor of approximately 0.104719755. This is because one complete revolution equals 2π radians, and one minute contains 60 seconds.
The precise formula to calculate angular velocity in rad/s from RPM is: ω (rad/s) = RPM × (2π / 60). This mathematical equation simplifies neatly to ω = RPM × (π / 30). This conversion is heavily utilized in physics and engineering for accurate dynamic calculations involving rotational motion.
Radians per second is the standard SI unit for angular velocity and is strongly preferred in physics and advanced engineering. It drastically simplifies equations in calculus and rotational dynamics, making it far easier to calculate centripetal acceleration, torque, and rotational kinetic energy.
One Revolution Per Minute (RPM) is equal to exactly π/30 radians per second, which evaluates to approximately 0.10472 rad/s. This foundational conversion factor is essential for translating standard motor specifications into a mathematically usable format for precise academic and engineering models.
Yes, radians per second is a specific measure of angular speed or angular velocity. It describes how fast an object is rotating by measuring the exact angle through which it turns every second. Unlike linear speed, it is completely independent of the object's radius or overall physical dimensions.
