Radian/s to Revolution/min Converter
Enter the value that you want to convert radian/s (rad/s) to revolution/min (rpm) or revolution/min to radian/s.Also written as RAD/S to RPM conversion.
1 radian/s = 9.5492743 revolution/min
Formula: revolution/min = radian/s value × 9.5492743
RAD/S to RPM — radian/s to revolution/min
10 radian/s = 95.49274 revolution/min
Popular Angular Velocity Converters:
Why Convert Radian/s to Revolution/min?
What is Radian/s?
Radian/s (rad/s) is a unit of angular velocity measurement. 1 radian/s is equal to 9.5492743 revolution/min.
About the Revolution/min
Revolution/min (rpm) is a unit of angular velocity measurement. 1 revolution/min is equal to 0.1047200 radian/s.
radian/s to revolution/min metric conversion table
| 0.01 rad/s | = | 0.09549 rpm |
| 0.1 rad/s | = | 0.95493 rpm |
| 1 rad/s | = | 9.54927 rpm |
| 2 rad/s | = | 19.09855 rpm |
| 3 rad/s | = | 28.64782 rpm |
| 4 rad/s | = | 38.19710 rpm |
| 5 rad/s | = | 47.74637 rpm |
| 6 rad/s | = | 57.29565 rpm |
| 7 rad/s | = | 66.84492 rpm |
| 8 rad/s | = | 76.39419 rpm |
| 9 rad/s | = | 85.94347 rpm |
| 10 rad/s | = | 95.49274 rpm |
| 11 rad/s | = | 105.04202 rpm |
| 12 rad/s | = | 114.59129 rpm |
| 13 rad/s | = | 124.14057 rpm |
| 14 rad/s | = | 133.68984 rpm |
| 15 rad/s | = | 143.23911 rpm |
| 16 rad/s | = | 152.78839 rpm |
| 17 rad/s | = | 162.33766 rpm |
| 18 rad/s | = | 171.88694 rpm |
| 19 rad/s | = | 181.43621 rpm |
| 20 rad/s | = | 190.98549 rpm |
| 30 rad/s | = | 286.47823 rpm |
| 40 rad/s | = | 381.97097 rpm |
| 50 rad/s | = | 477.46371 rpm |
| 60 rad/s | = | 572.95646 rpm |
| 70 rad/s | = | 668.44920 rpm |
| 80 rad/s | = | 763.94194 rpm |
| 90 rad/s | = | 859.43468 rpm |
| 100 rad/s | = | 954.92743 rpm |
| 200 rad/s | = | 1909.85485 rpm |
| 300 rad/s | = | 2864.78228 rpm |
| 400 rad/s | = | 3819.70970 rpm |
| 500 rad/s | = | 4774.63713 rpm |
| 600 rad/s | = | 5729.56455 rpm |
| 700 rad/s | = | 6684.49198 rpm |
| 800 rad/s | = | 7639.41940 rpm |
| 900 rad/s | = | 8594.34683 rpm |
| 1000 rad/s | = | 9549.27426 rpm |
How to Convert RAD/S to RPM (Radian/s to Revolution/min)?
We can convert radian/s to revolution/min by using an example.
Example:
Convert 20 Radian/s to Revolution/min?
We know 1 Radian/s = 9.5492743 revolution/min; 1 Revolution/min = 0.1047200 radian/s.
20 radian/s = ___rpm
20 × 9.5492743 = 190.98549 rpm (we know 1 radian/s = 9.5492743 revolution/min)
Answer:
20 radian/s = 190.98549 revolution/min
Radians per Second to RPM: From Physics to Motor Specifications
Radians per second (rad/s) is the SI unit of angular velocity used in physics and engineering calculations, while revolutions per minute (RPM) is the practical unit used on motor nameplates, tachometers, and machinery specifications. Converting between them is essential when translating theoretical calculations into real-world motor selection. One revolution = 2π radians, and one minute = 60 seconds.
- Start with the angular velocity in rad/s.
- Multiply by 60 to convert seconds to minutes (giving rad/min).
- Divide by 2π (≈ 6.2832) to convert radians to revolutions.
- Or simply multiply by 9.5493 (which equals 60 ÷ 2π) for the direct conversion.
rad/s to RPM Common Values for Motors
Angular velocities you will encounter in robotics, CNC machines, and motor datasheets:
| Radian/s | Revolution/min |
|---|---|
| 1 rad/s | 9.55 RPM |
| 10 rad/s | 95.49 RPM |
| 50 rad/s | 477.46 RPM |
| 100 rad/s | 954.93 RPM |
| 150 rad/s | 1,432.39 RPM |
| 200 rad/s | 1,909.86 RPM |
| 314.16 rad/s | 3,000 RPM |
| 523.60 rad/s | 5,000 RPM |
Solved Examples: rad/s to RPM
Question 1: A robotic arm joint rotates at 3.14 rad/s. What is this in RPM?
Solution:
RPM = rad/s × 9.5493
= 3.14 × 9.5493
= 29.98 RPM ≈ 30 RPM
Answer: 3.14 rad/s ≈ 30 RPM — appropriate for a controlled robotic movement.
Question 2: A centrifuge motor runs at 628 rad/s. Convert to RPM.
Solution:
RPM = rad/s × 9.5493
= 628 × 9.5493
= 5,996.96 RPM ≈ 6,000 RPM
Answer: 628 rad/s ≈ 6,000 RPM — a standard laboratory centrifuge speed.
Question 3: A drone propeller spins at 837 rad/s. Express in RPM.
Solution:
RPM = rad/s × 9.5493
= 837 × 9.5493
= 7,992.77 RPM ≈ 7,993 RPM
Answer: 837 rad/s ≈ 7,993 RPM — typical for a racing drone.
Practice: rad/s to RPM Conversions
Try solving these on your own to test your understanding:
- Convert 25 rad/s to RPM. (Answer: 238.73 RPM)
- A wheel spins at 72 rad/s. What is that in RPM? (Answer: 687.55 RPM)
- Convert 157.08 rad/s to RPM. (Answer: 1,500 RPM)
- A turbocharger runs at 15,000 rad/s. Express in RPM. (Answer: 143,239 RPM)
- Convert 0.5 rad/s to RPM. (Answer: 4.77 RPM)
Why Physics Uses rad/s While Industry Uses RPM
Radians per second is the natural unit for angular velocity in physics because it simplifies equations: torque × angular velocity (in rad/s) gives power in watts directly. RPM is preferred in industry because it is intuitive — people can visualize "turns per minute." The conversion factor 9.5493 bridges these two worlds, appearing whenever you translate textbook formulas into real motor specifications.
Synchronous Motor Speeds and the Grid Frequency Connection
AC motors have synchronous speeds determined by grid frequency and pole count: RPM = (120 × frequency) ÷ poles. On a 60 Hz grid, a 2-pole motor runs at 3,600 RPM (376.99 rad/s). On 50 Hz grids (Europe, Asia), the same motor runs at 3,000 RPM (314.16 rad/s). Understanding this relationship is critical when deploying equipment across different power grids.
Key Takeaways
- Multiply rad/s by 9.5493 (or 60/2π) to get RPM.
- 1 rad/s ≈ 9.55 RPM is the key conversion factor.
- Physics uses rad/s because it simplifies torque and power equations.
- Industry uses RPM because it is intuitive for operators.
- AC synchronous speeds: 3,000 RPM (50 Hz) or 3,600 RPM (60 Hz) for 2-pole motors.
Radian/s to Revolution/min Conversion Formula
revolution/min = radian/s × 9.5492743
1 radian/s = 9.5492743 revolution/min
1 revolution/min = 0.1047200 radian/s
Reverse: radian/s = revolution/min × 0.1047200
Frequently Asked Questions
How many revolution/min are in 1 radian/s?
There are 9.5492743 revolution/min in 1 radian/s. To convert radian/s to revolution/min, multiply the value by 9.5492743.
How do I convert radian/s to revolution/min?
Multiply your radian/s value by 9.5492743 to get the equivalent in revolution/min. For example, 5 radian/s = 5 × 9.5492743 = 47.74637 revolution/min.
How do I convert revolution/min to radian/s?
Multiply your revolution/min value by 0.1047200 to get the equivalent in radian/s. Alternatively, divide by 9.5492743.
What is 10 radian/s in revolution/min?
10 radian/s is equal to 95.49274 revolution/min.
What is 100 radian/s in revolution/min?
100 radian/s is equal to 954.92743 revolution/min.