How to Convert Radians Per Second to RPM: The Reverse Guide

You have solved the physics equation, and your answer is sitting perfectly on your paper: 50 rad/s. But the assignment (or your boss) wants the final answer in Revolutions Per Minute (RPM) so they can actually go buy the right motor. If you are stuck wondering how to convert radians per second to rpm, don't panic. Going backward is just as easy as going forward.

Let's look at the numbers. Drop your rad/s value in the calculator below to get your RPM instantly.

The Reverse Math Explained

When you convert from RPM to rad/s, you multiply by π/30. To convert radians per second to rpm, you simply multiply by the reciprocal of that fraction.

The exact multiplier you need is 30/π.

RPM = rad/s × (30 / π)

Why Does That Work?

1. Seconds to Minutes: You multiply by 60.
2. Radians to Revolutions: You divide by 2π.
3. Combine: 60 / 2π cleanly reduces to 30 / π.

Step-by-Step Example

Let's walk through exactly how to convert radians per second to rpm for a theoretical angular velocity of 100 rad/s.

1. Take your starting value: 100 rad/s
2. Multiply by 30: 100 × 30 = 3000
3. Divide by π: 3000 / π
4. The exact theoretical answer is 3000/π RPM.
5. As a usable decimal, that is approximately 954.93 RPM.

Now that you know exactly how to run the numbers backward, you will never get stuck translating a theoretical physics answer into a real-world mechanical spec. If you need a refresher on the forward math, check our guide on how to convert rpm to radians per second.