RPM to Angular Velocity Calculator

When we talk about rotating machines, motors, or even record players, one common question arises: How do we convert RPM to angular velocity? To make this process simple, we have developed an RPM to Angular Velocity Calculator that lets you convert revolutions per minute (RPM) into different angular velocity units such as radians per second (rad/s), radians per minute (rad/min), degrees per second (°/s), degrees per minute (°/min), and Hertz (Hz).

This tool is especially useful for engineers, physics students, and hobbyists who often need quick and accurate conversions. Instead of doing lengthy calculations, you can simply enter the RPM value into the calculator and get instant results.

How to Convert RPM to Angular Velocity?

Angular velocity measures how fast an object rotates or spins around a fixed point. It is usually expressed in radians per second (rad/s). The relationship between RPM and angular velocity comes from the fact that:

• One revolution equals 2π radians
• One minute equals 60 seconds

So, the general formula is:

ω = RPM × (2π / 60)

Where:

• ω = angular velocity in radians per second
• RPM = revolutions per minute

Example Calculations

Let’s see how this formula works in practice.

What is the angular velocity of 45 RPM?

ω = 45 × (2π / 60)

ω = 45 × 0.10472

ω ≈ 4.712 rad/s

What is the angular velocity of 60 RPM?

ω = 60 × (2π / 60)

ω = 60 × 0.10472

ω ≈ 6.283 rad/s

So, 60 RPM corresponds exactly to 2π radians per second, which makes sense because it completes one full revolution in one second.

How Does RPM Relate to Angular Velocity?

RPM tells you how many full turns something makes in one minute, while angular velocity explains how fast it rotates in terms of radians, degrees, or frequency. Both are connected, but angular velocity gives a more precise scientific measurement.

For example:

• A motor running at 3000 RPM has an angular velocity of about 314 rad/s.
• A fan spinning at 1200 RPM has an angular velocity of about 126 rad/s.

This shows how we can switch from everyday RPM values into scientific units that are useful in physics and engineering.

How to Use the RPM to Angular Velocity Calculator

1. Enter the RPM value into the input box.
2. Choose the output unit (rad/s, rad/min, deg/s, deg/min, Hz).
3. Click the calculate button.
4. Instantly see the step-by-step calculation along with the final result.

Our calculator also displays all possible conversions at once, so you can easily compare values in different units.

Final Verdict

Converting RPM to angular velocity doesn’t need to be complicated. With the right formula, you can do it manually, but using our RPM to Angular Velocity Calculator makes it quick and error-free. Whether you are solving physics problems, testing motors, or just satisfying your curiosity, this tool gives you instant answers.

FAQs

How to convert RPM to angular velocity?

Use the formula ω = RPM × (2π / 60). Multiply RPM by 2π, then divide by 60.

How does RPM relate to angular velocity?

RPM measures rotations per minute, while angular velocity measures the rate of rotation in radians per second, degrees per second, or Hertz.

What is the angular velocity of 45 RPM?

At 45 RPM, the angular velocity is about 4.712 rad/s.

What is the angular velocity of 60 RPM?

At 60 RPM, the angular velocity is about 6.283 rad/s, which equals 2π rad/s.

Can I convert RPM to Hz?

Yes. Simply divide RPM by 60. For example, 120 RPM = 2 Hz.