Radians Per Second to RPM Calculator

Formula

The formula to convert radians per second to revolutions per minute (RPM) is:

\[ RPM = \frac{ω \times 60}{2 \pi} \]

Where:

\( RPM \) is the revolutions per minute
\( ω \) is the angular velocity in radians per second
\( \pi \) is the mathematical constant Pi (approximately 3.14159)

What is Radians Per Second?

Radians per second is a unit of angular velocity that describes the rate of rotation around a central point. It measures how many radians an object rotates in one second. One radian is the angle created when the arc length is equal to the radius of the circle. This unit is commonly used in physics and engineering to describe rotational motion.

Example Calculation

Let's assume the following value:

Angular Velocity (ω) = 10 radians per second

Using the formula to calculate the RPM:

\[ RPM = \frac{10 \times 60}{2 \pi} \approx \frac{600}{6.2832} \approx 95.49 \]

The RPM is approximately 95.49.