How to Convert Rotational Speed

The RPM to rad/s Calculator converts between revolutions per minute (RPM) and radians per second (rad/s) using the following conversion formulas:

From RPM to rad/s:

From rad/s to RPM:

Where:

• \( \text{RPM} \): Revolutions per minute, a unit of rotational speed commonly used in automotive and mechanical applications.
• \( \text{rad/s} \): Radians per second, a metric unit of angular velocity used in physics and engineering.
• \( \pi \): Approximately 3.14159, representing the ratio of a circle's circumference to its diameter.

Enter the rotational speed value and select the unit to convert between RPM and rad/s. The conversion is linear, with 1 RPM approximately equal to 0.10472 rad/s.

Using the RPM to rad/s Calculator

This calculator is designed to assist with converting rotational speed between RPM and rad/s, useful in physics, engineering, and automotive applications.

Input the rotational speed value and select the unit (RPM or rad/s). The calculator will display the converted values in both units.

Example: Convert 100 RPM to rad/s.

1. Rotational Speed: \( 100 \, \text{RPM} \)
2. Conversion: \( \frac{100 \times 2 \times \pi}{60} \approx 10.471975 \, \text{rad/s} \)
3. Result: \( 100 \, \text{RPM} = 10.471975 \, \text{rad/s} \)

Use this tool for quick and accurate conversions in scientific and engineering applications.

Common Conversion Table

The following table provides quick reference conversions for common rotational speed values between RPM and rad/s:

RPM	rad/s
1	0.1047
10	1.0472
100	10.4720
500	52.3599
1000	104.7198

Use this table for quick lookups or to verify calculator results.

Common FAQ

Below are frequently asked questions about rotational speed conversions between RPM and rad/s:

• Q: Why is the conversion factor \( \frac{2\pi}{60} \) used for RPM to rad/s?
  A: One revolution is \( 2\pi \) radians, and there are 60 seconds in a minute. Thus, \( \frac{2\pi}{60} \) converts revolutions per minute to radians per second.
• Q: What is the difference between RPM and rad/s?
  A: RPM measures complete revolutions per minute, while rad/s measures angular velocity in radians per second. RPM is practical for mechanical contexts, while rad/s is standard in physics.
• Q: Why convert between RPM and rad/s?
  A: Conversions are needed in engineering and physics to align measurements with different systems or standards, such as when calculating angular momentum or torque.
• Q: How accurate is this converter?
  A: The converter uses the precise value of \( \pi \) and provides results rounded to 2 decimal places for RPM and 4 for rad/s, ensuring high accuracy.
• Q: Can negative values be converted?
  A: Yes, negative values can be converted, representing rotation in the opposite direction, and the calculator handles them accurately.