Angular Velocity Converter
Angular velocity describes how fast something rotates. Engineers use radians per second; machinists and motors use revolutions per minute; many instruments report degrees per second. Enter a value, pick the units, and the converter applies exact definitions (one full turn is 2 pi radians or 360 degrees). The base unit is radians per second.
How the conversion works
value in rad/s = value * (from factor)
result = value in rad/s / (to factor)
1 rev = 2 pi rad = 360 deg
Every factor is the unit's size in radians per second. The input is converted to radians per second, then to the target unit.
Worked example
60 RPM uses the factor 2 pi over 60, so it equals 2 pi radians per second, about 6.28 rad/s. That is the same as 1 revolution per second.
Angular velocity: frequently asked questions
What is angular velocity?
Angular velocity is the rate at which an object rotates, measured as the angle swept per unit time. Its SI unit is radians per second. One full turn is 2 pi radians, or 360 degrees.
How do I convert RPM to radians per second?
Multiply revolutions per minute by 2 pi divided by 60. For example 60 RPM is exactly 2 pi radians per second, about 6.28 rad/s, because one revolution per second is 2 pi radians per second.
How are degrees and radians related here?
There are 2 pi radians in a full circle and 360 degrees in a full circle, so 1 radian equals 180 divided by pi degrees, about 57.30 degrees. The converter uses the exact factor of pi over 180 to move between degree-based and radian-based rates.
What is the base unit used by this converter?
The base unit is radians per second. Each input is converted to radians per second using its exact factor, then divided by the target unit's factor, which keeps every conversion consistent and reversible.
Official sources
- NIST Guide to the SI, units and conversions: nist.gov SP 811.
- BIPM SI Brochure, the radian: bipm.org.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.