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Angular Velocity Converter

Convert angular velocity between radians per second, degrees per second, revolutions per minute (RPM), and other rotational speed units.

What this tool does

Convert angular velocity between radians per second, degrees per second, revolutions per minute (RPM), and other rotational speed units. Type an amount in radians per second, choose the units, and the tool converts it to revolutions per minute (rpm). It offers 12 angular velocity units and also shows the same amount in the others.

Inputs

  • Value: A number.
  • From: Choose one from 12 options, including Radian per second, Milliradian per second, Radian per minute, Radian per hour, Degree per second, Degree per minute. Starts as Radian per second.
  • To: Choose one of the same 12 units as "From". Starts as Revolution per minute (rpm).

How to use

  1. Enter the amount you want to convert.
  2. Choose the unit to convert from and the unit to convert to.
  3. Read the result: the converted amount and the same amount in the other units. It appears once every required field has a valid value.

Worked examples

Conversions from radians per second to revolutions per minute (rpm):

  • 1 rad/s ≈ 9.549297 rpm
  • 5 rad/s ≈ 47.746483 rpm
  • 10 rad/s ≈ 95.492966 rpm
  • 50 rad/s ≈ 477.464829 rpm
  • 100 rad/s ≈ 954.929659 rpm

Multiply the number of radians per second by about 9.549297 to get revolutions per minute (rpm). The factor follows from exact definitions. It has more digits than fit here, so it is shown rounded.

Sources: Radian per second: SI Brochure, 9th edition (2019). Revolution per minute (rpm): NIST SP 811 (2008), Appendix B.8.

Limitations

  • Converts the unit of a rotation rate only. It does not work out speed, torque or power from it.
  • Hertz is a frequency unit and is not listed here. One revolution per second is one cycle per second, so use the revolutions per second entry.
  • Revolutions per minute is the same unit as RPM and is listed once.

FAQs

Q: What is angular velocity?
A: It is how fast something turns: the angle it sweeps per unit of time. The SI unit is the radian per second.
Q: How are RPM and rad/s related?
A: One RPM is 2 pi / 60 radians per second. To go the other way, multiply radians per second by 60 and divide by 2 pi.
Q: Why is hertz missing?
A: Hertz measures cycles per second, a frequency. For a turning object one cycle is one revolution, so use revolutions per second.

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