Convert rotation

Convert angles and angular speeds among degrees, radians, gradians, revolutions, rpm, and hertz.

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ToolRotation Converter
Input
Output
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Preview

How it works

Angle units convert through one revolution: degrees ÷ 360, radians ÷ 2π, and gradians ÷ 400. Angular speeds likewise pass through revolutions per second before producing rpm, radians per second, degrees per second, and hertz.

  • Angle and angular speed are separate quantities.
  • No time interval is invented to turn one into the other.

Worked example

180 degrees in every angle unit
Input
											Angle value: 180
Angle unit: degrees
Output
												Angle degrees: 180
Angle radians: 3.141593
Angle gradians: 200
Angle revolutions: 0.5
Speed rpm: 0
Speed rad per second: 0
Speed deg per second: 0
Speed hz: 0

When to use this

CAD drawings convert degrees to radians, motor sheets change rpm to radians per second, and surveying compares gradians with degrees.

Edge cases

  • One revolution is 360 degrees, 2π radians, and 400 gradians, so rounded cross-conversions can differ in the last digit.
  • Negative angles and speeds preserve direction through the sign.
  • Supplying neither an angle nor a speed is rejected because no quantity is selected.