Revolutions per second.
Revolutions per second to Radians per second Converter — rps to rad/s
Convert Revolutions per second (rps) to Radians per second (rad/s) using the exact conversion factor (1 revolutions per second = 6.283185307 radians per second). See the formula, worked examples, and conversion table.
Revolutions per second to Radians per second converter
Converter
Frequency Converter
Convert hertz, SI frequency prefixes, RPM, beats per minute, and angular frequency.
Context values
Some unit families need one extra value for a physically accurate result.
Angular frequency converted by one revolution equals 2*pi radians.
Result = input x 1 / 0.1591549431.
Frequency uses hertz as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Revolutions per second to Radians per second
Revolutions per second and Radians per second both describe how fast something cycles or rotates, and the conversion is a routine part of reading a car tachometer or motor spec sheet against a scientific frequency figure. Specifically: Revolutions per second, and angular frequency converted by one revolution equals 2*pi radians.
Formula
radians per second = revolutions per second × 6.28318530718
This factor comes from each unit's defined relationship to the category's base unit: 1 revolutions per second equals 1 base unit, and 1 radians per second equals 0.159154943092 base units, so dividing one by the other gives the direct revolutions per second-to-radians per second factor of 6.28318530718.
Simple example
1 rps × 6.283185307 = 6.283185307 rad/s
1 revolutions per second = 6.283185307 radians per second.
Real-world example
1,000 rps × 6.283185307 = 6,283.185307 rad/s
1,000 revolutions per second = 6,283.185307 radians per second.
Conversion table
| Revolutions per second (rps) | Radians per second (rad/s) |
|---|---|
| 60 rps | 376.9911184 rad/s |
| 600 rps | 3,769.911184 rad/s |
| 1,000 rps | 6,283.185307 rad/s |
| 3,000 rps | 18,849.55592 rad/s |
| 6,000 rps | 37,699.11184 rad/s |
| 10,000 rps | 62,831.85307 rad/s |
Reverse conversion: Radians per second to Revolutions per second
6.283185307 rad/s × 0.1591549431 = 1 rps
6.283185307 radians per second = 1 revolutions per second.
revolutions per second = radians per second × 0.159154943092
For a page dedicated to this direction, see Radians per second to Revolutions per second.
Understanding the Revolutions per second (rps)
Revolutions per second.
Understanding the Radians per second (rad/s)
Angular frequency converted by one revolution equals 2*pi radians.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many radians per second are in 1 revolutions per second?
1 revolutions per second equals 6.283185307 radians per second, using the exact defined conversion factor rather than an estimate.
How do I convert revolutions per second to radians per second?
Multiply the revolutions per second value by 6.283185307. The converter above does this instantly to whatever precision you set.
How do I convert radians per second back to revolutions per second?
Use the reverse factor: 1 radians per second equals 0.1591549431 revolutions per second. You can also use the swap control in the converter above to flip the direction instantly.
What is a revolutions per second?
Revolutions per second (rps) is a unit of frequency.
What is a radians per second?
Radians per second (rad/s) is a unit of frequency.
Is the revolutions per second to radians per second conversion exact?
Yes. Both revolutions per second and radians per second are defined by fixed standards rather than physical artifacts, so the factor of 6.283185307 used above is exact to as many digits as you choose to display.