Angular frequency converted by one revolution equals 2*pi radians.
Radians per second to Revolutions per second Converter — rad/s to rps
Convert Radians per second (rad/s) to Revolutions per second (rps) using the exact conversion factor (1 radians per second = 0.1591549431 revolutions per second). See the formula, worked examples, and conversion table.
Radians per second to Revolutions 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.
Revolutions per second.
Result = input x 0.1591549431 / 1.
Frequency uses hertz as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Radians per second to Revolutions per second
Radians per second and Revolutions 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: Angular frequency converted by one revolution equals 2*pi radians, and revolutions per second.
Formula
revolutions per second = radians per second × 0.159154943092
This factor comes from each unit's defined relationship to the category's base unit: 1 radians per second equals 0.159154943092 base units, and 1 revolutions per second equals 1 base unit, so dividing one by the other gives the direct radians per second-to-revolutions per second factor of 0.159154943092.
Simple example
1 rad/s × 0.1591549431 = 0.1591549431 rps
1 radians per second = 0.1591549431 revolutions per second.
Real-world example
1,000 rad/s × 0.1591549431 = 159.1549431 rps
1,000 radians per second = 159.1549431 revolutions per second.
Conversion table
| Radians per second (rad/s) | Revolutions per second (rps) |
|---|---|
| 60 rad/s | 9.549296586 rps |
| 600 rad/s | 95.49296586 rps |
| 1,000 rad/s | 159.1549431 rps |
| 3,000 rad/s | 477.4648293 rps |
| 6,000 rad/s | 954.9296586 rps |
| 10,000 rad/s | 1,591.549431 rps |
Reverse conversion: Revolutions per second to Radians per second
0.1591549431 rps × 6.283185307 = 1 rad/s
0.1591549431 revolutions per second = 1 radians per second.
radians per second = revolutions per second × 6.28318530718
For a page dedicated to this direction, see Revolutions per second to Radians per second.
Understanding the Radians per second (rad/s)
Angular frequency converted by one revolution equals 2*pi radians.
Understanding the Revolutions per second (rps)
Revolutions per second.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many revolutions per second are in 1 radians per second?
1 radians per second equals 0.1591549431 revolutions per second, using the exact defined conversion factor rather than an estimate.
How do I convert radians per second to revolutions per second?
Multiply the radians per second value by 0.1591549431. The converter above does this instantly to whatever precision you set.
How do I convert revolutions per second back to radians per second?
Use the reverse factor: 1 revolutions per second equals 6.283185307 radians per second. You can also use the swap control in the converter above to flip the direction instantly.
What is a radians per second?
Radians per second (rad/s) is a unit of frequency.
What is a revolutions per second?
Revolutions per second (rps) is a unit of frequency.
Is the radians per second to revolutions per second conversion exact?
Yes. Both radians per second and revolutions per second are defined by fixed standards rather than physical artifacts, so the factor of 0.1591549431 used above is exact to as many digits as you choose to display.