Revolutions per minute converted to hertz.
Revolutions per minute to Radians per second Converter — rpm to rad/s
Convert Revolutions per minute (rpm) to Radians per second (rad/s) using the exact conversion factor (1 revolutions per minute = 0.1047197551 radians per second). See the formula, worked examples, conversion table, history, and common uses.
Revolutions per minute 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 0.01666666667 / 0.1591549431.
Frequency uses hertz as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Revolutions per minute to Radians per second
Revolutions per minute 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. Revolutions per minute is most often used for engine and motor speed specifications (car tachometers).
Formula
radians per second = revolutions per minute × 0.10471975512
This factor comes from each unit's defined relationship to the category's base unit: 1 revolutions per minute equals 0.0166666666667 base units, and 1 radians per second equals 0.159154943092 base units, so dividing one by the other gives the direct revolutions per minute-to-radians per second factor of 0.10471975512.
Simple example
1 rpm × 0.1047197551 = 0.1047197551 rad/s
1 revolutions per minute = 0.1047197551 radians per second.
Real-world example
1,000 rpm × 0.1047197551 = 104.7197551 rad/s
1,000 revolutions per minute = 104.7197551 radians per second.
Conversion table
| Revolutions per minute (rpm) | Radians per second (rad/s) |
|---|---|
| 60 rpm | 6.283185307 rad/s |
| 600 rpm | 62.83185307 rad/s |
| 1,000 rpm | 104.7197551 rad/s |
| 3,000 rpm | 314.1592654 rad/s |
| 6,000 rpm | 628.3185307 rad/s |
| 10,000 rpm | 1,047.197551 rad/s |
Reverse conversion: Radians per second to Revolutions per minute
0.1047197551 rad/s × 9.549296586 = 0.9999999998 rpm
0.1047197551 radians per second = 0.9999999998 revolutions per minute.
revolutions per minute = radians per second × 9.54929658551
For a page dedicated to this direction, see Radians per second to Revolutions per minute.
Understanding the Revolutions per minute
Revolutions per minute (rpm) measures rotational speed. RPM (revolutions per minute) equals hertz divided by 60, since one revolution per minute is 1/60 of a cycle per second. It is classified as a Non-SI unit (mechanical/automotive).
Where it's used: Used worldwide in automotive, mechanical, and industrial contexts
Uses of the Revolutions per minute today
- Engine and motor speed specifications (car tachometers)
- Industrial machinery and turbine speed ratings
- Hard drive and disc rotational speed
History of the Revolutions per minute
RPM developed alongside rotating machinery in the 19th-century industrial era as a practical, directly-readable way to describe rotational speed (a tachometer counting revolutions per minute), rather than converting to the more abstract cycles-per-second used in physics.
Historical origin. Revolutions per minute was not the invention of a single named person; it developed through the process described above.
Understanding the Radians per second (rad/s)
Angular frequency converted by one revolution equals 2*pi radians.
Revolutions per minute — sources
- NIST Special Publication 811 — General guide to non-SI unit conventions including rotational speed.
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 minute?
1 revolutions per minute equals 0.1047197551 radians per second, using the exact defined conversion factor rather than an estimate.
How do I convert revolutions per minute to radians per second?
Multiply the revolutions per minute value by 0.1047197551. The converter above does this instantly to whatever precision you set.
How do I convert radians per second back to revolutions per minute?
Use the reverse factor: 1 radians per second equals 9.549296586 revolutions per minute. You can also use the swap control in the converter above to flip the direction instantly.
What is a revolutions per minute?
Revolutions per minute (rpm) measures rotational speed. RPM (revolutions per minute) equals hertz divided by 60, since one revolution per minute is 1/60 of a cycle per second. It is classified as a Non-SI unit (mechanical/automotive).
What is a radians per second?
Radians per second (rad/s) is a unit of frequency.
Is the revolutions per minute to radians per second conversion exact?
Yes. Both revolutions per minute and radians per second are defined by fixed standards rather than physical artifacts, so the factor of 0.1047197551 used above is exact to as many digits as you choose to display.
Where is the revolutions per minute still used today?
Used worldwide in automotive, mechanical, and industrial contexts