Angular frequency converted by one revolution equals 2*pi radians.
Radians per second to Revolutions per minute Converter — rad/s to rpm
Convert Radians per second (rad/s) to Revolutions per minute (rpm) using the exact conversion factor (1 radians per second = 9.549296586 revolutions per minute). See the formula, worked examples, conversion table, history, and common uses.
Radians per second to Revolutions per minute converter
Converter
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Context values
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Revolutions per minute converted to hertz.
Result = input x 0.1591549431 / 0.01666666667.
Frequency units are compatible.
Reserved above the conversion cards and below the converter.
About Converting Radians per second to Revolutions per minute
Radians per second and Revolutions per minute are both scientific-measurement units, spanning everything from atomic and laboratory scales to astronomical distances — the kind of conversion that comes up constantly in physics, chemistry, and astronomy when a result needs to move between conventions used in different subfields. Specifically: Angular frequency converted by one revolution equals 2*pi radians, and revolutions per minute converted to hertz.
Formula
revolutions per minute = radians per second × 9.54929658551
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 minute equals 0.0166666666667 base units, so dividing one by the other gives the direct radians per second-to-revolutions per minute factor of 9.54929658551.
Simple example
1 rad/s × 9.549296586 = 9.549296586 rpm
1 radians per second = 9.549296586 revolutions per minute.
Real-world example
10 rad/s × 9.549296586 = 95.49296586 rpm
10 radians per second = 95.49296586 revolutions per minute.
Conversion table
| Radians per second (rad/s) | Revolutions per minute (rpm) |
|---|---|
| 0.001 rad/s | 0.0095492966 rpm |
| 0.01 rad/s | 0.0954929659 rpm |
| 1 rad/s | 9.549296586 rpm |
| 10 rad/s | 95.49296586 rpm |
| 100 rad/s | 954.9296586 rpm |
| 1,000 rad/s | 9,549.296586 rpm |
Reverse conversion: Revolutions per minute to Radians per second
9.549296586 rpm × 0.1047197551 = 1 rad/s
9.549296586 revolutions per minute = 1 radians per second.
radians per second = revolutions per minute × 0.10471975512
For a page dedicated to this direction, see Revolutions per minute 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 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.
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 revolutions per minute are in 1 radians per second?
1 radians per second equals 9.549296586 revolutions per minute, using the exact defined conversion factor rather than an estimate.
How do I convert radians per second to revolutions per minute?
Multiply the radians per second value by 9.549296586. The converter above does this instantly to whatever precision you set.
How do I convert revolutions per minute back to radians per second?
Use the reverse factor: 1 revolutions per minute equals 0.1047197551 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 scientific units.
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).
Is the radians per second to revolutions per minute conversion exact?
Yes. Both radians per second and revolutions per minute are defined by fixed standards rather than physical artifacts, so the factor of 9.549296586 used above is exact to as many digits as you choose to display.
Why does this category span everything from atomic to astronomical scales?
Scientific work spans an enormous range of physical scales, from atomic distances (measured in angstroms or atomic mass units) to interstellar distances (measured in astronomical units or parsecs), so this category groups SI-derived and scale-specific units that researchers commonly need to convert between within their field.