Angular Velocity Converter
Quick answer: Choose a starting unit and a target unit, then enter a value. Common conversions: 1 rad/s = 57.29578 °/s; 1 rad/s = 9.549297 rpm; 1 rad/s = 0.1591549 rev/s. This converter covers 7 angular velocity units.
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Use the Angular Velocity Converter
Angular Velocity formula and what each symbol means
target = value × (factor of starting unit ÷ factor of target unit), where each factor is the unit value in rad/s.
| Symbol | Meaning |
|---|---|
| value | The number you want to convert |
| factor | The unit’s size expressed in the base unit (rad/s) |
Angular Velocity examples
rad/s to °/s
10 rad/s = 572.9578 °/s.
rad/s to rpm
10 rad/s = 95.49297 rpm.
rad/s to rev/s
10 rad/s = 1.591549 rev/s.
How to calculate Angular Velocity step by step
- Choose the starting unit and the target unit.
- Enter your value.
- Read the converted value, plus the conversion factor in both directions.
Popular angular velocity conversions
- Radians per second to Degrees per second converter
- Radians per second to Revolutions per minute converter
- Radians per second to Revolutions per second converter
- Degrees per second to Radians per second converter
- Degrees per second to Revolutions per minute converter
- Degrees per second to Revolutions per second converter
- Revolutions per minute to Radians per second converter
- Revolutions per minute to Degrees per second converter
- Revolutions per minute to Revolutions per second converter
- Revolutions per second to Radians per second converter
- Revolutions per second to Degrees per second converter
- Revolutions per second to Revolutions per minute converter
How to read your Angular Velocity result
One full revolution is 2π radians or 360 degrees. So 1 rev/s equals 6.2832 rad/s and 360 °/s, and 1 rpm equals about 0.10472 rad/s and 6 °/s. Divide rad/s by 2π to get revolutions per second, and multiply by 60 for rpm.
| UNIT | SYMBOL | EQUALS | VALUE OF 1 RAD/S |
|---|---|---|---|
| Radian per second | rad/s | 1 rad/s = 1 rad/s | 1 rad/s |
| Degree per second | °/s | 1 °/s = 0.017453293 rad/s | 57.29578 °/s |
| Revolution per minute | rpm | 1 rpm = 0.10471976 rad/s | 9.549297 rpm |
| Revolution per second | rev/s | 1 rev/s = 6.2831853 rad/s | 0.1591549 rev/s |
| Degree per minute | °/min | 1 °/min = 0.00029088821 rad/s | 3,437.747 °/min |
| Radian per minute | rad/min | 1 rad/min = 0.016666667 rad/s | 60 rad/min |
| Revolution per hour | rev/h | 1 rev/h = 0.0017453293 rad/s | 572.9578 rev/h |
Common mistakes when calculating Angular Velocity
- Treating rpm and rad/s as interchangeable: 1 rad/s is about 9.549 rpm.
- Mixing up frequency in hertz (cycles per second) with angular velocity in rad/s, which differs by a factor of 2π.
- Forgetting that trigonometric functions in most software expect radians, not degrees.
Angular Velocity FAQ
How many rad/s is 1 rpm?
1 rpm is 2π/60, or about 0.1047198 rad/s.
How do I convert rpm to rad/s?
Multiply the rpm value by 2π and divide by 60.
Is angular velocity the same as frequency?
No. A rotation at 1 Hz (1 revolution per second) has an angular velocity of 2π rad/s, about 6.283 rad/s.
What is the base unit for angular velocity?
This converter uses radian per second (rad/s) as the common base unit: every value is first converted to it and then to the target unit.
How do I convert between two angular velocity units?
Choose the starting and target units, enter the value and read the result. By hand: convert to the base unit with the table, then divide by the target unit factor.
How many degrees per second are in 1 radian per second?
1 rad/s = 57.29578 °/s.
How many revolutions per minute are in 1 radian per second?
1 rad/s = 9.549297 rpm.
How many revolutions per second are in 1 radian per second?
1 rad/s = 0.1591549 rev/s.
Which angular velocity units does this converter support?
It covers 7 units: radian per second (rad/s), degree per second (°/s), revolution per minute (rpm), revolution per second (rev/s), degree per minute (°/min), radian per minute (rad/min), revolution per hour (rev/h).
How accurate is the angular velocity converter?
Results are calculated at full double precision and shown to about 8 significant figures. Round the answer to the precision of your original measurement; a result cannot be more accurate than the number you started with.
More in Angular Velocity converters
- Degrees per second to Radians per second Converter
- Revolutions per second to Revolutions per minute Converter
- Degrees per second to Revolutions per minute Converter
- Revolutions per second to Radians per second Converter
- Degrees per second to Revolutions per second Converter
- Revolutions per second to Degrees per second Converter
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Method, review and disclaimer
Edited by: Hemant Kumar and Anjita Rai, founders of ToolsVault (SEO and content professional, not a licensed adviser). Method: this tool runs in your browser using the formula shown on this page; the numbers you enter are not sent to our servers. Sources: NIST SP 811, Appendix B.8: conversion factors, BIPM: the International System of Units (SI)