Revolutions per Second to Radians per Second Converter
Enter the angular velocity in revolutions per second below to convert it to radians per second.
Convert Revolutions per Second to Radians per Second
Enter a value in revolutions per second (r/s) to convert to radians per second (rad/s).
Revolution per Second to Radian per Second Conversion Table
Table showing various revolution per second measurements converted to radians per second. Click any preset value or arrow to load it into the converter.
| Revolutions per Second (r/s) | Radians per Second (rad/s) |
|---|---|
| 1 r/s | 6.2831853 rad/s |
| 2 r/s | 12.5663706 rad/s |
| 5 r/s | 31.4159265 rad/s |
| 10 r/s | 62.8318531 rad/s |
| 15 r/s | 94.2477796 rad/s |
| 20 r/s | 125.6637061 rad/s |
| 25 r/s | 157.0796327 rad/s |
| 30 r/s | 188.4955592 rad/s |
| 50 r/s | 314.1592654 rad/s |
| 75 r/s | 471.238898 rad/s |
How to Convert Revolutions per Second to Radians per Second
To convert revolutions per second to radians per second, multiply the angular velocity by the following conversion ratio: 6.2831853 radians per second/revolution per second.
Since one revolution per second is equal to 6.2831853 radians per second, you can use this simple formula to convert:
The angular velocity in radians per second is equal to the angular velocity in revolutions per second multiplied by 6.2831853.
For example, here's how to convert 10 revolutions per second to radians per second using the formula above.
How Many Radians per Second Are in a Revolution per Second?
There are 6.2831853 radians per second in a revolution per second, which is why we use this value in the formula above.
Our revolution per second to radian per second calculator automatically converts your angular velocity measurements with full decimal and scientific precision across US customary, imperial, and SI metric standards.
Revolutions per Second and radians per second are both units used to measure angular velocity. Keep reading to learn more about each unit.
What Is a Revolution per Second?
A revolution per second is a unit of angular velocity equal to 6.2831853 radians per second (rad/s), the base unit for angular velocity. One full rotation per second (2π ≈ 6.28319 rad/s). [1]
The revolution per second is classified as a standard unit of angular velocity. Revolutions per Second can be abbreviated as r/s; for example, 1 revolution per second can be written as 1 r/s.
When working with revolutions per second (r/s) in formulas or technical specifications, always verify whether your target system uses SI metric, US customary, or British imperial standards.
In practice, revolutions per second (r/s) are widely used across standard angular velocity applications within international standard workflows, engineering documentation, and technical data sheets.
What Is a Radian per Second?
SI unit of angular velocity. It serves as a primary reference unit for measuring angular velocity across scientific and practical applications. [2]
The radian per second is classified as an International System of Units (SI) unit of angular velocity. Radians per Second can be abbreviated as rad/s; for example, 1 radian per second can be written as 1 rad/s.
As the primary coherent reference unit for angular velocity in this category, all other angular velocity units are mathematically anchored to the radian per second (rad/s).
In practice, radians per second (rad/s) are widely used across standard angular velocity applications within International System of Units (SI) workflows, engineering documentation, and technical data sheets.
When converting angular velocity between revolutions per second (r/s) and radians per second (rad/s), keep full floating-point precision (1 r/s = 6.2831853 rad/s; 1 rad/s = 0.1591549 r/s) during intermediate calculations and round only the final radian per second figure to match your instrument tolerance.
More Revolution per Second & Radian per Second Conversions
Need to calculate in the opposite direction? Use our radians per second to revolutions per second converter (rad/s to r/s) to switch your starting unit immediately. You can also explore related tools such as converting degrees per second to radians per second, converting revolutions per minute to radians per second, or converting radians per second to degrees per second.
Convert from Revolutions per Second
Frequently Asked Questions
References
- [1]NIST OWM StandardNIST OWM (SI Units — Length)·Velocity - Angular Metrology Standard — Revolutions per Second (r/s) to Radians per Second (rad/s)
- [2]BIPM SpecificationBIPM (SI Base Unit: Metre (m))·Unit Specifications: Revolution per Second (r/s) & Radian per Second (rad/s)
- [3]NIST HB 133 ReferenceNIST HB 133 (NIST Handbook 133 (2019 Ed.))·Conversion Factors & Mathematical Basis (r/s to rad/s)