Degrees per Second to Radians per Second Converter
Enter the angular velocity in degrees per second below to convert it to radians per second.
Convert Degrees per Second to Radians per Second
Enter a value in degrees per second (°/s) to convert to radians per second (rad/s).
Degree per Second to Radian per Second Conversion Table
Table showing various degree per second measurements converted to radians per second. Click any preset value or arrow to load it into the converter.
| Degrees per Second (°/s) | Radians per Second (rad/s) |
|---|---|
| 1 °/s | 0.0174533 rad/s |
| 2 °/s | 0.0349066 rad/s |
| 5 °/s | 0.0872665 rad/s |
| 10 °/s | 0.1745329 rad/s |
| 15 °/s | 0.2617994 rad/s |
| 20 °/s | 0.3490659 rad/s |
| 25 °/s | 0.4363323 rad/s |
| 30 °/s | 0.5235988 rad/s |
| 50 °/s | 0.8726646 rad/s |
| 75 °/s | 1.3089969 rad/s |
How to Convert Degrees per Second to Radians per Second
To convert degrees per second to radians per second, multiply the angular velocity by the following conversion ratio: 0.0174533 radians per second/degree per second.
Since one degree per second is equal to 0.0174533 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 degrees per second multiplied by 0.0174533.
For example, here's how to convert 10 degrees per second to radians per second using the formula above.
How Many Radians per Second Are in a Degree per Second?
There are 0.0174533 radians per second in a degree per second, which is why we use this value in the formula above.
Our degree 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.
Degrees 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 Degree per Second?
A degree per second is a unit of angular velocity equal to 0.0174533 radians per second (rad/s), the base unit for angular velocity. Angular rotation of 1 degree per second (π/180 rad/s). [1]
The degree per second is classified as a standard unit of angular velocity. Degrees per Second can be abbreviated as °/s; for example, 1 degree per second can be written as 1 °/s.
When working with degrees per second (°/s) in formulas or technical specifications, always verify whether your target system uses SI metric, US customary, or British imperial standards.
In practice, degrees per second (°/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 degrees per second (°/s) and radians per second (rad/s), keep full floating-point precision (1 °/s = 0.0174533 rad/s; 1 rad/s = 57.2957795 °/s) during intermediate calculations and round only the final radian per second figure to match your instrument tolerance.
More Degree per Second & Radian per Second Conversions
Need to calculate in the opposite direction? Use our radians per second to degrees per second converter (rad/s to °/s) to switch your starting unit immediately. You can also explore related tools such as converting revolutions per minute to radians per second, converting revolutions per second to radians per second, or converting radians per second to revolutions per minute.
Convert from Degrees per Second
Frequently Asked Questions
References
- [1]NIST OWM StandardNIST OWM (SI Units — Length)·Velocity - Angular Metrology Standard — Degrees per Second (°/s) to Radians per Second (rad/s)
- [2]BIPM SpecificationBIPM (SI Base Unit: Metre (m))·Unit Specifications: Degree per Second (°/s) & Radian per Second (rad/s)
- [3]NIST HB 133 ReferenceNIST HB 133 (NIST Handbook 133 (2019 Ed.))·Conversion Factors & Mathematical Basis (°/s to rad/s)