Degrees per second to Radians per second Converter
Quick answer: To convert degrees per second to radians per second, multiply by 0.01745329. For example, 10 °/s is 0.1745329 rad/s. One degree per second equals 0.01745329 rad/s.
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Use the Degrees per second to Radians per second Converter
Degrees per second to Radians per second formula and what each symbol means
rad/s = °/s × 0.01745329
| Symbol | Meaning |
|---|---|
| °/s | Degree per second |
| rad/s | Radian per second |
Degrees per second to Radians per second examples
1 °/s
1 °/s × 0.01745329 = 0.01745329 rad/s.
10 °/s
10 °/s × 0.01745329 = 0.1745329 rad/s.
100 °/s
100 °/s × 0.01745329 = 1.745329 rad/s.
Degrees per second compared with Radians per second
One rad/s is 57.3 times as large as one °/s, so your number gets smaller when you convert degrees per second to radians per second and bigger when you convert back. If the answer is not smaller than what you typed, you multiplied instead of dividing.
About degrees per second and radians per second
Degree per second (°/s): Degrees turned each second; 360 °/s is one revolution per second. Radian per second (rad/s): The SI unit of angular velocity: an angle of one radian turned each second.
How to calculate Degrees per second to Radians per second step by step
- Enter the value in °/s (the starting unit).
- Multiply by 0.01745329, because 1 °/s = 0.01745329 rad/s.
- The product is the value in rad/s. To go back, divide by 0.01745329 or multiply by 57.29578.
Popular angular velocity conversions
How to read your Degrees per second to Radians per second result
Quick estimate: multiply by about 0.0175 to get radians per second from degrees per second; this is within 0.3% of the exact factor. One full revolution is 2π radians or 360 degrees.
| DEGREES PER SECOND | RADIANS PER SECOND |
|---|---|
| 1 | 0.01745329 |
| 2 | 0.03490659 |
| 5 | 0.08726646 |
| 10 | 0.1745329 |
| 20 | 0.3490659 |
| 50 | 0.8726646 |
| 100 | 1.745329 |
| 1,000 | 17.45329 |
Radians per second to Degrees per second: quick table
| RADIANS PER SECOND | DEGREES PER SECOND |
|---|---|
| 1 | 57.29578 |
| 5 | 286.4789 |
| 10 | 572.9578 |
| 25 | 1,432.394 |
| 50 | 2,864.789 |
| 100 | 5,729.578 |
| 250 | 14,323.94 |
| 500 | 28,647.89 |
Common mistakes when calculating Degrees per second to Radians per second
- Mixing up frequency in hertz (cycles per second) with angular velocity in rad/s, which differs by a factor of 2π.
- Dividing when you should multiply: from °/s to rad/s multiply by 0.01745329; from rad/s to °/s divide by 0.01745329.
Degrees per second to Radians per second FAQ
How many rad/s are in 1 °/s?
1 °/s equals 0.01745329 rad/s.
How many °/s are in 1 rad/s?
1 rad/s equals 57.29578 °/s.
Is 1 °/s = 0.01745329 rad/s an exact conversion?
The factor is shown rounded to 7 significant figures (0.01745329). The calculator above uses more digits.
What is a radian per second (rad/s)?
The SI unit of angular velocity: an angle of one radian turned each second.
How can I estimate degrees per second to radians per second in my head?
Quick estimate: multiply by about 0.0175 to get radians per second from degrees per second; this is within 0.3% of the exact factor.
What is 25 °/s in radians per second?
25 °/s = 0.4363323 rad/s (since 25 × 0.01745329).
What is 80 °/s in radians per second?
80 °/s = 1.396263 rad/s (since 80 × 0.01745329).
What is 500 °/s in radians per second?
500 °/s = 8.726646 rad/s (since 500 × 0.01745329).
How many decimals should I keep when converting °/s to rad/s?
Match the precision of your original measurement. For example, 0.1745329 rad/s rounds to 0.175 rad/s at 3 significant figures; keep more digits only for engineering or scientific work.
More in Angular Velocity converters
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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)