Radians per second to Degrees per second Converter
Quick answer: To convert radians per second to degrees per second, multiply by 57.29578. For example, 10 rad/s is 572.9578 °/s. One radian per second equals 57.29578 °/s.
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Use the Radians per second to Degrees per second Converter
Radians per second to Degrees per second formula and what each symbol means
°/s = rad/s × 57.29578
| Symbol | Meaning |
|---|---|
| rad/s | Radian per second |
| °/s | Degree per second |
Radians per second to Degrees per second examples
1 rad/s
1 rad/s × 57.29578 = 57.29578 °/s.
10 rad/s
10 rad/s × 57.29578 = 572.9578 °/s.
100 rad/s
100 rad/s × 57.29578 = 5,729.578 °/s.
Radians per second compared with Degrees per second
One rad/s is 57.3 times as large as one °/s, so your number gets bigger when you convert radians per second to degrees per second and smaller when you convert back. If the answer is not larger than what you typed, you divided instead of multiplying.
About radians per second and degrees per second
Radian per second (rad/s): The SI unit of angular velocity: an angle of one radian turned each second. Degree per second (°/s): Degrees turned each second; 360 °/s is one revolution per second.
How to calculate Radians per second to Degrees per second step by step
- Enter the value in rad/s (the starting unit).
- Multiply by 57.29578, because 1 rad/s = 57.29578 °/s.
- The product is the value in °/s. To go back, divide by 57.29578 or multiply by 0.01745329.
Popular angular velocity conversions
How to read your Radians per second to Degrees per second result
Quick estimate: multiply by about 57 to get degrees per second from radians per second; this is within 0.6% of the exact factor. So 1 rev/s equals 6.2832 rad/s and 360 °/s, and 1 rpm equals about 0.10472 rad/s and 6 °/s.
| RADIANS PER SECOND | DEGREES PER SECOND |
|---|---|
| 1 | 57.29578 |
| 2 | 114.5916 |
| 5 | 286.4789 |
| 10 | 572.9578 |
| 20 | 1,145.916 |
| 50 | 2,864.789 |
| 100 | 5,729.578 |
| 1,000 | 57,295.78 |
Degrees per second to Radians per second: quick table
| DEGREES PER SECOND | RADIANS PER SECOND |
|---|---|
| 1 | 0.01745329 |
| 5 | 0.08726646 |
| 10 | 0.1745329 |
| 25 | 0.4363323 |
| 50 | 0.8726646 |
| 100 | 1.745329 |
| 250 | 4.363323 |
| 500 | 8.726646 |
Common mistakes when calculating Radians per second to Degrees 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 rad/s to °/s multiply by 57.29578; from °/s to rad/s divide by 57.29578.
Radians per second to Degrees per second FAQ
How many °/s are in 1 rad/s?
1 rad/s equals 57.29578 °/s.
How many rad/s are in 1 °/s?
1 °/s equals 0.01745329 rad/s.
Is 1 rad/s = 57.29578 °/s an exact conversion?
The factor is shown rounded to 7 significant figures (57.29578). The calculator above uses more digits.
What is a degree per second (°/s)?
Degrees turned each second; 360 °/s is one revolution per second.
How can I estimate radians per second to degrees per second in my head?
Quick estimate: multiply by about 57 to get degrees per second from radians per second; this is within 0.6% of the exact factor.
What is 12 rad/s in degrees per second?
12 rad/s = 687.5494 °/s (since 12 × 57.29578).
What is 60 rad/s in degrees per second?
60 rad/s = 3,437.747 °/s (since 60 × 57.29578).
What is 250 rad/s in degrees per second?
250 rad/s = 14,323.94 °/s (since 250 × 57.29578).
How many decimals should I keep when converting rad/s to °/s?
Match the precision of your original measurement. For example, 572.9578 °/s rounds to 573 °/s at 3 significant figures; keep more digits only for engineering or scientific work.
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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)