Radians to Degrees Converter
Quick answer: To convert radians to degrees, multiply by 57.29578. For example, 10 rad is 572.9578 °. One radian equals 57.29578 °.
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Use the Radians to Degrees Converter
Radians to Degrees formula and what each symbol means
° = rad × 57.29578
| Symbol | Meaning |
|---|---|
| rad | Radian |
| ° | Degree |
Radians to Degrees examples
1 rad
1 rad × 57.29578 = 57.29578 °.
10 rad
10 rad × 57.29578 = 572.9578 °.
100 rad
100 rad × 57.29578 = 5,729.578 °.
Radians compared with Degrees
One rad is 57.3 times as large as one °, so your number gets bigger when you convert radians to degrees and smaller when you convert back. If the answer is not larger than what you typed, you divided instead of multiplying.
About radians and degrees
Radian (rad): The SI unit of plane angle: the angle subtended by an arc equal to the radius. Degree (°): 1/360 of a full turn.
Where radians to degrees conversions are used
Machining and construction use degrees; some drafting and military work uses gradians or mils. Trigonometry functions in most programming languages expect radians.
How to calculate Radians to Degrees step by step
- Enter the value in rad (the starting unit).
- Multiply by 57.29578, because 1 rad = 57.29578 °.
- The product is the value in °. To go back, divide by 57.29578 or multiply by 0.01745329.
Popular angle conversions
How to read your Radians to Degrees result
Quick estimate: multiply by about 57 to get degrees from radians; this is within 0.6% of the exact factor. To convert degrees to radians multiply by π/180, and to convert radians to degrees multiply by 180/π.
| RADIANS | DEGREES |
|---|---|
| 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 to Radians: quick table
| DEGREES | RADIANS |
|---|---|
| 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 to Degrees
- Using 3.14 for π when high accuracy is needed.
- Dividing when you should multiply: from rad to ° multiply by 57.29578; from ° to rad divide by 57.29578.
Radians to Degrees FAQ
How many ° are in 1 rad?
1 rad equals 57.29578 °.
How many rad are in 1 °?
1 ° equals 0.01745329 rad.
Is 1 rad = 57.29578 ° an exact conversion?
The factor is shown rounded to 7 significant figures (57.29578). The calculator above uses more digits.
What is a degree (°)?
1/360 of a full turn.
How can I estimate radians to degrees in my head?
Quick estimate: multiply by about 57 to get degrees from radians; this is within 0.6% of the exact factor.
What is 80 rad in degrees?
80 rad = 4,583.662 ° (since 80 × 57.29578).
What is 500 rad in degrees?
500 rad = 28,647.89 ° (since 500 × 57.29578).
What is 15 rad in degrees?
15 rad = 859.4367 ° (since 15 × 57.29578).
How many decimals should I keep when converting rad to °?
Match the precision of your original measurement. For example, 572.9578 ° rounds to 573 ° at 3 significant figures; keep more digits only for engineering or scientific work.
More in Angle 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 SI derived units