Degrees to Radians Converter
Quick answer: To convert degrees to radians, multiply by 0.01745329. For example, 10 ° is 0.1745329 rad. One degree equals 0.01745329 rad.
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Use the Degrees to Radians Converter
Degrees to Radians formula and what each symbol means
rad = ° × 0.01745329
| Symbol | Meaning |
|---|---|
| ° | Degree |
| rad | Radian |
Degrees to Radians examples
1 °
1 ° × 0.01745329 = 0.01745329 rad.
10 °
10 ° × 0.01745329 = 0.1745329 rad.
100 °
100 ° × 0.01745329 = 1.745329 rad.
Degrees compared with Radians
One rad is 57.3 times as large as one °, so your number gets smaller when you convert degrees to radians and bigger when you convert back. If the answer is not smaller than what you typed, you multiplied instead of dividing.
About degrees and radians
Degree (°): 1/360 of a full turn. Radian (rad): The SI unit of plane angle: the angle subtended by an arc equal to the radius.
Where degrees to radians 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 Degrees to Radians step by step
- Enter the value in ° (the starting unit).
- Multiply by 0.01745329, because 1 ° = 0.01745329 rad.
- The product is the value in rad. To go back, divide by 0.01745329 or multiply by 57.29578.
Popular angle conversions
How to read your Degrees to Radians result
Quick estimate: multiply by about 0.0175 to get radians from degrees; this is within 0.3% of the exact factor. To convert degrees to radians multiply by π/180, and to convert radians to degrees multiply by 180/π.
| DEGREES | RADIANS |
|---|---|
| 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 to Degrees: quick table
| RADIANS | DEGREES |
|---|---|
| 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 to Radians
- Using 3.14 for π when high accuracy is needed.
- Dividing when you should multiply: from ° to rad multiply by 0.01745329; from rad to ° divide by 0.01745329.
Degrees to Radians FAQ
How many rad are in 1 °?
1 ° equals 0.01745329 rad.
How many ° are in 1 rad?
1 rad equals 57.29578 °.
Is 1 ° = 0.01745329 rad an exact conversion?
The factor is shown rounded to 7 significant figures (0.01745329). The calculator above uses more digits.
What is a radian (rad)?
The SI unit of plane angle: the angle subtended by an arc equal to the radius.
How can I estimate degrees to radians in my head?
Quick estimate: multiply by about 0.0175 to get radians from degrees; this is within 0.3% of the exact factor.
What is 60 ° in radians?
60 ° = 1.047198 rad (since 60 × 0.01745329).
What is 250 ° in radians?
250 ° = 4.363323 rad (since 250 × 0.01745329).
What is 7 ° in radians?
7 ° = 0.122173 rad (since 7 × 0.01745329).
How many decimals should I keep when converting ° to rad?
Match the precision of your original measurement. For example, 0.1745329 rad rounds to 0.175 rad at 3 significant figures; keep more digits only for engineering or scientific work.
More in Angle converters
- Revolutions to Radians Converter
- Gradians to Revolutions Converter
- Revolutions to Gradians Converter
- Revolutions to Degrees Converter
- Radians to Gradians Converter
- Radians to Revolutions Converter
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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