degrees to radians
Convert degree to radian — instant, free, with the formula shown.
1 °=0.01745329 rad
How to convert degree to radian
To convert degree to radian, multiply by 0.01745329:
rad = ° × 0.01745329
For example, 10 ° × 0.017453 = 0.17453293 rad.
° to rad conversion table
| degrees (°) | radians (rad) |
|---|---|
| 1 ° | 0.01745329 rad |
| 2 ° | 0.03490659 rad |
| 5 ° | 0.08726646 rad |
| 10 ° | 0.17453293 rad |
| 25 ° | 0.43633231 rad |
| 50 ° | 0.87266463 rad |
| 100 ° | 1.74532925 rad |
| 250 ° | 4.36332313 rad |
| 500 ° | 8.72664626 rad |
| 1000 ° | 17.45329252 rad |
Other degree conversions
Convert to radian from another unit
° to rad — frequently asked
How many radians are in 1 degree?
1 degree = 0.01745329 radians (° × 0.017453 = rad).
What is the formula to convert degree to radian?
Multiply your degree value by 0.01745329 to get radian.
How do I convert 10 degrees to radians?
10 ° = 0.17453293 rad. For 100 ° the answer is 1.74532925 rad. Use the calculator on this page for any other value.
When to convert degree to radian
1Mathematics and trigonometry (radians)
2Surveying and navigation (degrees, minutes, seconds)
3Engineering (mrad for laser sights, optics)
4Astronomy (arc-seconds for stellar parallax)
Angle conversion — common questions
Why are radians used in math instead of degrees?
Because in radians, derivatives and series of trig functions take their simplest form (d/dx sin(x) = cos(x) only when x is in radians).
How many degrees in 1 radian?
1 rad = 180/π ≈ 57.2958°.
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