Degrees to Radians
One degree equals 0.017453 radians.
Radians = degrees × 0.0174532925
By Piero Nanni · Last checked
Degrees to Radians Calculator
How to Convert Degrees to Radians
Formula:
Radians = degrees × 0.0174532925
Worked example:
75 degrees × 0.0174532925 = 1.309 radians
Degrees to Radians Conversion Table
| ° | rad |
|---|---|
| 1 | 0.0175 |
| 1.5 | 0.0262 |
| 2 | 0.0349 |
| 2.5 | 0.0436 |
| 3 | 0.0524 |
| 4 | 0.0698 |
| 5 | 0.0873 |
| 6 | 0.1047 |
| 7 | 0.1222 |
| 7.5 | 0.1309 |
| 8 | 0.1396 |
| 9 | 0.1571 |
| 10 | 0.1745 |
| 15 | 0.2618 |
| 20 | 0.3491 |
| 25 | 0.4363 |
| 30 | 0.5236 |
| 40 | 0.6981 |
| 45 | 0.7854 |
| 50 | 0.8727 |
| 60 | 1.0472 |
| 70 | 1.2217 |
| 75 | 1.309 |
| 80 | 1.3963 |
| 90 | 1.5708 |
| 100 | 1.7453 |
| 120 | 2.0944 |
| 135 | 2.3562 |
| 150 | 2.618 |
| 180 | 3.1416 |
| 200 | 3.4907 |
| 250 | 4.3633 |
| 270 | 4.7124 |
| 300 | 5.236 |
| 360 | 6.2832 |
About This Conversion
Degrees to radians multiplies by π/180, about 0.0174533. Radians are the natural unit for angles because they measure arc length in radii: an angle of one radian cuts an arc exactly as long as the radius, which is what makes the calculus of sine and cosine come out clean.
Every programming language trigonometric function expects radians, so this conversion is the most common source of silent errors in graphics and geometry code. Passing 90 to a sine function returns 0.894, not 1, because it read the input as 90 radians, roughly fourteen full turns.
Frequently Asked Questions
How many radians is 90 degrees?
90° is π/2 radians, about 1.5708.
How many radians is 180 degrees?
180° is exactly π radians, about 3.14159.
What is the formula?
Multiply degrees by π/180, which is about 0.0174533.
Why do programming languages use radians?
The trigonometric identities and derivatives only hold in radians, so the standard libraries define their functions that way.
Sources
Related Conversions
Converting the other way? Radians to Degrees
Need a different unit? Open the full angle converter