Degrees to Radians Converter
1 degree (°) equals 0.01745329252 radians (rad).
Quick answer
To convert degrees to radians, multiply by π/180 (about 0.017453): 90° = π/2 ≈ 1.5708 rad.
- 1 degree = 0.01745329252 radians
- 1 radian = 57.29577951 degrees
- Formula: rad = ° × 0.01745329252
- Quick estimate: multiply by 0.01745, or divide by 57.3.
1 degree = 0.01745329252 radians
How to convert degrees to radians
rad = ° × 0.01745329252
To convert degrees to radians, multiply the number of degrees by 0.01745329252.
Example: 42 ° to rad
- Start with the value in degrees: 42 °.
- Multiply by 0.01745329252: 42 × 0.01745329252 = 0.7330382858.
- Result: 42 degrees = 0.7330382858 radians.
Going the other way, 1 radian = 57.2957795131 degrees, so to convert radians back to degrees you divide by the same number. See radians to degrees.
Where the conversion factor comes from
A full circle is 360 degrees or 2π radians, so π rad = 180°, 1 rad = 180/π ≈ 57.2958° and 1° = π/180 ≈ 0.0174533 rad. A radian is the angle whose arc length equals the radius, which is why calculus and physics formulas use radians.
Mental math: ° to rad in your head
Divide by 57.3. Common angles: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 360° = 2π.
When you need to convert degrees to radians
- Programming (sin, cos and tan functions use radians).
- Physics, calculus and engineering.
Common mistakes
- Passing degrees to Math.sin() or sin() in code, which expect radians.
- Leaving a calculator in the wrong angle mode.
Everyday degrees in radians
| Example | Degrees | Radians |
|---|---|---|
| 30° | 30 ° | 0.5236 rad |
| 45° | 45 ° | 0.7854 rad |
| 60° | 60 ° | 1.0472 rad |
| 90° | 90 ° | 1.5708 rad |
| 180° | 180 ° | 3.1416 rad |
| 360° | 360 ° | 6.2832 rad |
Degrees to radians conversion table
| Degrees (°) | Radians (rad) |
|---|---|
| 0.1 ° | 0.001745329252 rad |
| 0.2 ° | 0.003490658504 rad |
| 0.3 ° | 0.005235987756 rad |
| 0.4 ° | 0.006981317008 rad |
| 0.5 ° | 0.00872664626 rad |
| 0.6 ° | 0.01047197551 rad |
| 0.7 ° | 0.01221730476 rad |
| 0.8 ° | 0.01396263402 rad |
| 0.9 ° | 0.01570796327 rad |
| 1 ° | 0.01745329252 rad |
| 1.5 ° | 0.02617993878 rad |
| 2 ° | 0.03490658504 rad |
| 2.5 ° | 0.0436332313 rad |
| 3 ° | 0.05235987756 rad |
| 3.5 ° | 0.06108652382 rad |
| 4 ° | 0.06981317008 rad |
| 4.5 ° | 0.07853981634 rad |
| 5 ° | 0.0872664626 rad |
| 6 ° | 0.1047197551 rad |
| 7 ° | 0.1221730476 rad |
| 7.5 ° | 0.1308996939 rad |
| 8 ° | 0.1396263402 rad |
| 9 ° | 0.1570796327 rad |
| 10 ° | 0.1745329252 rad |
| 11 ° | 0.1919862177 rad |
| 12 ° | 0.2094395102 rad |
| 13 ° | 0.2268928028 rad |
| 14 ° | 0.2443460953 rad |
| 15 ° | 0.2617993878 rad |
| 16 ° | 0.2792526803 rad |
| 17 ° | 0.2967059728 rad |
| 18 ° | 0.3141592654 rad |
| 19 ° | 0.3316125579 rad |
| 20 ° | 0.3490658504 rad |
| 21 ° | 0.3665191429 rad |
| 22 ° | 0.3839724354 rad |
| 23 ° | 0.401425728 rad |
| 24 ° | 0.4188790205 rad |
| 25 ° | 0.436332313 rad |
| 26 ° | 0.4537856055 rad |
More ° to rad values
- 27 °
- 28 °
- 29 °
- 30 °
- 31 °
- 32 °
- 33 °
- 34 °
- 35 °
- 36 °
- 37 °
- 38 °
- 39 °
- 40 °
- 41 °
- 42 °
- 43 °
- 44 °
- 45 °
- 46 °
- 47 °
- 48 °
- 49 °
- 50 °
- 51 °
- 52 °
- 53 °
- 54 °
- 55 °
- 56 °
- 57 °
- 58 °
- 59 °
- 60 °
- 61 °
- 62 °
- 63 °
- 64 °
- 65 °
- 66 °
- 67 °
- 68 °
- 69 °
- 70 °
- 71 °
- 72 °
- 73 °
- 74 °
- 75 °
- 76 °
- 77 °
- 78 °
- 79 °
- 80 °
- 81 °
- 82 °
- 83 °
- 84 °
- 85 °
- 86 °
- 87 °
- 88 °
- 89 °
- 90 °
- 91 °
- 92 °
- 93 °
- 94 °
- 95 °
- 96 °
- 97 °
- 98 °
- 99 °
- 100 °
- 110 °
- 120 °
- 130 °
- 140 °
- 150 °
- 160 °
- 170 °
- 180 °
- 190 °
- 200 °
- 210 °
- 220 °
- 230 °
- 240 °
- 250 °
- 260 °
- 270 °
- 280 °
- 290 °
- 300 °
- 310 °
- 320 °
- 330 °
- 340 °
- 350 °
- 360 °
- 370 °
- 380 °
- 390 °
- 400 °
- 410 °
- 420 °
- 430 °
- 440 °
- 450 °
- 460 °
- 470 °
- 480 °
- 490 °
- 500 °
- 600 °
- 700 °
- 800 °
- 900 °
- 1,000 °
- 1,200 °
- 1,500 °
- 2,000 °
- 2,500 °
- 3,000 °
- 4,000 °
- 5,000 °
- 10,000 °
What is a degree?
The degree is the most common unit of angle: a full rotation is 360 degrees and a right angle 90.
What is a radian?
The radian is the SI unit of angle: the angle at the center of a circle where the arc length equals the radius.
Convert degrees to other units
Convert other units to radians
Frequently asked questions
How many radians are in a degree?
One degree is 0.01745329252 radians.
How many degrees are in a radian?
One radian is 57.29577951 degrees.
What is the formula to convert degrees to radians?
rad = ° × 0.01745329252.
How many radians is 180 degrees?
π radians (3.14159).