Degrees to Radians
Type degrees and the radians come back as the exact fraction of π in lowest terms, with the decimal beside it: 30° is π/6, 150° is 5π/6 and 25° is 5π/36. This page opens on 30° in the degrees box, and the radians box can be typed in as well to go back the other way. The degrees box reads 90, 90°, -45.5, a fraction of a degree such as 1/2, and degrees, minutes and seconds such as 45°30'15". Under the tool is a degrees to radians chart: every 5° from 0° to 360°, the small angles, every multiple of 18° and the common angles past a full turn, each row worked out by the same code as the boxes. It runs in this tab, with no upload and no account.
degrees = radians × 180 / π, and radians = degrees × π / 180. The radians box takes a multiple of π, written 3pi/4, pi/2 or 2pi, the degrees box takes plain degrees or degrees, minutes and seconds written 45°30'15", and the other box follows as you type.
- Where it lands
- first quadrant
- Measured from zero
- 30° from the positive x-axis
- Angle type
- Acute: under a quarter turn
A unit circle with an angle of 30 degrees drawn from the positive x-axis. It lands in the first quadrant.
Worked examples
Each one is converted by the same code the boxes above use. Press Use to put it in the tool.
Degrees to radians chart
Every 5° from 0° to 360°, the small angles 1°, 2°, 3°, 6° and 12°, every multiple of 18° used for pentagons, and the common angles past a full turn. Each row is worked out by the same code as the boxes above. The exact column is the fraction of π in lowest terms, so 25° reads 5π/36; the decimal is rounded to 12 significant digits.
| Degrees | Radians, exact | Radians, decimal |
|---|---|---|
| 0° | 0 | 0 |
| 1° | π/180 | 0.0174532925199 |
| 2° | π/90 | 0.0349065850399 |
| 3° | π/60 | 0.0523598775598 |
| 5° | π/36 | 0.0872664625997 |
| 6° | π/30 | 0.10471975512 |
| 10° | π/18 | 0.174532925199 |
| 12° | π/15 | 0.209439510239 |
| 15° | π/12 | 0.261799387799 |
| 18° | π/10 | 0.314159265359 |
| 20° | π/9 | 0.349065850399 |
| 25° | 5π/36 | 0.436332312999 |
| 30° | π/6 | 0.523598775598 |
| 35° | 7π/36 | 0.610865238198 |
| 36° | π/5 | 0.628318530718 |
| 40° | 2π/9 | 0.698131700798 |
| 45° | π/4 | 0.785398163397 |
| 50° | 5π/18 | 0.872664625997 |
| 54° | 3π/10 | 0.942477796077 |
| 55° | 11π/36 | 0.959931088597 |
| 60° | π/3 | 1.0471975512 |
| 65° | 13π/36 | 1.1344640138 |
| 70° | 7π/18 | 1.2217304764 |
| 72° | 2π/5 | 1.25663706144 |
| 75° | 5π/12 | 1.308996939 |
| 80° | 4π/9 | 1.3962634016 |
| 85° | 17π/36 | 1.4835298642 |
| 90° | π/2 | 1.57079632679 |
| 95° | 19π/36 | 1.65806278939 |
| 100° | 5π/9 | 1.74532925199 |
| 105° | 7π/12 | 1.83259571459 |
| 108° | 3π/5 | 1.88495559215 |
| 110° | 11π/18 | 1.91986217719 |
| 115° | 23π/36 | 2.00712863979 |
| 120° | 2π/3 | 2.09439510239 |
| 125° | 25π/36 | 2.18166156499 |
| 126° | 7π/10 | 2.19911485751 |
| 130° | 13π/18 | 2.26892802759 |
| 135° | 3π/4 | 2.35619449019 |
| 140° | 7π/9 | 2.44346095279 |
| 144° | 4π/5 | 2.51327412287 |
| 145° | 29π/36 | 2.53072741539 |
| 150° | 5π/6 | 2.61799387799 |
| 155° | 31π/36 | 2.70526034059 |
| 160° | 8π/9 | 2.79252680319 |
| 162° | 9π/10 | 2.82743338823 |
| 165° | 11π/12 | 2.87979326579 |
| 170° | 17π/18 | 2.96705972839 |
| 175° | 35π/36 | 3.05432619099 |
| 180° | π | 3.14159265359 |
| 185° | 37π/36 | 3.22885911619 |
| 190° | 19π/18 | 3.31612557879 |
| 195° | 13π/12 | 3.40339204139 |
| 198° | 11π/10 | 3.45575191895 |
| 200° | 10π/9 | 3.49065850399 |
| 205° | 41π/36 | 3.57792496659 |
| 210° | 7π/6 | 3.66519142919 |
| 215° | 43π/36 | 3.75245789179 |
| 216° | 6π/5 | 3.76991118431 |
| 220° | 11π/9 | 3.83972435439 |
| 225° | 5π/4 | 3.92699081699 |
| 230° | 23π/18 | 4.01425727959 |
| 234° | 13π/10 | 4.08407044967 |
| 235° | 47π/36 | 4.10152374219 |
| 240° | 4π/3 | 4.18879020479 |
| 245° | 49π/36 | 4.27605666739 |
| 250° | 25π/18 | 4.36332312999 |
| 252° | 7π/5 | 4.39822971503 |
| 255° | 17π/12 | 4.45058959259 |
| 260° | 13π/9 | 4.53785605519 |
| 265° | 53π/36 | 4.62512251778 |
| 270° | 3π/2 | 4.71238898038 |
| 275° | 55π/36 | 4.79965544298 |
| 280° | 14π/9 | 4.88692190558 |
| 285° | 19π/12 | 4.97418836818 |
| 288° | 8π/5 | 5.02654824574 |
| 290° | 29π/18 | 5.06145483078 |
| 295° | 59π/36 | 5.14872129338 |
| 300° | 5π/3 | 5.23598775598 |
| 305° | 61π/36 | 5.32325421858 |
| 306° | 17π/10 | 5.3407075111 |
| 310° | 31π/18 | 5.41052068118 |
| 315° | 7π/4 | 5.49778714378 |
| 320° | 16π/9 | 5.58505360638 |
| 324° | 9π/5 | 5.65486677646 |
| 325° | 65π/36 | 5.67232006898 |
| 330° | 11π/6 | 5.75958653158 |
| 335° | 67π/36 | 5.84685299418 |
| 340° | 17π/9 | 5.93411945678 |
| 342° | 19π/10 | 5.96902604182 |
| 345° | 23π/12 | 6.02138591938 |
| 350° | 35π/18 | 6.10865238198 |
| 355° | 71π/36 | 6.19591884458 |
| 360° | 2π | 6.28318530718 |
| 390° | 13π/6 | 6.80678408278 |
| 405° | 9π/4 | 7.06858347058 |
| 420° | 7π/3 | 7.33038285838 |
| 450° | 5π/2 | 7.85398163397 |
| 480° | 8π/3 | 8.37758040957 |
| 510° | 17π/6 | 8.90117918517 |
| 540° | 3π | 9.42477796077 |
| 630° | 7π/2 | 10.9955742876 |
| 720° | 4π | 12.5663706144 |
Common questions
- What is the formula for degrees to radians?
- Radians = degrees × π / 180, so converting degrees to radians means multiplying by π/180, which is about 0.0174532925. 60° × π / 180 is π/3, or 1.0471975512 as a decimal. The factor comes from a half turn being both 180° and π radians. Multiplying by 180/π instead goes the other way, from radians back to degrees.
- How do I write degrees in terms of π?
- Put the degrees over 180, reduce the fraction, and write π on top. 150/180 reduces to 5/6, so 150° is 5π/6; 225/180 is 5/4, so 225° is 5π/4; 25/180 is 5/36, so 25° is 5π/36. No calculator is needed. The exact-form line under the tool does the same reduction for any number of degrees you type, decimals included: 22.5° is π/8 and 57° is 19π/60.
- Can I type degrees, minutes and seconds?
- Yes. Write the degree sign, then minutes with ' or ′ and seconds with " or ″: 45°30' is exactly 91π/360 radians, about 0.794124809657, and 45°30'15" is 10921π/43200. Minutes or seconds of 60 or more are refused with a note to carry them into the next unit. The Degrees, minutes, seconds reading shows any answer split the same way.
- What are 360°, 720° and other angles past a full turn in radians?
- A full turn is 2π, so 360° is 2π, 720° is 4π and 540° is 3π. An angle past a full turn keeps its own value: 450° is 5π/2, not π/2, though it ends at the same place. The unit circle beside the tool shows where it lands and counts the whole turns, so 450° reads as one turn forward plus 90°. The chart under the tool lists 390°, 405°, 420°, 450°, 480°, 510°, 540°, 630° and 720°.
Degrees and radians are related by an exact definition, so a multiple of π converts exactly and this page shows that fraction when there is one. The decimal beside it is a rounding: π radians is exactly 180°, but 3.14159 radians is not.