Angle Degrees to Radians Conversion Table
Angles in degrees, radians, turns, and π form are all ways of describing the same angle, as shown in the tables below. Each row represents a single angle expressed in different formats. An angle is fundamentally a rotation around a circle by a certain amount.
Engineers use angles daily to describe rotation, orientation, slope, motion, and direction. It is key to be familiar with all these formats as an engineer, so that when you come across them, you can easily recognise them.
Common Angles from 0° to 90°
| Angle (°) | Radians | Turns | Pi | Sine | Cosine | Tangent |
|---|---|---|---|---|---|---|
| 0° | 0.0000 | 0.0000 | 0 | 0.0000 | 1.0000 | 0.0000 |
| 5° | 0.0873 | 0.0139 | π/36 | 0.0872 | 0.9962 | 0.0875 |
| 10° | 0.1745 | 0.0278 | π/18 | 0.1736 | 0.9848 | 0.1763 |
| 15° | 0.2618 | 0.0417 | π/12 | 0.2588 | 0.9659 | 0.2679 |
| 20° | 0.3491 | 0.0556 | π/9 | 0.3420 | 0.9397 | 0.3640 |
| 25° | 0.4363 | 0.0694 | 5π/36 | 0.4226 | 0.9063 | 0.4663 |
| 30° | 0.5236 | 0.0833 | π/6 | 0.5000 | 0.8660 | 0.5774 |
| 35° | 0.6109 | 0.0972 | 7π/36 | 0.5736 | 0.8192 | 0.7002 |
| 40° | 0.6981 | 0.1111 | 2π/9 | 0.6428 | 0.7660 | 0.8391 |
| 45° | 0.7854 | 0.1250 | π/4 | 0.7071 | 0.7071 | 1.0000 |
| 50° | 0.8727 | 0.1389 | 5π/18 | 0.7660 | 0.6428 | 1.1918 |
| 55° | 0.9599 | 0.1528 | 11π/36 | 0.8192 | 0.5736 | 1.4281 |
| 60° | 1.0472 | 0.1667 | π/3 | 0.8660 | 0.5000 | 1.7321 |
| 65° | 1.1345 | 0.1806 | 13π/36 | 0.9063 | 0.4226 | 2.1445 |
| 70° | 1.2217 | 0.1944 | 7π/18 | 0.9397 | 0.3420 | 2.7475 |
| 75° | 1.3090 | 0.2083 | 5π/12 | 0.9659 | 0.2588 | 3.7321 |
| 80° | 1.3963 | 0.2222 | 4π/9 | 0.9848 | 0.1736 | 5.6713 |
| 85° | 1.4835 | 0.2361 | 17π/36 | 0.9962 | 0.0872 | 11.4301 |
| 90° | 1.5708 | 0.2500 | π/2 | 1.0000 | 0.0000 | ∞ |
Extended Angles from 0° to 360°
| Angle (°) | Radians | Turns | Pi | Sine | Cosine | Tangent |
|---|---|---|---|---|---|---|
| 0° | 0.0000 | 0.0000 | 0 | 0.0000 | 1.0000 | 0.0000 |
| 5° | 0.0873 | 0.0139 | π/36 | 0.0872 | 0.9962 | 0.0875 |
| 10° | 0.1745 | 0.0278 | π/18 | 0.1736 | 0.9848 | 0.1763 |
| 15° | 0.2618 | 0.0417 | π/12 | 0.2588 | 0.9659 | 0.2679 |
| 20° | 0.3491 | 0.0556 | π/9 | 0.3420 | 0.9397 | 0.3640 |
| 25° | 0.4363 | 0.0694 | 5π/36 | 0.4226 | 0.9063 | 0.4663 |
| 30° | 0.5236 | 0.0833 | π/6 | 0.5000 | 0.8660 | 0.5774 |
| 35° | 0.6109 | 0.0972 | 7π/36 | 0.5736 | 0.8192 | 0.7002 |
| 40° | 0.6981 | 0.1111 | 2π/9 | 0.6428 | 0.7660 | 0.8391 |
| 45° | 0.7854 | 0.1250 | π/4 | 0.7071 | 0.7071 | 1.0000 |
| 50° | 0.8727 | 0.1389 | 5π/18 | 0.7660 | 0.6428 | 1.1918 |
| 55° | 0.9599 | 0.1528 | 11π/36 | 0.8192 | 0.5736 | 1.4281 |
| 60° | 1.0472 | 0.1667 | π/3 | 0.8660 | 0.5000 | 1.7321 |
| 65° | 1.1345 | 0.1806 | 13π/36 | 0.9063 | 0.4226 | 2.1445 |
| 70° | 1.2217 | 0.1944 | 7π/18 | 0.9397 | 0.3420 | 2.7475 |
| 75° | 1.3090 | 0.2083 | 5π/12 | 0.9659 | 0.2588 | 3.7321 |
| 80° | 1.3963 | 0.2222 | 4π/9 | 0.9848 | 0.1736 | 5.6713 |
| 85° | 1.4835 | 0.2361 | 17π/36 | 0.9962 | 0.0872 | 11.4301 |
| 90° | 1.5708 | 0.2500 | π/2 | 1.0000 | 0.0000 | ∞ |
| 95° | 1.6581 | 0.2639 | 19π/36 | 0.9962 | -0.0872 | -11.4301 |
| 100° | 1.7453 | 0.2778 | 5π/9 | 0.9848 | -0.1736 | -5.6713 |
| 105° | 1.8326 | 0.2917 | 7π/12 | 0.9659 | -0.2588 | -3.7321 |
| 110° | 1.9199 | 0.3056 | 11π/18 | 0.9397 | -0.3420 | -2.7475 |
| 115° | 2.0071 | 0.3194 | 23π/36 | 0.9063 | -0.4226 | -2.1445 |
| 120° | 2.0944 | 0.3333 | 2π/3 | 0.8660 | -0.5000 | -1.7321 |
| 125° | 2.1817 | 0.3472 | 25π/36 | 0.8192 | -0.5736 | -1.4281 |
| 130° | 2.2689 | 0.3611 | 13π/18 | 0.7660 | -0.6428 | -1.1918 |
| 135° | 2.3562 | 0.3750 | 3π/4 | 0.7071 | -0.7071 | -1.0000 |
| 140° | 2.4435 | 0.3889 | 7π/9 | 0.6428 | -0.7660 | -0.8391 |
| 145° | 2.5307 | 0.4028 | 29π/36 | 0.5736 | -0.8192 | -0.7002 |
| 150° | 2.6180 | 0.4167 | 5π/6 | 0.5000 | -0.8660 | -0.5774 |
| 155° | 2.7053 | 0.4306 | 31π/36 | 0.4226 | -0.9063 | -0.4663 |
| 160° | 2.7925 | 0.4444 | 8π/9 | 0.3420 | -0.9397 | -0.3640 |
| 165° | 2.8798 | 0.4583 | 11π/12 | 0.2588 | -0.9659 | -0.2679 |
| 170° | 2.9671 | 0.4722 | 17π/18 | 0.1736 | -0.9848 | -0.1763 |
| 175° | 3.0543 | 0.4861 | 35π/36 | 0.0872 | -0.9962 | -0.0875 |
| 180° | 3.1416 | 0.5000 | π | 0.0000 | -1.0000 | -0.0000 |
| 185° | 3.2289 | 0.5139 | 37π/36 | -0.0872 | -0.9962 | 0.0875 |
| 190° | 3.3161 | 0.5278 | 19π/18 | -0.1736 | -0.9848 | 0.1763 |
| 195° | 3.4034 | 0.5417 | 13π/12 | -0.2588 | -0.9659 | 0.2679 |
| 200° | 3.4907 | 0.5556 | 10π/9 | -0.3420 | -0.9397 | 0.3640 |
| 205° | 3.5779 | 0.5694 | 41π/36 | -0.4226 | -0.9063 | 0.4663 |
| 210° | 3.6652 | 0.5833 | 7π/6 | -0.5000 | -0.8660 | 0.5774 |
| 215° | 3.7525 | 0.5972 | 43π/36 | -0.5736 | -0.8192 | 0.7002 |
| 220° | 3.8397 | 0.6111 | 11π/9 | -0.6428 | -0.7660 | 0.8391 |
| 225° | 3.9270 | 0.6250 | 5π/4 | -0.7071 | -0.7071 | 1.0000 |
| 230° | 4.0143 | 0.6389 | 23π/18 | -0.7660 | -0.6428 | 1.1918 |
| 235° | 4.1015 | 0.6528 | 47π/36 | -0.8192 | -0.5736 | 1.4281 |
| 240° | 4.1888 | 0.6667 | 4π/3 | -0.8660 | -0.5000 | 1.7321 |
| 245° | 4.2761 | 0.6806 | 49π/36 | -0.9063 | -0.4226 | 2.1445 |
| 250° | 4.3633 | 0.6944 | 25π/18 | -0.9397 | -0.3420 | 2.7475 |
| 255° | 4.4506 | 0.7083 | 17π/12 | -0.9659 | -0.2588 | 3.7321 |
| 260° | 4.5379 | 0.7222 | 13π/9 | -0.9848 | -0.1736 | 5.6713 |
| 265° | 4.6251 | 0.7361 | 53π/36 | -0.9962 | -0.0872 | 11.4301 |
| 270° | 4.7124 | 0.7500 | 3π/2 | -1.0000 | -0.0000 | ∞ |
| 275° | 4.7997 | 0.7639 | 55π/36 | -0.9962 | 0.0872 | -11.4301 |
| 280° | 4.8869 | 0.7778 | 14π/9 | -0.9848 | 0.1736 | -5.6713 |
| 285° | 4.9742 | 0.7917 | 19π/12 | -0.9659 | 0.2588 | -3.7321 |
| 290° | 5.0615 | 0.8056 | 29π/18 | -0.9397 | 0.3420 | -2.7475 |
| 295° | 5.1487 | 0.8194 | 59π/36 | -0.9063 | 0.4226 | -2.1445 |
| 300° | 5.2360 | 0.8333 | 5π/3 | -0.8660 | 0.5000 | -1.7321 |
| 305° | 5.3233 | 0.8472 | 61π/36 | -0.8192 | 0.5736 | -1.4281 |
| 310° | 5.4105 | 0.8611 | 31π/18 | -0.7660 | 0.6428 | -1.1918 |
| 315° | 5.4978 | 0.8750 | 7π/4 | -0.7071 | 0.7071 | -1.0000 |
| 320° | 5.5851 | 0.8889 | 16π/9 | -0.6428 | 0.7660 | -0.8391 |
| 325° | 5.6723 | 0.9028 | 65π/36 | -0.5736 | 0.8192 | -0.7002 |
| 330° | 5.7596 | 0.9167 | 11π/6 | -0.5000 | 0.8660 | -0.5774 |
| 335° | 5.8469 | 0.9306 | 67π/36 | -0.4226 | 0.9063 | -0.4663 |
| 340° | 5.9341 | 0.9444 | 17π/9 | -0.3420 | 0.9397 | -0.3640 |
| 345° | 6.0214 | 0.9583 | 23π/12 | -0.2588 | 0.9659 | -0.2679 |
| 350° | 6.1087 | 0.9722 | 35π/18 | -0.1736 | 0.9848 | -0.1763 |
| 355° | 6.1959 | 0.9861 | 71π/36 | -0.0872 | 0.9962 | -0.0875 |
| 360° | 6.2832 | 1.0000 | 2π | -0.0000 | 1.0000 | -0.0000 |
Definitions
Angles (°)
Measured in degrees, which divide a circle into 360 equal parts from its
center. The number 360 was chosen because it is highly divisible, making
it convenient for measurement and calculation.
Radians
Radians are the standard unit used for scientific and mathematical purposes
and are part of the International System of Units (SI). One radian is defined
as the angle subtended at the center of a circle by an arc whose length is
equal to the radius. Radians are commonly used in programming, physics, and
advanced mathematics.
Turns
A turn represents a fraction of a full rotation. One full turn equals 360°.
For example, 180° is 0.5 (½ turn), and 90° is 0.25 (¼ turn).
Pi (π)
The angle is expressed as a fraction of π, where π radians equals 180°. Therefore,
a full rotation of 360° is equal to 2π radians.
Sine, Cosine, and Tangent
These are the primary trigonometric functions. Sine represents the vertical
component of an angle on the unit circle, cosine represents the horizontal
component, and tangent represents the slope of the angle, calculated as sine
divided by cosine.