Converticious
Convert degrees to radians (and back) and print the table of special angles with their sine, cosine and tangent values. To go from degrees to radians, multiply by π/180; to go back, multiply by 180/π.
Converter: degrees to radians and back
° = rad
Sine, cosine and tangent of an angle of ° : sin = cos = tan =
Special angles: degrees, radians, sin, cos, tan
| Degrees | Radians | Radians (≈) | sin | cos | tan |
|---|---|---|---|---|---|
| 0° | 0 | 0 | 0 | 1 | 0 |
| 30° | π/6 | 0.5236 | 1/2 | √3/2 | √3/3 |
| 45° | π/4 | 0.7854 | √2/2 | √2/2 | 1 |
| 60° | π/3 | 1.0472 | √3/2 | 1/2 | √3 |
| 90° | π/2 | 1.5708 | 1 | 0 | undefined |
| 120° | 2π/3 | 2.0944 | √3/2 | −1/2 | −√3 |
| 135° | 3π/4 | 2.3562 | √2/2 | −√2/2 | −1 |
| 150° | 5π/6 | 2.618 | 1/2 | −√3/2 | −√3/3 |
| 180° | π | 3.1416 | 0 | −1 | 0 |
| 210° | 7π/6 | 3.6652 | −1/2 | −√3/2 | √3/3 |
| 225° | 5π/4 | 3.927 | −√2/2 | −√2/2 | 1 |
| 240° | 4π/3 | 4.1888 | −√3/2 | −1/2 | √3 |
| 270° | 3π/2 | 4.7124 | −1 | 0 | undefined |
| 300° | 5π/3 | 5.236 | −√3/2 | 1/2 | −√3 |
| 315° | 7π/4 | 5.4978 | −√2/2 | √2/2 | −1 |
| 330° | 11π/6 | 5.7596 | −1/2 | √3/2 | −√3/3 |
| 360° | 2π | 6.2832 | 0 | 1 | 0 |
The sin, cos and tan values are exact (with square roots). “undefined” means the tangent does not exist (division by zero).
Trigonometry table from 0° to 90° (decimal values)
Values rounded to 4 decimals, in steps of 5°.
| Angle | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 5° | 0.0873 | 0.0872 | 0.9962 | 0.0875 |
| 10° | 0.1745 | 0.1736 | 0.9848 | 0.1763 |
| 15° | 0.2618 | 0.2588 | 0.9659 | 0.2679 |
| 20° | 0.3491 | 0.342 | 0.9397 | 0.364 |
| 25° | 0.4363 | 0.4226 | 0.9063 | 0.4663 |
| 30° | 0.5236 | 0.5 | 0.866 | 0.5774 |
| 35° | 0.6109 | 0.5736 | 0.8192 | 0.7002 |
| 40° | 0.6981 | 0.6428 | 0.766 | 0.8391 |
| 45° | 0.7854 | 0.7071 | 0.7071 | 1 |
| 50° | 0.8727 | 0.766 | 0.6428 | 1.1918 |
| 55° | 0.9599 | 0.8192 | 0.5736 | 1.4281 |
| 60° | 1.0472 | 0.866 | 0.5 | 1.7321 |
| 65° | 1.1345 | 0.9063 | 0.4226 | 2.1445 |
| 70° | 1.2217 | 0.9397 | 0.342 | 2.7475 |
| 75° | 1.309 | 0.9659 | 0.2588 | 3.7321 |
| 80° | 1.3963 | 0.9848 | 0.1736 | 5.6713 |
| 85° | 1.4835 | 0.9962 | 0.0872 | 11.4301 |
| 90° | 1.5708 | 1 | 0 | undefined |
Radians to degrees
| Radians | Degrees |
|---|---|
| 0.1 rad | 5.7296° |
| 0.25 rad | 14.3239° |
| 0.5 rad | 28.6479° |
| 1 rad | 57.2958° |
| 1.5 rad | 85.9437° |
| 2 rad | 114.5916° |
| 3 rad | 171.8873° |
| 4 rad | 229.1831° |
| 5 rad | 286.4789° |
| 6 rad | 343.7747° |
Signs of sin, cos and tan by quadrant
| Quadrant | Angle | sin | cos | tan |
|---|---|---|---|---|
| I | 0° – 90° | + | + | + |
| II | 90° – 180° | + | − | − |
| III | 180° – 270° | − | − | + |
| IV | 270° – 360° | − | + | − |
Formulas and definitions
A full turn = 360° = 2π rad and a half turn = 180° = π rad. Degrees to radians: rad = ° × π/180. Radians to degrees: ° = rad × 180/π. So 1 rad ≈ 57.2958° and 1° ≈ 0.017453 rad. In a right triangle: sin = opposite / hypotenuse, cos = adjacent / hypotenuse and tan = opposite / adjacent (= sin / cos). Fundamental identity: sin²(x) + cos²(x) = 1.
Frequently asked questions
How do you convert degrees to radians? Multiply the degrees by π/180. Example: 90° = 90 × π/180 = π/2 rad ≈ 1.5708 rad.
How many degrees in a radian? 1 radian = 180/π ≈ 57.2958°.
What is π radians in degrees? π rad = 180° and 2π rad = 360° (a full turn).
What are sin 30° and cos 60°? sin 30° = 0.5 and cos 60° = 0.5.
What is tan 45°? tan 45° = 1, because sin 45° = cos 45° = √2/2.
Why is tan 90° undefined? Because tan = sin / cos and cos 90° = 0: division by zero is impossible.
Other conversion tables
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