Degrees to Radians Converter
Exact multiples of π where they exist, not just a decimal, because that is how the answer is usually written.
Enter a number.
The formula
degrees = radians × 180 / π
A full turn is 360 degrees or 2π radians, which is where the ratio comes from. A radian is the angle subtended by an arc equal in length to the radius, so the relationship is geometric rather than arbitrary.
Where the result is a neat multiple of π, this tool shows it that way. 90 degrees is π/2, not merely 1.5708, and the exact form is what a textbook or a proof expects.
Conversion table
| Degrees | Radians (exact) | Radians (decimal) | Gradians |
|---|---|---|---|
| 0° | 0 | 0.000000 | 0 |
| 15° | π/12 | 0.261799 | 16.6667 |
| 30° | π/6 | 0.523599 | 33.3333 |
| 45° | π/4 | 0.785398 | 50 |
| 60° | π/3 | 1.047198 | 66.6667 |
| 90° | π/2 | 1.570796 | 100 |
| 120° | 2π/3 | 2.094395 | 133.333 |
| 135° | 3π/4 | 2.356194 | 150 |
| 150° | 5π/6 | 2.617994 | 166.667 |
| 180° | π | 3.141593 | 200 |
| 270° | 3π/2 | 4.712389 | 300 |
| 360° | 2π | 6.283185 | 400 |
Common questions
What is 90 degrees in radians?
90 degrees is exactly π/2 radians, about 1.5708. A full turn is 2π radians and 360 degrees, so a quarter turn is π/2. This tool shows the exact multiple of π wherever one exists rather than only the decimal.
What is the formula?
Radians equal degrees multiplied by π and divided by 180. Going the other way, degrees equal radians multiplied by 180 and divided by π.
Why do calculators use radians?
Because the calculus of trigonometric functions is simpler in radians. The derivative of sine is cosine only when the angle is in radians, which is why programming languages and scientific calculators default to them.
What is a gradian?
A less common unit where a right angle is 100 gradians rather than 90 degrees. It appears mainly in some surveying contexts.
Related converters and guides
Sources
- The relationship between degrees and radians is definitional: a full turn is 360 degrees or 2π radians. There is no measured conversion factor to cite. The radian is the SI coherent unit for plane angle.