If a trigonometry calculation or a line of code produces a wildly wrong result, mixing up degrees and radians is usually why.
The exact formula
radians = degrees × (π/180), and degrees = radians × (180/π).
Why it's confusing — most languages default to radians
Trig functions in most languages — JavaScript's Math.sin(), Python's math.sin(), and so on — expect their argument in radians. Passing a degree value directly produces a completely different result, so always convert to radians first.
Memorizing common angles
0°, 30°, 45°, 60°, 90°, 180°, and 360° correspond to 0, π/6, π/4, π/3, π/2, π, and 2π radians respectively. Memorizing these makes trig calculations much faster.
Gradians exist too
Some surveying and engineering fields use gradians, which divide a right angle into 100 units (360° = 400 gradians). It's uncommon, but worth recognizing if it shows up on a drawing.
Conversion table
| Degrees | Radians |
|---|---|
| 30° | 0.524 |
| 45° | 0.785 |
| 90° | 1.571 |
| 180° | 3.1416 (π) |
Try it now
FastestUnitConverter's angle converter handles degrees and radians along with gradians, all at once.
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