Common Angles: Radians and Degrees Table
A complete reference table for converting angles between degrees and radians. Covers every 15° from 0° to 360° with exact radian expressions and 6-decimal approximations. Both units are used throughout trigonometry, calculus, and physics — this table lets you switch between them instantly.
Conversion Formulas
- Degrees to radians: radians = degrees × π / 180
- Radians to degrees: degrees = radians × 180 / π
- One full turn: 360° = 2π rad ≈ 6.283185 rad
- One radian: 1 rad = 180/π ≈ 57.2958°
Degrees and Radians (0° to 360°, every 15°)
Exact radian values expressed as fractions of π, plus decimal approximations rounded to 6 places.
| Degrees | Radians (exact) | Radians (decimal) | Turns |
|---|---|---|---|
| 0° | 0 | 0.000000 | 0 |
| 15° | π/12 | 0.261799 | 1/24 |
| 30° | π/6 | 0.523599 | 1/12 |
| 45° | π/4 | 0.785398 | 1/8 |
| 60° | π/3 | 1.047198 | 1/6 |
| 75° | 5π/12 | 1.308997 | 5/24 |
| 90° | π/2 | 1.570796 | 1/4 |
| 105° | 7π/12 | 1.832596 | 7/24 |
| 120° | 2π/3 | 2.094395 | 1/3 |
| 135° | 3π/4 | 2.356194 | 3/8 |
| 150° | 5π/6 | 2.617994 | 5/12 |
| 165° | 11π/12 | 2.879793 | 11/24 |
| 180° | π | 3.141593 | 1/2 |
| 195° | 13π/12 | 3.403392 | 13/24 |
| 210° | 7π/6 | 3.665191 | 7/12 |
| 225° | 5π/4 | 3.926991 | 5/8 |
| 240° | 4π/3 | 4.188790 | 2/3 |
| 255° | 17π/12 | 4.450590 | 17/24 |
| 270° | 3π/2 | 4.712389 | 3/4 |
| 285° | 19π/12 | 4.974188 | 19/24 |
| 300° | 5π/3 | 5.235988 | 5/6 |
| 315° | 7π/4 | 5.497787 | 7/8 |
| 330° | 11π/6 | 5.759587 | 11/12 |
| 345° | 23π/12 | 6.021386 | 23/24 |
| 360° | 2π | 6.283185 | 1 |
Key Radian Landmarks
A handful of radian values appear constantly in trigonometry and calculus. Memorizing these removes the need to convert during problem-solving.
| Radians | Degrees | Notes |
|---|---|---|
| π/6 | 30° | Smallest standard angle in a right triangle |
| π/4 | 45° | Isoceles right triangle angle |
| π/3 | 60° | Equilateral triangle angle |
| π/2 | 90° | Right angle; sin = 1, cos = 0 |
| π | 180° | Straight angle; sin = 0, cos = −1 |
| 3π/2 | 270° | sin = −1, cos = 0 |
| 2π | 360° | Full rotation; equivalent to 0 |
Quick Tips
- Multiples of π/6 (30°): denominators stay at 6 until simplified — π/6, 2π/6 = π/3, 3π/6 = π/2…
- Negative angles: rotate clockwise; −π/2 = 270° (or −90°).
- Angles beyond 360°: subtract 2π (or 360°) repeatedly to find the reference angle.
- Calculator mode: always check whether your calculator is set to DEG or RAD before computing.