Geometry Lab formula guide
Radians & degrees
To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π. A full turn is 360° = 2π radians, so 180° = π radians and 1 radian ≈ 57.296°.
radians = degrees × π / 180
| Use it to | Formula |
|---|---|
| Degrees → radians | radians = degrees × π / 180 |
| Radians → degrees | degrees = radians × 180 / π |
| One radian | 1 rad ≈ 57.296° |
Try it with your own numbers
Radians & degrees calculator
Two ways to describe the very same turn. Change a value and the diagram, result, and working update together.
Degrees, radians & turnsLIVE EXPLORATION
Change a value to see the connection
Your measurements
For π-based input, choose radians and enter a decimal, or use a preset below. Negative angles rotate clockwise.
Why it works
180° = π radians = ½ turn
The idea
A radian is the angle that spans an arc equal in length to the radius. A full circle has circumference 2πr, so a full turn is 2π radians. That same turn is 360°.
Degrees to radians chart
| Degrees | Radians (exact) | Radians (decimal) |
|---|---|---|
| 0° | 0 | 0 |
| 30° | π/6 | 0.524 |
| 45° | π/4 | 0.785 |
| 60° | π/3 | 1.047 |
| 90° | π/2 | 1.571 |
| 120° | 2π/3 | 2.094 |
| 135° | 3π/4 | 2.356 |
| 150° | 5π/6 | 2.618 |
| 180° | π | 3.142 |
| 210° | 7π/6 | 3.665 |
| 270° | 3π/2 | 4.712 |
| 360° | 2π | 6.283 |
Worked examples
1Convert 2 radians to degrees
- degrees = 2 × 180 / π.
- = 360 / π ≈ 114.59°.
Answer: 2 radians ≈ 114.59°.
2Convert 225° to radians
- radians = 225 × π / 180.
- Simplify 225/180 = 5/4.
Answer: 225° = 5π/4 ≈ 3.927 radians.
Common mistakes
- Check the angle mode when using a calculator. sin(30°) is ½, but sin(30 radians) is a different value. This lab’s triangle inputs use degrees.
Make the formula move.
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