Degrees to Radians Converter
Convert degrees to radians.
Result
0
Radians
1 Degrees = 0.0174533 Radians
How to convert Degrees to Radians?
Degrees and radians are two common ways to measure angles. The relationship is:
- 180° = π radians
- 1° = π/180 radians
To convert Degrees to Radians, multiply degrees by π/180.
Formula: Radians = Degrees × (π ÷ 180)
Step-by-Step Calculation
- Take the number of Degrees you want to convert (e.g., 90).
- Multiply that value by π/180.
- The result is the value in Radians. (Example: 90 × π/180 = π/2 ≈ 1.5708 rad).
How to use this converter?
Enter degrees and instantly get radians—useful for trigonometry, calculus, engineering, and programming.
Common Degrees to Radians Conversions
Quick reference guide for common angles.
0° = 0 rad
30° = π/6 ≈ 0.5236 rad
45° = π/4 ≈ 0.7854 rad
60° = π/3 ≈ 1.0472 rad
90° = π/2 ≈ 1.5708 rad
120° = 2π/3 ≈ 2.0944 rad
180° = π ≈ 3.1416 rad
270° = 3π/2 ≈ 4.7124 rad
360° = 2π ≈ 6.2832 rad
15° = π/12 ≈ 0.2618 rad
Tip: Radians are natural for trig
Many math formulas (especially in calculus) work cleanly in radians. That’s why radians are widely used in advanced math and programming.
Common Degrees to Radians Conversions
| Degrees Input | Radians Result |
|---|---|
| 0° | 0 rad |
| 15° | 0.2618 rad |
| 30° | 0.5236 rad |
| 45° | 0.7854 rad |
| 60° | 1.0472 rad |
| 90° | 1.5708 rad |
| 120° | 2.0944 rad |
| 180° | 3.1416 rad |
| 270° | 4.7124 rad |
| 360° | 6.2832 rad |
Frequently Asked Questions
How do I convert degrees to radians?
Multiply degrees by π/180 to get radians.
How many radians is 180 degrees?
180° equals π radians.
How many radians is 90 degrees?
90° equals π/2 radians (≈ 1.5708).
Why use radians instead of degrees?
Radians simplify many trigonometry and calculus formulas, especially derivatives and integrals.
Is the factor 0.0174533 exact?
It’s a rounded decimal form of π/180. Using π/180 is the exact formula.