Degrees to Radians Converter (° to rad)
Table of Contents
- How to Convert Degrees to Radians (° to rad)?
- Conversion Example: Degrees to Radians
- Degrees to Radians Conversion Table
- Frequently Asked Questions
How to Convert Degrees to Radians (° to rad)?
The conversion from degrees to radians is simple: 1 degree equals π/180 radians. To convert, multiply the number of degrees by π/180.
Formula
Conversion Example: Degrees to Radians
With these steps, you can easily convert degrees to radians. Below, we provide practical examples to ensure the procedure is clear and easy to follow.
Example 1
Example 1: Convert 180 degrees to radians.
Result: 180 degrees equals π radians.
Example 2
Example 2: Convert 45 degrees to radians.
Result: 45 degrees equals π/4 radians.
Degrees to radians with a non-round value: 50°
To convert 50°: 50 × π/180 = 5π/18 ≈ 0.8727 rad. As a reference, 1° is about 0.017453 rad.
How many radians is 45 degrees?
45° is one eighth of a full turn, which is π/4 ≈ 0.7854 rad. Other common angles: 30° = π/6, 60° = π/3, 90° = π/2 and 180° = π.
Mental shortcut: what fraction of 180° is it?
Divide the degrees by 180 and multiply the result by π. For example, 135° → 135/180 = 3/4 → 3π/4, and 270° → 270/180 = 3/2 → 3π/2.
Common mistakes
- Multiplying by 180/π instead of π/180. That is the inverse formula, used to go from radians to degrees.
- Giving only the decimal when the exact answer is requested. Many exercises expect the form with π, such as π/4.
- Forgetting to simplify the fraction: 90π/180 should be written as π/2.
Degrees to Radians Conversion Table
| Degrees | Radians | Decimal Value (rad) |
|---|---|---|
| 30° | π/6 rad | 0.5236 rad |
| 45° | π/4 rad | 0.7854 rad |
| 60° | π/3 rad | 1.0472 rad |
| 90° | π/2 rad | 1.5708 rad |
| 120° | 2π/3 rad | 2.0944 rad |
| 135° | 3π/4 rad | 2.3562 rad |
| 150° | 5π/6 rad | 2.6180 rad |
| 180° | π rad | 3.1416 rad |
| 210° | 7π/6 rad | 3.6652 rad |
| 225° | 5π/4 rad | 3.9269 rad |
| 240° | 4π/3 rad | 4.1888 rad |
| 270° | 3π/2 rad | 4.7124 rad |
| 300° | 5π/3 rad | 5.2360 rad |
| 315° | 7π/4 rad | 5.4978 rad |
| 330° | 11π/6 rad | 5.7596 rad |
| 360° | 2π rad | 6.2832 rad |
Frequently Asked Questions
How do I convert degrees to radians?
To convert degrees to radians, multiply the degrees by π and divide by 180. Formula: radians = degrees * (π / 180).
How many radians are in 180 degrees?
180 degrees equal π radians.
How many radians are in 90 degrees?
90 degrees equal π/2 radians.
What is a radian in terms of degrees?
1 radian is approximately equal to 57.2958 degrees.
How many radians are in 360 degrees?
360 degrees equal 2π radians.
How do I convert 45 degrees to radians?
To convert 45 degrees to radians, use the formula: 45 * (π / 180) = π/4 radians.
Cite this page
You can use the following citation format when referencing this calculator in academic or professional work.
Ramos, J., Degrees to radians converter (° to rad), Available at: https://calcuclub.com/convert/degrees-to-radians/ (Accessed: 11 October 2026).