Degrees To.radians Calculator
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Reviewed by Calculator Editorial Team
Convert degrees to radians with our free online calculator. Learn the conversion formula, see examples, and understand radians vs degrees.
How to Use This Calculator
Using our degrees to radians calculator is simple:
- Enter the angle in degrees in the input field
- Click the "Calculate" button
- View the result in radians
- Use the "Reset" button to clear the form
The calculator will show you the exact conversion and provide a visual representation of the angle in both units.
Conversion Formula
The relationship between degrees and radians is defined by the formula:
Degrees to Radians Formula
radians = degrees × (π / 180)
Where π (pi) is approximately 3.141592653589793.
This formula comes from the fact that a full circle is 360 degrees or 2π radians. Therefore, one degree equals π/180 radians.
Examples
Example 1: 90 Degrees to Radians
90° × (π / 180) = 1.5708 radians
This is a right angle, which is π/2 radians.
Example 2: 180 Degrees to Radians
180° × (π / 180) = 3.1416 radians
This is a straight angle, which is π radians.
Example 3: 360 Degrees to Radians
360° × (π / 180) = 6.2832 radians
This is a full circle, which is 2π radians.
Common Angle Conversions
Here's a table showing common angle conversions between degrees and radians:
| Degrees | Radians | Description |
|---|---|---|
| 0° | 0 | No angle |
| 30° | π/6 | Common angle in right triangles |
| 45° | π/4 | Diagonal of a square |
| 60° | π/3 | Common angle in equilateral triangles |
| 90° | π/2 | Right angle |
| 180° | π | Straight angle |
| 270° | 3π/2 | Three-quarters of a circle |
| 360° | 2π | Full circle |
FAQ
- Why do we need to convert degrees to radians?
- Many mathematical functions and formulas in physics, engineering, and computer graphics use radians instead of degrees. Radians provide a more natural unit for measuring angles in circular functions like sine and cosine.
- Is there a difference between degrees and radians?
- Yes, degrees and radians measure the same thing - angles - but they use different scales. A full circle is 360 degrees or 2π radians. This means 1 degree equals π/180 radians.
- Can I convert radians to degrees using this calculator?
- No, this calculator only converts degrees to radians. For the reverse conversion, you would use the formula: degrees = radians × (180 / π).
- What are some practical applications of degrees to radians conversion?
- Degrees to radians conversion is used in many fields including physics (angular momentum, rotational motion), engineering (mechanical systems), computer graphics (3D modeling), and navigation (GPS systems).
- Is there a simple way to remember the degrees to radians formula?
- You can remember that 180 degrees is equal to π radians, so to convert degrees to radians, you multiply by π and divide by 180. This gives you the formula: radians = degrees × (π / 180).