Degrees in Radians Calculator
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Reviewed by Calculator Editorial Team
Convert degrees to radians quickly and accurately with our online calculator. Learn the conversion formula, see practical examples, and understand when to use radians versus degrees.
Conversion Formula
The relationship between degrees and radians is defined by the formula:
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.
How to Use This Calculator
- Enter the angle in degrees in the input field.
- Click the "Calculate" button to convert the value to radians.
- View the result in the result panel below the calculator.
- Use the "Reset" button to clear the input and result.
The calculator will display the result with up to 10 decimal places for precision.
Examples
Example 1: 90 Degrees to Radians
Using the formula:
Calculation
Radians = 90 × (π / 180) ≈ 1.57079632679 radians
This is a quarter turn (90 degrees) in radians.
Example 2: 180 Degrees to Radians
Using the formula:
Calculation
Radians = 180 × (π / 180) ≈ 3.14159265359 radians
This is a half turn (180 degrees) in radians.
Example 3: 360 Degrees to Radians
Using the formula:
Calculation
Radians = 360 × (π / 180) ≈ 6.28318530718 radians
This is a full turn (360 degrees) in radians.
Degrees vs Radians
Degrees and radians are two different units for measuring angles. Here's how they compare:
- Degrees: A full circle is 360 degrees. This system is commonly used in everyday life and geometry.
- Radians: A full circle is 2π radians (approximately 6.283 radians). This system is more common in advanced mathematics, physics, and engineering.
Radians are often preferred in calculus and physics because they simplify many formulas, especially those involving trigonometric functions.
Common Angle Conversions
Here are some common angle conversions between degrees and radians:
| Degrees | Radians | Description |
|---|---|---|
| 0° | 0 | No rotation |
| 30° | π/6 ≈ 0.5236 | One sixth of a circle |
| 45° | π/4 ≈ 0.7854 | One eighth of a circle |
| 60° | π/3 ≈ 1.0472 | One third of a circle |
| 90° | π/2 ≈ 1.5708 | One quarter of a circle |
| 180° | π ≈ 3.1416 | One half of a circle |
| 270° | 3π/2 ≈ 4.7124 | Three quarters of a circle |
| 360° | 2π ≈ 6.2832 | One full circle |
Frequently Asked Questions
What is the difference between degrees and radians?
Degrees and radians are both units for measuring angles. A full circle is 360 degrees or 2π radians. Radians are based on the radius of a circle, while degrees are based on dividing a circle into 360 equal parts.
When should I use degrees instead of radians?
Degrees are typically used in everyday contexts, such as measuring angles in geometry or navigation. Radians are more common in advanced mathematics, physics, and engineering, where they simplify many formulas.
How do I convert radians to degrees?
To convert radians to degrees, use the formula: Degrees = Radians × (180 / π). This is the inverse of the degrees to radians conversion formula.
What is the value of π (pi) in radians?
π (pi) is approximately 3.141592653589793. In radians, π represents 180 degrees, which is half of a full circle.
Can I use this calculator for negative angles?
Yes, the calculator will work with negative angles. The conversion formula applies to both positive and negative angles.