Angle to Degrees Calculator

Convert angles between radians and degrees with our angle to degrees calculator. This tool helps you quickly and accurately convert between these two common angular units used in mathematics, physics, and engineering.

How to Use This Calculator

Using our angle to degrees calculator is simple:

Enter the angle value in the input field.
Select the unit you're converting from (degrees or radians).
Click the "Calculate" button to see the converted value.
The result will appear in the result panel below the calculator.

The calculator will automatically convert the angle to the opposite unit. For example, if you enter 90 degrees, it will show the equivalent in radians, and vice versa.

Conversion Formulas

Angle conversion between degrees and radians is based on the relationship between these units:

Degrees to Radians

To convert degrees to radians, multiply the degree value by π/180.

Formula: radians = degrees × (π/180)

Radians to Degrees

To convert radians to degrees, multiply the radian value by 180/π.

Formula: degrees = radians × (180/π)

These formulas are fundamental in trigonometry and are used in various scientific and engineering calculations.

Common Angle Conversions

Here are some common angle conversions between degrees and radians:

Degrees	Radians
0°	0
30°	π/6 ≈ 0.5236
45°	π/4 ≈ 0.7854
60°	π/3 ≈ 1.0472
90°	π/2 ≈ 1.5708
180°	π ≈ 3.1416
270°	3π/2 ≈ 4.7124
360°	2π ≈ 6.2832

This table provides quick reference points for common angle conversions that you might encounter in various calculations.

Practical Applications

Angle conversion is essential in many fields:

Physics: Used in calculations involving circular motion, waves, and optics.
Engineering: Important for designing structures, calculating forces, and analyzing mechanical systems.
Navigation: Used in GPS systems and aviation to determine directions and distances.
Computer Graphics: Essential for rendering 3D models and animations.
Trigonometry: Fundamental for solving triangles and various geometric problems.

Understanding how to convert between degrees and radians is crucial for accurate calculations in these fields.

Frequently Asked Questions

What is the difference between degrees and radians?: Degrees and radians are two different units for measuring angles. A full circle is 360 degrees or 2π radians. Radians are the standard unit in many scientific calculations because they simplify trigonometric functions.
How do I convert degrees to radians?: To convert degrees to radians, multiply the degree value by π/180. For example, 90 degrees is 90 × (π/180) ≈ 1.5708 radians.
How do I convert radians to degrees?: To convert radians to degrees, multiply the radian value by 180/π. For example, π radians is π × (180/π) = 180 degrees.
When should I use degrees and when should I use radians?: Degrees are commonly used in everyday applications and navigation, while radians are preferred in scientific and engineering calculations because they simplify many mathematical operations.
What is the value of π used in these conversions?: The value of π (pi) used in these conversions is approximately 3.141592653589793. Most calculators and programming languages use this value for π.