360 Degrees Calculator

This 360 degrees calculator converts between degrees, radians, and gradians. It's useful for geometry, navigation, and engineering applications where full-circle measurements are needed.

What is 360 Degrees?

360 degrees represents a full circle in the plane geometry system. It's the standard unit for measuring angles in most Western countries. The degree is divided into 60 minutes, each minute into 60 seconds, creating a sexagesimal system.

In contrast, radians measure angles based on the radius of a circle, where 2π radians equals 360 degrees. Gradians divide the circle into 400 parts, with 100 gradians equal to 90 degrees.

Key fact: The 360-degree circle system was developed by the Babylonians around 2000 BCE and later adopted by the Greeks.

How to Use This Calculator

Enter a value in the input field and select the units you want to convert from and to. Click "Calculate" to see the result. The calculator will show the converted value and display a visual representation of the angle.

Example

Convert 180 degrees to radians:
180° × (π/180) = π radians ≈ 3.1416 radians

Formula

The conversion formulas are:

Degrees to Radians: angle_radians = angle_degrees × (π/180) Radians to Degrees: angle_degrees = angle_radians × (180/π) Degrees to Gradians: angle_gradians = angle_degrees × (10/9) Gradians to Degrees: angle_degrees = angle_gradians × (9/10)

Where π (pi) is approximately 3.141592653589793.

Examples

Here are some common angle conversions:

Degrees	Radians	Gradians
0°	0	0
45°	0.7854	50
90°	1.5708	100
180°	3.1416	200
270°	4.7124	300
360°	6.2832	400

FAQ

Why is a full circle 360 degrees?

The 360-degree circle system was developed by the Babylonians and Greeks. They divided the circle into 360 parts because 360 has many divisors, making it practical for calculations in astronomy and geometry.

What's the difference between degrees and radians?

Degrees are based on the sexagesimal system (divided into 60 parts), while radians are based on the radius of a circle. 2π radians equals 360 degrees, making the conversion factor π/180.

When would I use gradians instead of degrees?

Gradians are used in some European countries and in certain technical fields where the decimal system is preferred. They divide the circle into 400 parts, making calculations simpler for some applications.