Degrees Calculator Angles

Convert between degrees, radians, and gradians with our free degrees calculator angles tool. This calculator helps you quickly convert angle measurements between different units used in mathematics, physics, and engineering.

What is a Degrees Calculator?

A degrees calculator is a tool that converts angle measurements between degrees, radians, and gradians. These are the three primary units used to measure angles in different fields of study.

Degrees are commonly used in everyday contexts and geometry, while radians are more common in calculus and advanced mathematics. Gradians, also known as gons, are used in some European countries and certain engineering applications.

How to Use This Calculator

Using our degrees calculator is simple:

Enter the angle value you want to convert in the input field.
Select the unit you're converting from in the "From" dropdown.
Select the unit you want to convert to in the "To" dropdown.
Click the "Calculate" button to see the result.
Use the "Reset" button to clear all fields and start over.

The calculator will display the converted value and provide a visual representation of the angle on a circle chart.

Conversion Formulas

Here are the formulas used to convert between different angle units:

Degrees to Radians

Radians = Degrees × (π / 180)

Radians to Degrees

Degrees = Radians × (180 / π)

Degrees to Gradians

Gradians = Degrees × (10 / 9)

Gradians to Degrees

Degrees = Gradians × (9 / 10)

Note

π (pi) is approximately equal to 3.141592653589793.

Common Angle Conversions

Here are some common angle conversions you might need:

Degrees	Radians	Gradians
0°	0 rad	0 gon
30°	0.5236 rad	33.333 gon
45°	0.7854 rad	50 gon
60°	1.0472 rad	66.667 gon
90°	1.5708 rad	100 gon
180°	3.1416 rad	200 gon
270°	4.7124 rad	300 gon
360°	6.2832 rad	400 gon

This table provides quick reference points for common angle conversions. You can use these values as a guide when working with angle measurements in different units.

Frequently Asked Questions

What is the difference between degrees and radians?

Degrees and radians are both units of measurement for angles, but they are based on different systems. A full circle is 360 degrees, but it's 2π radians. This means that 1 radian is approximately equal to 57.2958 degrees.

When should I use degrees versus radians?

Degrees are typically used in everyday contexts and geometry, while radians are more common in calculus and advanced mathematics. The choice between them often depends on the specific application and the conventions used in the field.

What are gradians used for?

Gradians, also known as gons, are used in some European countries and certain engineering applications. They are based on a system where a full circle is divided into 400 gradians, making them easier to work with in certain calculations.

Can I convert between degrees and radians using this calculator?

Yes, our degrees calculator can convert between degrees, radians, and gradians. Simply enter the angle value, select the units you're converting from and to, and click the "Calculate" button to see the result.