Angle Converter

Convert angles between degrees, radians, and gradians instantly. Enter a value in any unit to see conversions.

Convert from Degrees

Convert from Radians

Convert from Gradians

Conversion Formulas

Degrees to Radians

radians = degrees × (π / 180)

Example: 90° = 90 × (π / 180) = π/2 ≈ 1.571 rad

Radians to Degrees

degrees = radians × (180 / π)

Example: π rad = π × (180 / π) = 180°

Degrees to Gradians

gradians = degrees × (10 / 9)

Example: 90° = 90 × (10 / 9) = 100 gon

How to Use This Converter

1

Enter Value

Type a value in any of the three fields: degrees, radians, or gradians.

2

Instant Conversion

The other two fields automatically update with the converted values as you type.

3

View Results

All three angle measurements are displayed in the result box below the converter.

Common Angle Conversions

Right Angle

90 degrees

Radians: π/2 ≈ 1.571
Gradians: 100 gon

Straight Angle

180 degrees

Radians: π ≈ 3.142
Gradians: 200 gon

Full Circle

360 degrees

Radians: 2π ≈ 6.283
Gradians: 400 gon

Where Angle Conversion Is Used

Programming

Most programming languages use radians for trigonometric functions. Convert degrees to radians for calculations.

Mathematics

Calculus and advanced math often use radians. Convert between units for different mathematical contexts.

Navigation

GPS systems and navigation use various angle units. Convert for accurate positioning and direction.

Engineering

Different engineering fields use different angle units. Convert for technical drawings and calculations.

Frequently Asked Questions

What are radians?

Radians are a unit of angle measurement based on the radius of a circle. One radian is the angle created when the arc length equals the radius. A full circle is 2π radians (approximately 6.283).

What are gradians?

Gradians (also called gons) divide a circle into 400 equal parts. A right angle is 100 gradians. This system is used in some surveying and civil engineering applications.

Why use radians instead of degrees?

Radians are the natural unit for angles in mathematics and physics. They simplify many formulas and are required for calculus operations involving trigonometric functions.

How many degrees are in π radians?

π radians equals 180 degrees. This is a fundamental relationship: π rad = 180°. Therefore, 2π radians equals 360 degrees (a full circle).