Angle Converter Tool

Options
Quick Conversions
=
Conversion Formula:
degrees = radians × (180/π)
Unit Descriptions
Degrees (°)

A degree is a measurement of plane angle, representing 1/360 of a full rotation. Degrees are the most common unit for measuring angles in everyday applications.

Radians (rad)

A radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. There are 2π radians in a full circle.

Gradians (grad)

A gradian is a unit of angle equal to 1/400 of a full circle. Also known as gon, it's primarily used in surveying and some engineering applications.

Frequently Asked Questions

There are exactly 2π radians in a full circle (approximately 6.28318 radians). This comes from the definition of a radian as the angle subtended by an arc equal in length to the radius of the circle.

Gradians (also called gons) are primarily used in surveying, civil engineering, and some military applications. The gradian system divides a right angle into 100 gradians, making calculations involving right angles simpler in some cases.

Degrees are more intuitive for everyday use and visualization. Radians are more natural for mathematical calculations, especially in calculus and trigonometry, because they simplify many formulas. Most programming languages use radians for trigonometric functions.
Popular Conversions
  • 90° to radians π/2
  • 180° to radians π
  • 360° to radians 2π
  • 1 radian to degrees 57.30°
  • 100 gradians to degrees 90°
Common Angle Values
Degrees Radians Gradians
0° 0 0ᵍ
30° π/6 33.33ᵍ
45° π/4 50ᵍ
60° π/3 66.67ᵍ
90° π/2 100ᵍ
180° π 200ᵍ
360° 2π 400ᵍ