Theta / Angle Calculator

Convert angles between degrees, radians, and gradians. Visualize on the unit circle with trigonometric values.

Enter Angle

Conversions

Degrees
45
°
Radians
--
rad
Gradians
--
gon
sin(θ)--
cos(θ)--
tan(θ)--
Quadrant--
Reference Angle--

Conversion Formulas

radians = degrees x (pi / 180)

Understanding Angle Measurement

Angles can be measured in several different units. The three most common systems are degrees, radians, and gradians. Each serves different purposes in mathematics, science, and engineering.

Angle Unit Systems

Degrees

A full circle is divided into 360 equal parts. Each part is one degree. This is the most commonly used unit in everyday applications.

Full circle = 360°

Radians

The angle subtended by an arc equal in length to the radius. Preferred in calculus and physics.

Full circle = 2π rad

Gradians

A full circle is 400 gradians. Used in surveying and some European countries. A right angle is exactly 100 gradians.

Full circle = 400 gon

Conversion Formulas

  • Degrees to Radians: radians = degrees x (π / 180)
  • Degrees to Gradians: gradians = degrees x (10 / 9)
  • Radians to Degrees: degrees = radians x (180 / π)
  • Radians to Gradians: gradians = radians x (200 / π)
  • Gradians to Degrees: degrees = gradians x (9 / 10)
  • Gradians to Radians: radians = gradians x (π / 200)

The Unit Circle

The unit circle is a circle of radius 1 centered at the origin. It provides a visual way to understand trigonometric functions: for any angle θ, the coordinates of the point on the unit circle are (cos θ, sin θ). The unit circle is fundamental to trigonometry and is used extensively in physics and engineering.