Angle Converter

Angles live in several unit systems: degrees for everyday geometry, radians for mathematics and engineering, gradians for surveying, turns for rotation. Convert between all four with exact factors.

Results

Formula

Radians tie angle to circle geometry, which is why calculus uses them:
Radians = Degrees × π ÷ 180 · Degrees = Radians × 180 ÷ π · Full turn = 360° = 2π rad = 400 grad

How to use this calculator

  1. Enter the angle.
  2. Select the unit you have and the unit you need.
  3. Press Calculate.
Angle Converter — how the calculation works, illustratedr
Angle Converter — how the calculation works, illustrated

Worked example

Convert 1 radian to degrees.

  1. 1 × 180 ÷ π ≈ 57.2958.

Result: 1 radian is about 57.296 degrees.

Frequently asked questions

Why do mathematicians prefer radians?

In radians, the arc-length formula is just arc = r × angle, and the derivatives of sine and cosine are clean. Degrees introduce an ugly π/180 factor into all of that.

What is a gradian?

A gradian (or gon) divides a right angle into 100 parts, so a full turn is 400 gradians. It appears in surveying and some European instruments.

How many radians in a half circle?

Exactly π radians (180°). A quarter circle is π/2, a full circle 2π.

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