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LunaCalc

Conversion

Angle Conversion Calculator

Convert between degrees, radians and gradians.

Calculator
°
rad
gon

About this calculator

This angle converter translates between degrees, radians, and gradians instantly in both directions.

Formula notes

radians = degrees × π / 180; gradians = degrees × 10/9; a full circle is 360° = 2π rad = 400 gon.

Worked examples

  1. Example: 180° = π ≈ 3.142 rad = 200 gradians, as the default conversion shows.
  2. An angle of 150 degrees equals 5pi/6 radians and approximately 166.667 gradians.

How to use it

  1. Enter the angle in any one unit.
  2. Read the other units filled in automatically.
  3. Use radians for calculus and gradians for surveying.

Frequently asked questions

Why do formulas use radians instead of degrees?

Radian-based derivatives of sin and cos stay clean (d/dx sin x = cos x) without extra factors.

What is a gradian used for?

It divides a right angle into 100 parts, which some surveying and engineering fields prefer.

Limits and interpretation

  • The converter changes angular units but does not normalize direction into a preferred range such as 0 to 360 degrees.
  • Rounded decimal radians can hide exact pi-based values, so preserve symbolic forms when exact geometry matters.

References