Angle Converter

Degrees ↔ radians ↔ gradians

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About Angle Converter

An angle converter that translates between degrees (°), radians (rad), gradians (gon), turns, arcminutes (′), and arcseconds (″). Features visual angle representation, common angle presets, and bidirectional conversion. All processing is client-side. Essential for trigonometry, surveying, navigation, astronomy, and engineering.

Angle Converter Features

  • 6 units
  • Bidirectional
  • Visual arc
  • Presets
  • DMS format
Degrees: full circle = 360°. Radians: full circle = 2π rad. Gradians: full circle = 400 gon. Turns: full circle = 1 turn. Conversions: 1° = π/180 rad = 10/9 gon. Each degree = 60 arcminutes, each arcminute = 60 arcseconds.

How to Use

Enter an angle in any unit:

  • Degrees: 0-360°
  • Radians: 0-2π
  • All: Convert simultaneously

Angle Units

  • Degree: 1/360 circle (navigation)
  • Radian: arc/radius ratio (math)
  • Gradian: 1/400 circle (surveying)
  • Turn: full revolutions

DMS Format

45.5° = 45° 30′ 0″. Multiply decimal by 60 for minutes, remainder by 60 for seconds. Used in GPS coordinates.

Step-by-Step Instructions

  1. 1Enter an angle value.
  2. 2Select the input unit.
  3. 3View all conversions.
  4. 4Try common presets.
  5. 5Check DMS format.

Angle Converter — Frequently Asked Questions

Why do mathematicians prefer radians?+

Radians make calculus formulas simpler: d/dx sin(x) = cos(x) only works in radians. In degrees, you'd need a π/180 factor everywhere.

What are gradians used for?+

Surveying! A right angle is exactly 100 gon, making percentage-based slope calculations intuitive. 1 gon = 1/400 of a circle.

How do I convert DMS to decimal degrees?+

45° 30′ 15″ = 45 + 30/60 + 15/3600 = 45.504167°. Reverse: take the decimal part, multiply by 60 for minutes, take that decimal part × 60 for seconds.

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