Angle calculators

Professional online calculators for all types of angle calculations

Angle format conversion

Degrees to Decimal (DMS ↔ DD) Popular
Conversion between degrees-minutes-seconds and decimal degrees
Degrees to Percent (tan(α) × 100%) Popular
Slope measurement: conversion between angle and percent slope

Triangle angle calculations

Angles from side lengths (Law of cosines)
Calculate all angles of a triangle from the three side lengths

Polygon angle calculations

Angle sum of polygons ((n-2) × 180°)
Calculate angle sums and individual angles for all polygons

About Angle Calculations

Angle calculations form the heart of trigonometry and find practical application in:

  • Surveying - GPS, triangulation
  • Navigation - Maritime, aviation
  • Construction - Roof slopes, gradients
  • Engineering - Gear design, robotics
  • Astronomy - Position determination
  • Computer Graphics - 3D rendering
Fundamental Angle Formulas
Angle Format Conversion
Decimal: DD.dddd°
DMS: DD°MM'SS"
Slope Measurement
Percent: tan(α) × 100%
Angle: α = arctan(slope/100)
Law of Cosines
α = arccos((b²+c²-a²)/(2bc))
Triangle angles from sides
Polygon Angle Sum
Sum: (n-2) × 180°
Individual: (n-2) × 180°/n
Tip: The 360° system originates from Babylonian astronomy. For precise GPS calculations, the decimal degree system is mostly used.

Practical Application Examples

Surveying & Navigation
  • GPS Coordinates: Position determination
  • Land Surveying: Triangulation methods
  • Maritime: Course calculations
Construction & Architecture
  • Roof Slopes: Gradient calculations
  • Road Construction: Route planning
  • Structural Engineering: Construction angles
Engineering & Technology
  • Mechanical Engineering: Gear design
  • Robotics: Motion control
  • Optics: Laser applications
Digital Applications
  • Computer Graphics: 3D rendering
  • Gaming: Camera angles
  • CAD Software: Technical drawings
Quick Reference
360°
Full Circle
180°
Semicircle
90°
Right Angle
tan(α)×100
Slope %
DD°MM'SS"
Degrees-Minutes-Seconds
Angle Systems

Degrees (°): 360° = full circle, most common system in practice.

Radians (rad): 2π rad = full circle, mathematical system.

Gradians (gon): 400 gon = full circle, surveying system.

Historical Context

Babylonians: Developed the 360° system based on astronomical observations.

Hipparchus: Created the first trigonometric tables (190-120 BC).

Modern Era: GPS and satellite navigation are based on precise angle calculations.

Key Applications
GPS Navigation: Position accuracy Critical
Construction: Slope calculations Common
Robotics: Movement control Advanced
3D Graphics: Rendering Digital