Angle Converter

Transform angles between degrees, radians, and gradians with precision. Essential tool for engineering, mathematics, and navigation calculations.

About Angle Converter

Understanding Angular Measurement

Angular measurement quantifies rotation and direction in various fields, from navigation to mathematics. The mathematical community primarily uses radians, while degrees remain common in everyday applications. The relationship between these units stems from the fundamental properties of circles: one complete rotation equals 360 degrees, 2π radians, 400 gradians, or one turn. Each unit system offers advantages in specific contexts, which is why multiple systems persist in modern use.

Common Angular Units

Unit	Full Circle	Common Use
Degrees (°)	360°	General use
Radians	2π	Mathematics
Gradians	400	Engineering
Turns	1	Computer graphics

Precision Units

Arc Units

1° = 60 arcminutes
1′ = 60 arcseconds
1″ ≈ 0.000004848 radians
Used in astronomy

Military Units

1 circle = 6400 mils
1 mil ≈ 0.05625 degrees
Used in artillery
Based on milliradian

Applications

Navigation

Compass bearings (degrees)
GPS coordinates (dec. degrees)
Nautical navigation
Aviation headings

Science

Trigonometry (radians)
Physics calculations
Wave analysis
Orbital mechanics

Engineering

CAD design (degrees)
Surveying (gradians)
Mechanical systems
Robot kinematics

Astronomy

Celestial coordinates
Angular diameter
Stellar parallax
Telescope positioning

Frequently Asked Questions

Why are there so many different angle units?

Different fields developed their own units for practical reasons. Degrees are intuitive for everyday use, radians are natural for mathematics, gradians are useful in surveying, and military mils provide precise artillery calculations. Each unit system offers advantages in specific contexts.

What's the difference between arc minutes and minutes?

Arc minutes (arcmin) and arc seconds (arcsec) are units of angular measurement, while minutes and seconds typically refer to time. One degree equals 60 arc minutes, and one arc minute equals 60 arc seconds. These precise angular measurements are crucial in astronomy and navigation.

Which unit should I use for my calculations?

Use degrees for general purposes and navigation, radians for mathematical calculations and physics, gradians for surveying and engineering, and arc minutes/seconds for astronomy. Most scientific calculators and software expect angles in radians for trigonometric functions.

Learn More

NIST Angle Standards Angular Units Guide