📐 Angle Unit Converter

Convert between degrees, radians, gradians, minutes, seconds, turns, and more angle units. Professional tool for math, navigation, and engineering.

Converter
Common Units
Formulas
Examples
Guide

Angle Converter

Common Angle Units

Degree
°

Most common angle unit. 360° = full circle

Radian
rad

SI unit for angles. 2π rad = full circle

Gradian
gon

400 gon = full circle. Used in surveying

Arc Minute
'

1/60 of a degree. Used in navigation

Arc Second
"

1/3600 of a degree. Precise measurements

Turn
rev

Full rotation. 1 turn = 360°

Mil
mil

Military unit. 6400 mils = full circle

Point
pt

Compass points. 32 points = full circle

🎯 Circle Reference
• Full circle: 360° = 2π rad = 400 gon
• Right angle: 90° = π/2 rad = 100 gon
• Straight angle: 180° = π rad = 200 gon
📐 Common Angles
• 0°: Starting position
• 30°: π/6 rad, 33.33 gon
• 45°: π/4 rad, 50 gon
• 60°: π/3 rad, 66.67 gon
• 90°: π/2 rad, 100 gon
🧭 Navigation Units
• Degrees: Standard navigation
• Minutes/Seconds: GPS coordinates
• Mils: Military targeting
• Points: Maritime compass
📊 Mathematical Context
Radians are the natural unit for calculus and trigonometry. They relate arc length directly to radius.
🌍 Real-World Usage
Degrees for general use, radians for math/physics, gradians for surveying, mils for military.
⚖️ Conversion Key
All angle conversions are based on the fact that a full circle equals 360°, 2π rad, or 400 gon.

Angle Conversion Formulas

Degree Conversions
rad = deg × π / 180
gon = deg × 10 / 9
turn = deg / 360
Radian Conversions
deg = rad × 180 / π
gon = rad × 200 / π
turn = rad / (2π)
Gradian Conversions
deg = gon × 9 / 10
rad = gon × π / 200
turn = gon / 400
Minute/Second Units
1° = 60 arc minutes
1' = 60 arc seconds
1° = 3600 arc seconds
Military & Navigation
1 mil = 360° / 6400
1 point = 360° / 32
1 turn = 1 revolution
Key Constants
π ≈ 3.14159
180° = π radians
1 rad ≈ 57.2958°

Quick Conversion Examples

90° → π/2 rad

Right Angle

180° → π rad

Straight Angle

360° → 2π rad

Full Circle

1 rad → 57.3°

Natural Unit

100 gon → 90°

Right Angle

1 turn → 360°

Full Rotation

45° → 50 gon

Half Right Angle

60' → 1°

Arc Minutes

How to Use This Angle Converter

Step 1: Enter Angle Value

Type the angle measurement you want to convert in the "From Angle" field.

Step 2: Select Source Unit

Choose the original angle unit from the dropdown (degrees, radians, gradians, etc.).

Step 3: Choose Target Unit

Select the unit you want to convert to from the "To Unit" dropdown.

Step 4: View Result

The converted value will appear automatically in the "To Angle" field.

Step 5: Use Tools

Use the swap button (⇄) to reverse conversion, or copy/round the result as needed.

🎯 Conversion Tips
• Use radians for calculus and trigonometry
• Use degrees for general measurements
• Use gradians for surveying applications
• Use mils for military and artillery calculations
📱 Applications
• Navigation: degrees, minutes, seconds
• Mathematics: radians for natural calculations
• Engineering: gradians for precise measurements
• Military: mils for targeting systems
⚡ Quick Reference
• 1 full circle = 360° = 2π rad = 400 gon
• 1° = 60' = 3600"
• 1 rad ≈ 57.2958°
• π ≈ 3.14159 radians = 180°