Angle Converter - Convert Degrees, Radians, Gradians & More

Convert between different angle units instantly with our free online angle converter. Easily convert degrees, radians, gradians, mils, and more with accurate results and step-by-step explanations.

Enter the angle value you want to convert
Select the unit of your input value
Select the unit you want to convert to

How to Use the Angle Converter

  1. Enter the angle value you want to convert in the input field
  2. Select the unit of your input value from the "From Unit" dropdown
  3. Choose the target unit you want to convert to from the "To Unit" dropdown
  4. Click the "Convert" button to see the result
  5. View the complete conversion table showing the value in all supported units
  6. Use the "Reset" button to clear all fields and start over

Supported Angle Units

Degrees (°)

The most common unit for measuring angles. A full circle is 360 degrees.

Radians (rad)

Mathematical unit where a full circle equals 2π radians. Commonly used in calculus and physics.

Gradians (gon)

Also called gons, where a full circle is divided into 400 gradians. Used in surveying.

Mils

Military unit where a full circle equals 6400 mils. Used for artillery and range calculations.

Minutes/Seconds of Arc

Subdivisions of degrees. 1 degree = 60 minutes, 1 minute = 60 seconds.

Turns

One complete rotation. 1 turn = 360 degrees = 2π radians.

Conversion Formulas

From Degrees to Other Units:

  • Radians: radians = degrees × (π / 180)
  • Gradians: gradians = degrees × (10 / 9)
  • Mils: mils = degrees × (6400 / 360)
  • Minutes: minutes = degrees × 60
  • Seconds: seconds = degrees × 3600

From Radians to Other Units:

  • Degrees: degrees = radians × (180 / π)
  • Gradians: gradians = radians × (200 / π)
  • Mils: mils = radians × (3200 / π)

Common Use Cases

Mathematics & Physics

  • Trigonometric calculations
  • Calculus problems involving circular functions
  • Physics equations for rotational motion
  • Engineering calculations

Practical Applications

  • Navigation and GPS coordinates
  • Surveying and construction
  • Astronomy observations
  • Military and artillery calculations

Conversion Examples

Example 1: Convert 90° to radians

90° × (π / 180) = π/2 ≈ 1.5708 radians

Example 2: Convert π radians to degrees

π × (180 / π) = 180°

Example 3: Convert 100 gradians to degrees

100 × (9 / 10) = 90°

Frequently Asked Questions (FAQ)

How do I convert degrees to radians?

To convert degrees to radians, multiply the degree value by π/180. For example, 180° = π radians, and 90° = π/2 radians.

What is the difference between degrees and gradians?

Degrees divide a circle into 360 parts, while gradians (or gons) divide a circle into 400 parts. 1 degree equals 10/9 gradians.

What are mils in angle measurement?

Mils are angular measurement units used primarily in military applications. One mil is approximately 1/6400 of a circle, making it useful for range estimation and artillery calculations.

When should I use radians instead of degrees?

Radians are preferred in mathematical calculations, especially calculus, physics, and engineering, because they make many formulas simpler and more natural.

How accurate is this angle converter?

Our converter provides high precision results with up to 10 decimal places, suitable for most professional and academic applications.