Angle Converter

Convert between different units of angles - degrees, radians, gradians, turns, and more.

Result: 0.000000

What It Does

An Angle Converter is a mathematical tool for converting between different units of angular measurement. It converts between degrees (°), radians (rad), gradians (gon), turns (revolutions), arcminutes ('), arcseconds ("), and milliradians (mrad). This tool is essential for mathematics, physics, engineering, navigation, programming, and any application involving angles. Degrees are the most common unit for everyday use (360° in a circle), radians are standard in mathematics and physics (2π radians in a circle), gradians divide a circle into 400 units, and arcminutes/arcseconds provide high precision for astronomy and surveying. Perfect for converting between mathematical and practical angle measurements, understanding trigonometric functions, and working with angular data in different formats.

Key Features:

  • Convert between 7 common angle units (degrees, radians, gradians, turns, arcminutes, arcseconds, milliradians)
  • Real-time conversion as you type - instant results
  • Swap button to quickly reverse conversion direction
  • High precision results with up to 6 decimal places
  • Mathematical units: radians for trigonometry and calculus
  • Practical units: degrees for everyday measurements
  • Precision units: arcminutes and arcseconds for astronomy
  • Mobile-responsive design for on-the-go conversions

How To Use

Convert angles instantly between different units. Perfect for mathematics, physics, programming, and angular measurements.

1

Enter the Angle Value

Type or paste the angle value you want to convert into the "Value" input field. You can enter whole numbers or decimals (e.g., 180, 3.14159, 0.5).

2

Select Source Unit

Choose the unit you're converting FROM using the "From" dropdown. Options include degrees, radians, gradians, turns, arcminutes, arcseconds, and milliradians.

3

Select Target Unit

Choose the unit you want to convert TO using the "To" dropdown. The result updates automatically as you make your selection.

4

View Result

See the converted angle value displayed prominently in the result box. The conversion happens in real-time as you type or change units.

5

Swap Units (Optional)

Click the swap button (⇄) to instantly reverse the conversion direction, swapping the "From" and "To" units without re-entering the value.

Pro Tips

  • •360 degrees = 2π radians = 400 gradians = 1 turn
  • •1 degree = 60 arcminutes = 3,600 arcseconds
  • •1 radian ≈ 57.2958 degrees
  • •Radians are used in mathematics and programming (JavaScript, Python, etc.)
  • •Degrees are used for everyday measurements and navigation
  • •Gradians divide a circle into 400 units (used in some surveying)
  • •Arcminutes and arcseconds provide high precision for astronomy

Benefits

Mathematics: Convert between degrees and radians for trigonometry
Programming: Convert angles for code that uses radians
Navigation: Convert angular measurements for navigation and surveying
Astronomy: Convert precise angles using arcminutes and arcseconds
Education: Learn angle relationships and unit conversions
Accuracy: Eliminate manual calculation errors in angle conversions
Time Saving: Instant conversions save time over manual calculations
Versatility: Handle everything from degrees to milliradians

Use Cases

Programming and Trigonometry

Convert angles between degrees and radians for programming. Most programming languages use radians for trigonometric functions, but humans think in degrees.

Convert 90 degrees to radians (1.5708 rad) for JavaScript Math.sin() function

Mathematics and Physics

Convert angles for mathematical calculations and physics problems. Radians are standard in calculus and physics, while degrees are more intuitive.

Convert π/2 radians to degrees (90°) for trigonometric calculations

Navigation and Surveying

Convert angular measurements for navigation, surveying, and mapping. Different applications may use different angle units.

Convert 45 degrees to gradians (50 gon) for surveying applications

Astronomy

Convert precise angular measurements for astronomy. Celestial coordinates use degrees, arcminutes, and arcseconds.

Convert 1 degree to arcseconds (3,600 arcseconds) for astronomical measurements

Engineering and Design

Convert angles for engineering drawings and design specifications. Different industries may use different angle units.

Convert 30 degrees to radians (0.5236 rad) for CAD software input

Frequently Asked Questions

1 What is the relationship between degrees and radians?
A full circle contains 360 degrees or 2π radians. Therefore, 180 degrees = π radians, 90 degrees = π/2 radians, and 1 degree = π/180 radians ≈ 0.017453 radians. Conversely, 1 radian = 180/π degrees ≈ 57.2958 degrees. Radians are preferred in mathematics because they simplify calculus and trigonometry formulas. For example, the derivative of sin(x) is cos(x) only when x is in radians.
2 Why do programming languages use radians?
Programming languages use radians because they're the standard in mathematics and make trigonometric calculations more efficient. Functions like Math.sin(), Math.cos(), and Math.tan() in JavaScript, Python, and other languages expect angles in radians. To use degrees, you must convert: radians = degrees × (π/180). Many languages provide conversion functions, but understanding the conversion helps when working with angles in code.
3 What are gradians and when are they used?
Gradians (also called "gons") divide a circle into 400 units instead of 360 degrees. One gradian = 0.9 degrees. Gradians are used in some surveying, navigation, and engineering applications, particularly in Europe. They offer the advantage of dividing a right angle (90°) into 100 gradians, making some calculations easier. However, degrees and radians are more commonly used in most applications.
4 What are arcminutes and arcseconds?
Arcminutes and arcseconds are subdivisions of degrees for high-precision angular measurements. One degree = 60 arcminutes ('), and one arcminute = 60 arcseconds ("). So one degree = 3,600 arcseconds. These units are commonly used in astronomy (celestial coordinates), navigation (latitude/longitude precision), and surveying. For example, the apparent size of the Moon is about 30 arcminutes, and GPS coordinates can be precise to arcseconds.
5 How do I convert degrees to radians manually?
To convert degrees to radians, multiply by π/180 (approximately 0.017453). For example, 90° × (π/180) = π/2 radians ≈ 1.5708 radians. To convert radians to degrees, multiply by 180/π (approximately 57.2958). For example, π/2 radians × (180/π) = 90°. The converter handles these calculations automatically with high precision.
6 What is a milliradian?
A milliradian (mrad) is one-thousandth of a radian (0.001 radians). One milliradian ≈ 0.0573 degrees or 3.44 arcminutes. Milliradians are used in military applications (for range estimation and targeting), optics (for angular measurements in scopes), and some engineering applications. They provide a convenient way to express small angles in radians without using decimals.

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