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Angle Converter Tool

Convert between different units of angles and rotations instantly. Professional-grade conversion tool supporting degrees, radians, gradians, mils, arc minutes and more. Get accurate results with formulas and visual representation.

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Angle Conversion Result
1.5708
radians
Formula: 90° × (π/180) = 1.5708 rad
Quick Angle Conversions from 90 degrees

Most Popular Angle Conversions

Quick access to the most commonly used angle conversions for geometry, trigonometry, and engineering applications.

⟂ Right Angle (90°)

90° = π/2 ≈ 1.5708 rad
Most common geometric angle
Quarter turn rotation

📏 Straight Angle (180°)

180° = π ≈ 3.1416 rad
Half circle rotation
Supplementary angle reference

📐 One Radian

1 rad ≈ 57.2958°
Natural unit of angle
Mathematical standard

🔄 Full Circle

360° = 400 gon
Complete rotation
Engineering reference

Complete Guide to Angle Conversion

Everything you need to know about converting between different units of angles and rotations, from basic geometry to advanced applications.

📐 What is Angle Conversion?

Angle conversion is the process of changing angular measurements from one unit to another while maintaining the same rotational value. This is essential for mathematics, engineering, navigation, and scientific calculations.

  • Converts between different angular measurement systems
  • Maintains measurement accuracy and precision
  • Essential for geometry and trigonometry
  • Used in engineering, navigation, and astronomy

🌍 Angle Units Around the World

Understanding different angle units helps in choosing the right measurements for your specific needs and application.

// Global Angle Systems Mathematical: - Degrees: 360° circle (most common) - Radians: 2π circle (SI standard) - Gradians: 400 gon circle Navigation/Military: - Mils: 6400 mil circle - Arc units: minutes, seconds

🔧 Common Use Cases

Angle conversion is used across many fields where precise angular measurements are critical.

  • Geometry and trigonometry problems
  • Engineering design and CAD systems
  • Navigation and GPS calculations
  • Astronomy and celestial mechanics
  • Military targeting and artillery
  • Robotics and automation systems

⚡ How Our Angle Converter Works

Our angle converter uses precise mathematical formulas to ensure accurate conversions between any supported angular units.

// Conversion Process 1. Input validation and parsing 2. Convert to base unit (degrees) 3. Apply target unit conversion factor 4. Handle special mathematical constants (π) 5. Display formula for transparency // Example: 90° to radians 90° × (π/180) → π/2 → 1.5708 rad

🎯 Accuracy and Precision

Our converter maintains high accuracy using exact mathematical relationships and proper handling of irrational numbers.

  • Uses exact conversion factors (e.g., π/180 for deg→rad)
  • Maintains up to 10 decimal places internally
  • Handles π and other mathematical constants precisely
  • Smart rounding for practical applications

📱 Visual Angle Representation

Our converter includes visual feedback to help you understand the angular measurement being converted.

  • Interactive angle visualization
  • Real-time arc representation
  • Mobile-friendly touch interface
  • Responsive design for all devices

Frequently Asked Questions

How do you convert degrees to radians? +
To convert degrees to radians, multiply by π/180 (approximately 0.01745). For example, 90° × (π/180) = π/2 ≈ 1.5708 radians. This conversion factor comes from the fact that there are 2π radians in a complete 360° circle.
How do you convert radians to degrees? +
To convert radians to degrees, multiply by 180/π (approximately 57.2958). For example, 1 radian × (180/π) ≈ 57.3 degrees. One radian is approximately equal to 57 degrees, 17 minutes, and 44 seconds.
What are gradians and why are they used? +
Gradians (also called gons) divide a circle into 400 equal parts, making a right angle exactly 100 gradians. They're used in surveying and some European countries because decimal calculations are easier than with 360°, providing a more convenient base-10 system for engineering applications.
What are mils and why are they used in military applications? +
Mils (milliradians) are angular units where 6400 mils equal a full circle. They're used in military applications because 1 mil at 1000 meters equals approximately 1 meter, making range calculations and targeting much easier for artillery and navigation purposes.
What are arc minutes and arc seconds used for? +
Arc minutes (1/60 of a degree) and arc seconds (1/60 of an arc minute) are used for very precise angular measurements in astronomy, navigation, and surveying. They allow for extremely accurate positioning and measurement of celestial objects and geographic coordinates.
Why do mathematicians prefer radians over degrees? +
Radians are the natural unit for angles in mathematics because they simplify many formulas. In radians, the arc length equals the radius times the angle, derivatives of trigonometric functions have simpler forms, and many mathematical relationships become more elegant and intuitive.
How many degrees is π radians? +
π radians equals exactly 180 degrees. This is a fundamental relationship in mathematics: π rad = 180°, which means 2π rad = 360° (a full circle), and π/2 rad = 90° (a right angle). This relationship is the basis for all degree-radian conversions.
How accurate are the angle conversions? +
Our angle converter uses precise mathematical formulas with high precision (up to 10 decimal places). The results are accurate for all practical applications, from basic geometry to advanced engineering calculations. We handle π and other mathematical constants with full precision.
Can I convert negative angles or angles larger than 360°? +
Yes! Our converter handles negative angles and angles larger than a full rotation. This is useful for rotational mechanics, where objects can rotate multiple times or in reverse directions, and for mathematical functions that extend beyond a single revolution.
What's the difference between degrees and gradians? +
Degrees divide a circle into 360 equal parts, while gradians divide it into 400 parts. A right angle is 90° or 100 gradians. Gradians simplify decimal calculations since 100 gradians = 90 degrees, making them useful in surveying and engineering where base-10 calculations are preferred.
Do I need to install anything to use this angle converter? +
No installation required! Our angle converter is a web-based tool that works directly in your browser. It includes visual angle representation, is mobile-friendly, fast-loading, and works on all devices including smartphones, tablets, and computers without needing any downloads or plugins.

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