📐 Angle Unit Converter - Convert between degrees, radians, and gradians
Professional angle unit converter for mathematics, engineering, and programming. Convert between degrees (°), radians (rad), and gradians (gon) with customizable precision, step-by-step calculations, and common angle references for academic and technical use.
Angle Conversion Results:
90° → Multiple Unit Conversions
Degrees to Radians, Gradians with precision
📊 Input Angle
Degrees
Original Value
Radians
π/2 radians
Gradians
Quarter Circle
🔢 Conversion Formulas
📋 Common Angle Reference
π/6 rad
π/4 rad
π/3 rad
π/2 rad
💡 Tip: 90° is a right angle, equal to π/2 radians or 100 gradians
How to Use This Angle Unit Converter - Convert between degrees, radians, and gradians
How to Use the Angle Unit Converter:
- Enter the angle value you want to convert in the input field
- Select the source unit (degrees, radians, or gradians) from the dropdown
- Choose your desired precision (number of decimal places) for results
- Optionally enable formula display to see conversion calculations
- Click "Convert Angles" to generate results for all three units
- Copy individual results or download the complete conversion report
Pro Tips: Use 6 decimal places for high precision mathematical work, enable formulas for educational purposes, and reference the common angles chart for quick verification. Perfect for trigonometry, engineering calculations, and programming tasks!
How It Works
Angle Unit Converter Technology:
Our converter uses precise mathematical algorithms for accurate angle conversions:
- Mathematical Precision: Uses JavaScript's Math.PI constant for exact radian calculations with IEEE 754 double precision
- Universal Conversion: Converts between degrees (360°), radians (2π), and gradians (400 gon) using standard mathematical formulas
- Formula Engine: Implements precise conversion ratios - degrees×(π/180) for radians, degrees×(10/9) for gradians
- Precision Control: Adjustable decimal places (0-10) with proper rounding to avoid floating-point errors
- Educational Display: Shows step-by-step calculations with mathematical notation and common angle references
Technical Note: All conversions maintain mathematical accuracy using standard conversion constants, with results validated against trigonometric identities for common angles like 30°, 45°, 60°, and 90°.
When You Might Need This
- • Mathematics Education - Students convert angles for trigonometry homework, geometry problems, and calculus exercises
- • Engineering Design - Engineers convert bearing angles, rotation measurements, and mechanical angles for technical drawings
- • Computer Programming - Developers convert angles for game development, graphics programming, and mathematical modeling
- • Surveying and Navigation - Land surveyors convert compass bearings, property boundaries, and GPS coordinates
- • Physics Calculations - Scientists convert angular measurements for circular motion, wave analysis, and rotational dynamics
- • Architecture Planning - Architects convert roof angles, staircase slopes, and structural inclinations for building design
- • Astronomy Research - Astronomers convert celestial coordinates, telescope pointing angles, and orbital parameters
- • Manufacturing Quality Control - Technicians convert cutting angles, drill bit inclinations, and assembly orientations
- • Geographic Information Systems - GIS specialists convert map projections, coordinate systems, and directional bearings
- • Robotics Programming - Engineers convert servo motor angles, robotic arm positions, and automated movement sequences
Frequently Asked Questions
What's the difference between degrees, radians, and gradians?
Degrees divide a circle into 360 equal parts (most common), radians use the mathematical relationship where 2π radians = 360°, and gradians (or gons) divide a circle into 400 parts. Radians are standard in mathematics and programming, while gradians are used in surveying.
How accurate are the angle conversions?
Our converter uses JavaScript's native Math.PI constant and IEEE 754 double-precision arithmetic, providing accuracy up to 15-17 significant digits. Results are rounded to your specified decimal places to prevent floating-point display errors while maintaining mathematical precision.
Why would I use radians instead of degrees?
Radians are the natural unit for mathematical calculations because they create direct relationships in calculus, trigonometry, and physics. Many programming languages and scientific calculations default to radians, making conversion essential for accurate results.
What are some common angle conversions I should know?
Key conversions: 30° = π/6 rad ≈ 0.524 rad, 45° = π/4 rad ≈ 0.785 rad, 60° = π/3 rad ≈ 1.047 rad, 90° = π/2 rad ≈ 1.571 rad, 180° = π rad ≈ 3.142 rad, 360° = 2π rad ≈ 6.283 rad. These appear frequently in trigonometry and engineering.
Can I convert negative angles or angles greater than 360°?
Yes! Our converter handles negative angles and angles greater than 360°. While the mathematical conversions are exact, remember that angles are often normalized (reduced to 0-360° range) in practical applications, though the converter shows the direct conversion result.