angle Converter

Convert angle measurements instantly with our free online angle converter. Whether you need to convert degrees to radians, radians to degrees, or work with gradians and mils, our calculator provides accurate results for mathematics, engineering, navigation, and surveying applications.

Angle conversion is fundamental in trigonometry, physics, engineering design, and navigation systems. Our tool supports all common angle units including degrees (°), radians (rad), gradians (gon), mils, and turns for comprehensive angle calculations.

Common Angle Measurements:

• Degrees (°): The most common angle unit. A full circle = 360°. Used in geometry, navigation, and everyday measurements.
• Radians (rad): The SI unit for angles. A full circle = 2π radians. Essential for calculus, physics, and advanced mathematics.
• Gradians (gon): A full circle = 400 gradians. Used in surveying and some European engineering applications.
• Mils: Military angular measurement. A full circle = 6400 mils. Used in artillery, navigation, and surveying.
• Turns (revolutions): A full circle = 1 turn. Used in mechanical engineering and rotational applications.

Essential Angle Conversions:

• Degrees to Radians: radians = degrees × π/180
• Radians to Degrees: degrees = radians × 180/π
• Degrees to Gradians: gradians = degrees × 400/360
• Gradians to Degrees: degrees = gradians × 360/400
• Degrees to Mils: mils = degrees × 6400/360
• Radians to Mils: mils = radians × 6400/(2π)

Step-by-Step Conversion Examples:

Convert 90° to radians:

radians = 90 × π/180 = π/2 ≈ 1.5708 rad

Convert π/4 radians to degrees:

degrees = (π/4) × 180/π = 45°

Convert 45° to gradians:

gradians = 45 × 400/360 = 50 gon

Common Uses for Angle Conversion:

• Engineering & CAD: Converting between degree and radian measurements for mechanical design and CAD software compatibility.
• Navigation & GPS: Converting bearing angles between different coordinate systems and navigation standards.
• Mathematics & Physics: Converting between degrees and radians for trigonometric calculations and scientific computations.
• Surveying & Mapping: Converting between gradians and degrees for land surveying and cartographic applications.
• Military & Artillery: Converting between mils and degrees for tactical calculations and targeting systems.
• Astronomy: Converting celestial coordinates and angular measurements for astronomical observations.
• Robotics & Automation: Converting joint angles and rotational movements between different control systems.