Free Online Angle Converter

Free Online Angle Conversion Tool

Our comprehensive Angle Converter is an essential tool for students, engineers, mathematicians, surveyors, and anyone working with angular measurements. This powerful converter allows you to instantly convert between dozens of angle units including degrees, radians, gradians, minutes, seconds, revolutions, mils, and many more. Whether you're working on geometry problems, engineering calculations, navigation, or astronomy, this tool provides accurate conversions with real-time results.

How to Use This Angle Converter (Step-by-Step):

• Enter Value: Input the numerical angle value you want to convert in the "Angle Value" field
• Select Source Unit: Choose the unit of your input value from the dropdown menu (e.g., degrees, radians, minutes)
• View Results: Instantly see the converted values in all major angle units in the results panel
• Additional Actions: Use the buttons to copy results, swap units, or reset the converter for new calculations

Real-Life Application Examples:

For Mathematics & Education: Convert between degrees and radians when working with trigonometric functions. Sine, cosine, and tangent calculations often require angle conversions between these units.

For Engineering & Construction: Convert between degrees and gradians for precise angle measurements in mechanical drawings and construction plans. Many European countries use gradians in technical drawings.

For Navigation & Surveying: Convert between degrees, minutes, and seconds for geographic coordinates. Latitude and longitude are typically expressed in DMS (Degrees, Minutes, Seconds) format.

For Military & Ballistics: Convert between degrees and mils for artillery and targeting calculations. NATO mils are commonly used in military applications for angular measurements.

Common Angle Unit Definitions:

• Degree (°): 1/360 of a full circle, the most commonly used angle unit
• Radian (rad): The SI unit of angle, defined as the angle subtended by an arc equal in length to the radius
• Gradian (gon): 1/400 of a full circle, also known as grade or gon
• Minute (′): 1/60 of a degree, used for more precise measurements
• Second (″): 1/60 of a minute = 1/3600 of a degree, used for very precise measurements
• Revolution (turn): A complete 360° rotation, equivalent to one full circle
• Mil (NATO mil): 1/6400 of a circle, used in military and artillery applications

Who Should Use This Angle Converter?

• Students & Educators: Essential for mathematics, physics, and engineering classes dealing with trigonometry and geometry
• Engineers & Architects: Perfect for technical drawings, mechanical design, and construction calculations
• Surveyors & Cartographers: Ideal for geographic coordinate conversions and land measurement
• Astronomers & Navigators: Useful for celestial navigation and astronomical calculations
• Military Personnel: Valuable for artillery targeting and tactical calculations
• DIY Enthusiasts: Great for woodworking, metalworking, and home improvement projects

Frequently Asked Questions

What's the relationship between degrees and radians?
180 degrees equals π radians (approximately 3.14159 radians). This means 1 degree = π/180 radians and 1 radian = 180/π degrees (approximately 57.2958 degrees).

Why are there 400 gradians in a circle instead of 360?
The gradian system was developed during the French Revolution as part of the metric system. It uses base-10 divisions, making calculations easier: 100 gradians = right angle, 200 gradians = straight angle, 400 gradians = full circle.

How accurate are the conversions?
Our converter uses precise conversion factors with high precision calculations. For most scientific and engineering purposes, the accuracy is more than sufficient.

Can I convert negative angles or angles larger than 360°?
Yes, the converter handles all real number values, including negative angles and angles exceeding 360 degrees (which represent multiple rotations).

Is this tool free to use?
Yes, this is a completely free online tool with no registration required and no usage limits.

Angle Conversion Factors Reference:

For quick reference, here are some key conversion factors (based on 1 degree):

• 1 degree = 0.0174533 radians = 1.11111 gradians = 60 minutes = 3600 seconds
• 1 radian = 57.2958 degrees = 63.6620 gradians = 3437.75 minutes = 206265 seconds
• 1 gradian = 0.9 degrees = 0.015708 radians = 54 minutes = 3240 seconds
• 1 minute = 0.0166667 degrees = 0.000290888 radians = 0.0185185 gradians = 60 seconds
• 1 second = 0.000277778 degrees = 0.00000484814 radians = 0.000308642 gradians
• 1 revolution = 360 degrees = 6.28319 radians = 400 gradians = 21600 minutes
• 1 NATO mil = 0.05625 degrees = 0.000981748 radians = 0.0625 gradians

Common Angle Measurements in Practice:

• Right Angle: 90° = π/2 rad = 100 gon = 1 quadrant
• Straight Angle: 180° = π rad = 200 gon = 2 quadrants
• Full Circle: 360° = 2π rad = 400 gon = 4 quadrants
• Equilateral Triangle: 60° = π/3 rad = 66.6667 gon
• Square Corner: 45° = π/4 rad = 50 gon
• Compass Directions: N=0°, E=90°, S=180°, W=270°
• Clock Hands: 30° per hour, 6° per minute