How to Convert Angles
Enter the angle value you want to convert in the Value field.
Select the unit you are converting from in the From dropdown.
Select the unit you want to convert to in the To dropdown.
Click Convert to see the result.
Precision and Rounding Behavior
Calculations maintain up to 10 significant figures and automatically switch to scientific notation for extremely large or small values, but trailing zeros are removed from the final display which may slightly reduce apparent precision for simple integers.
Understanding Angle Unit Groupings
Supported units are organized by their relationship to a full circle. Degrees, radians, and gradians form the core mathematical systems. Arcminutes and arcseconds provide fractional subdivisions for high-precision work. Turns represent full rotations, while military mils offer a specialized system for navigation and artillery calculations.
Angle Converter Tool Advantages and Limitations
Converting 45 Degrees to Radians
- Enter 45 in the Value field and select Degrees as the source unit.
- Select Radians as the target unit from the dropdown menu.
- The tool calculates 45 × (π/180) resulting in 0.7853981634 radians.
When to Use This Angle Converter
- Converting between degrees and radians for trigonometric functions in physics or calculus problems
- Translating surveying measurements from gradians to degrees for international project collaboration
- Calculating artillery aiming angles using military mils and converting them to degrees for standard maps
- Breaking down large angle values into arcminutes and arcseconds for precise astronomical observations
- Verifying architectural drafting angles when switching between software that uses different angular systems
Key Features
14 Angle Units
Convert instantly between degrees, radians, gradians, gon, arcminutes, arcseconds, turns, revolutions, circles, quadrants, right angles, sextants, signs, and angular mils for engineering and surveying tasks.
10-Significant Figure Precision
Maintain strict accuracy up to 10 significant figures with automatic scientific notation formatting for extreme values, ensuring reliable results for complex trigonometric calculations.
Client-Side Privacy
Process all conversions locally in your browser without sending data to any server, ensuring your calculations remain completely private and secure.
Privacy & Security
This tool runs entirely in your browser. No values are transmitted to any server, stored, or logged. Safe to use offline or with sensitive data.
Frequently Asked Questions
How accurate are the conversions?
Each unit is stored as its exact value relative to one degree. The formula is: result = value × (from unit in degrees) ÷ (to unit in degrees). Results are shown to 10 significant figures before trailing zeros are removed.
What is the difference between grad and gon?
They are the same unit. A gradian and a gon both equal 1/400 of a full circle (0.9 degrees). Both names are in common use, particularly in surveying and continental European engineering.
What is the difference between revolution, circle, and turn?
They are all equivalent names for one full rotation (360 degrees). Turn is the most common modern term; revolution and circle are used in older texts and specific engineering contexts.
What is an angular mil?
An angular mil is a unit used in military applications. One mil equals 1/6400 of a full circle, or approximately 0.05625 degrees. It is used for measuring small angles at distance, such as in artillery aiming.
How do I convert degrees to radians?
Multiply degrees by π/180 (approximately 0.01745329). For example, 90 degrees = 90 × π/180 = π/2 ≈ 1.5707963 radians. Select Degree and Radian in this tool to convert directly.