Angle Conversion Calculator

Angles describe rotation or the separation between two directions. Different disciplines express that rotation with different units, even though the underlying geometry is unchanged. Degrees divide a full turn into 360 parts, radians describe an arc relative to its radius, gradians divide a turn into 400 parts, NATO angular mils divide it into 6,400 parts, and revolutions count complete turns. This calculator converts among all five systems through a common radian reference. Degrees are familiar in geometry, navigation, construction, and everyday descriptions. A right angle is 90 degrees, a straight angle is 180 degrees, and one complete rotation is 360 degrees. Radians are standard in calculus, physics, and programming because they connect angle directly to circular arc length. One full rotation is two pi radians, so 180 degrees equals pi radians and 90 degrees equals pi divided by two radians. Gradians, sometimes called gon, are used in some surveying and civil-engineering workflows. A right angle is exactly 100 gradians and a full turn is 400 gradians. Angular mils are useful for navigation and field calculations because one mil subtends approximately one unit at a distance of one thousand units. Several mil definitions exist; this tool uses the common NATO convention of 6,400 mils per revolution. Confirm the convention when working with equipment or documents that use another standard. The conversion process first multiplies the source value by its factor to obtain radians. It then divides by the destination unit's radian factor. This approach handles every unit pair consistently, including negative angles and rotations greater than one turn. Negative values indicate rotation in the opposite orientation, while values above one full turn remain valid and are not automatically normalized. Floating-point results involving pi are approximations, so a displayed decimal may be rounded. Preserve more digits for intermediate engineering or scientific work and round only at the final reporting stage. Use this calculator for trigonometry, bearings, robotics, computer graphics, machining, surveying, physics, and any task that requires a transparent comparison between angular unit systems.