Convert Angle

Degrees divide a circle into 360 equal parts, while radians are based on the radius of the circle. One radian equals approximately 57.3 degrees. Radians are the standard unit in mathematics and physics because they create simpler formulas in calculus and trigonometry.

Gradians (also called gons) divide a circle into 400 equal parts, making a right angle exactly 100 gradians. They're primarily used in surveying and some European countries because they allow for easier decimal calculations when measuring land and construction angles.

To convert degrees to radians: multiply by π/180 (≈ 0.017453). To convert radians to degrees: multiply by 180/π (≈ 57.2958). Remember that π radians = 180 degrees exactly. Common conversions: 30° = π/6 rad, 45° = π/4 rad, 90° = π/2 rad.

Milliradians (mrad) are 1/1000 of a radian. Military forces use them because they provide a convenient relationship between angle and distance: at 1000 meters, 1 milliradian subtends approximately 1 meter. This makes range estimation and artillery calculations much easier.

A traditional compass rose has 32 points, making each point equal to 11.25 degrees. The main points are North, Northeast, East, Southeast, South, Southwest, West, and Northwest, with additional half-points and quarter-points for more precise navigation.

A turn (also called a revolution) is a complete rotation around a circle, equal to 360 degrees, 2π radians, or 400 gradians. It's useful in engineering and physics when describing rotational motion, gear ratios, or motor speeds.

Use degrees for everyday measurements and basic geometry, radians for calculus and advanced mathematics, gradians for surveying and construction, milliradians for military applications, and arcminutes/arcseconds for astronomy and precise navigation.