Angle Unit Conversion Calculator

The most common units for measuring angles are: 1) Degrees (°) - most widely used, ranges from 0° to 360°, 2) Radians (rad) - used in mathematics and physics, one complete circle is 2π radians, 3) Gradians (grad) - divides a circle into 400 parts, 4) Minutes and Seconds - subdivisions of degrees for precise measurements.

To convert between degrees and radians: 1) Degrees to Radians: multiply degrees by (π/180), 2) Radians to Degrees: multiply radians by (180/π). For example: 180° = π radians, 90° = π/2 radians, 360° = 2π radians.

Different angle measurements serve various purposes: 1) Degrees are intuitive for everyday use and navigation, 2) Radians are preferred in calculus and physics because they simplify many mathematical formulas, 3) Gradians are sometimes used in surveying, 4) Minutes and seconds provide precise measurements for astronomy and navigation.

The relationship between degrees and radians is based on the circle: 1) A complete circle is 360 degrees or 2π radians, 2) 180 degrees equals π radians, 3) 90 degrees equals π/2 radians, 4) 1 radian is approximately 57.2958 degrees. This relationship is fundamental in trigonometry and mathematics.