Angle - a geometric term describing a figure that consists of two rays with a common end point. These rays are referred to as sides. The units that are most commonly used to describe an angle are degrees and radians. All angle units are parts of a complete turn, for example a degree is 1/360th of a complete turn.
The radian is the angle subtended by an arc of a circle that has the same length as the circle's radius. The case of radian for the formula given earlier, a radian of n = 2π units is obtained by setting k = 2π/2π = 1. One turn is 2π radians, and one radian is 180/π degrees, or about 57.2958 degrees.
The degree, denoted by a small superscript circle (°), is 1/360 of a turn, so one turn is 360°. The case of degrees for the formula given earlier, a degree of n = 360° units is obtained by setting k = 360°/2π. One advantage of this old sexagesimal subunit is that many angles common in simple geometry are measured as a whole number of degrees.
The grad, also called grade, gradian, or gon, is 1/400 of a turn, so a right angle is 100 grads. It is a decimal subunit of the quadrant. A kilometre was historically defined as a centi-grad of arc along a great circle of the Earth, so the kilometer is the decimal analog to the sexagesimal nautical mile. The grad is used mostly in triangulation.
The minute of arc (or MOA, arcminute, or just minute) is 1/60 of a degree = 1/21,600 turn. It is denoted by a single prime ( ′ ). For example, 3° 30′ is equal to 3 × 60 + 30 = 210 minutes or 3 + 30/60 = 3.5 degrees.