Arc Minute (′)
An arc minute (′) represents one-sixtieth of a degree, so a full degree contains 60 arc minutes and a complete circle has 21,600 arc minutes. Its origins trace back to ancient astronomers in Babylon and Greece, who needed finer subdivisions of the degree for celestial observations and mapping. Today, arc minutes are still fundamental in fields such as astronomy, navigation, and land surveying. They are commonly used in geographic coordinate systems—latitude and longitude—where they offer a more precise measurement than whole degrees.
Radian (rad)
The radian, symbol rad, is the standard SI unit for measuring angles. It was introduced in the 18th century by mathematicians who sought a natural, dimensionless unit for angle measurement. One radian represents the angle created when the arc length of a circle equals the circle’s radius; therefore, a full circle contains exactly 2π radians, which is approximately 6.283 radians. This makes it fundamental in trigonometry, calculus, and physics, where radians simplify formulas involving angular velocity, periodic motion, and wave functions. Unlike degrees, which divide the circle into 360 parts, radians connect directly to the geometry of a circle, making them the preferred unit in mathematics, science, and engineering worldwide.