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.
Arc Second (″)
The arc second, symbol ″, is equal to 1/60 of an arc minute or 1/3,600 of a degree, so there are 3,600 arc seconds in one degree and 1,296,000 arc seconds in a full circle. Like the arc minute, it has deep roots in Babylonian astronomy and has remained vital for precision measurement. Arc seconds are heavily used in astronomy to describe angular distances between stars or the apparent size of celestial objects. In geodesy and cartography, arc seconds are used to define coordinates with extreme accuracy. Modern telescopes and space missions often measure distances in arc seconds, reflecting the importance of this unit in advancing scientific discovery.