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.
Degree (°)
The degree, symbol °, is one of the oldest units of angle measurement, with origins in ancient Babylonian astronomy dating back to around 3000 BCE. The Babylonians used a base-60 (sexagesimal) number system, which is why a full circle was divided into 360 degrees; in contrast, a full circle is 2π radians. This division allowed for convenient fractions and calculations. Degrees became the standard in Greek, Arabic, and later European science, eventually spreading globally. Although radians are preferred in higher mathematics due to their direct relationship to circle geometry, degrees remain dominant in navigation, cartography, geometry education, and everyday contexts, making them one of the most recognizable and widely used angle units in history.