The SI unit of angular measure, defined as the angle subtended at the center of a circle by an arc equal in length to the radius.The radian is the SI unit for measuring angles, defined as the angle created when the length of the arc on a circle equals the radius of that circle. Unlike degrees, which are arbitrary (360 in a full circle), the radian is a natural, dimensionless measure based on the geometry of the circle itself. This makes it the preferred unit in physics and mathematics because it simplifies many formulas.
The concept of measuring angles by arc length dates back to Indian and Islamic mathematicians, but the term 'radian' was coined by Thomas Muir in 1870, and the unit was adopted by the SI system in 1960.
Imagine drawing a circle with radius r. If you measure an arc along the circumference that is also length r, the angle subtended at the center is exactly 1 radian. A full circle contains 2π radians (about 6.283), so 1 radian equals 180/π degrees (about 57.3°). Because it is defined by a ratio of two lengths, it is dimensionless — the unit is essentially a placeholder.
Used universally in physics, engineering, and mathematics — from calculating rotational motion and wave phases to defining trigonometric functions in calculus.
In the International System of Units, the radian is officially considered a 'dimensionless derived unit', meaning it can be dropped from equations without changing their physical meaning.
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