The radian is a dimensionless unit of angle measurement derived from the SI base unit meter, preferred in mathematics due to its elegance and simplicity. The steradian is a related unit measuring solid angles.
A radian is a unit of measurement defined as 180/π°, or approximately 57.2958°. Sometimes abbreviated as rad or as the subscript c, which stands for “circular measure,” the radian is the standard unit of measure for angles in mathematics. The radian was first conceived by the English mathematician Roger Cotes in 1714, although he did not name the unit of measurement. The word radiant first appeared in print in 1873.
Originally, the radian was considered a supplementary unit in the International System of Units (SI), but the supplementary units were abolished in 1995 and are now known as derived units. The radian is derived from the SI base unit meter (m), being equal to m m-1 om/m. Because meters cancel each other out in the definition of the radian, the radian is considered dimensionless, and for this reason radians are often simply written as a number, with no unit symbol.
The radian is the angle formed by two radii, lines from the center to the outer circumference of a circle, where the arc formed equals the radius. An angle in radians can be calculated by dividing the length of the arc that the angle cuts out by the radius of the circle (s/r). There are 360° in any circle, equal to 2π radians. Another angle measurement system, the grad, divides a circle into 400 grads. 200/π grad equals one radian.
In mathematics, radians are preferred over other units of angle measurement, such as degrees and degrees, due to their naturalness or their ability to produce elegant and simple results, particularly in the field of trigonometry. Also, like all SI units, radians are used universally, so they allow mathematicians and scientists to easily understand each other’s calculations without the hassle of conversion.
Another SI derived unit related to the radian is the steradian (sr), or square radian, which measures solid angles. A solid angle can be visualized as a conical portion of a sphere. The steradian is another dimensionless unit of measurement, equal to m·m-2. Steradians can be calculated by dividing the area covered on the surface of the sphere by the radius squared (S/r2).
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