The measure of an angle is identified by the amount of rotation from the original side to the end side. In radians, one complete counterclockwise rotation is 2π. Whereas, in degrees, one complete counterclockwise rotation is 360°. Thus, the degree measure and radian measure are linked by the equations
360°= 2π radians
180°= π radians
From the latter, we get the equation 1° = π180 radians.
This results in the rule to convert degree measure to radian measure. In order of conversion from degrees to radians, multiply the degrees by π180° radians.
How to Convert Degrees to Radians?
The value of 180° is equivalent to π radians. In order to convert any given angle from the measure of degrees to radians, the value needs to be multiplied by π/180. A standard formula for converting from degrees to radians is to simply multiply the number of degrees by π/180
Thus, Angle in Radian = Angle in degree × π / 180°
Radian Measure Formula
In any circle of radius r, the ratio of the arc length ℓ to the circumference is equivalent to the ratio of the angle θ subtended by the arc at the midpoint and the angle in one rotation. Therefore, radian formula to measure the angles in radians, ℓ2πr=θ2π⟹ ℓ=rθ.
Degree Calculation Formula
The measure of the angle is considered in degrees (°). Radian is often considered while computing the angles of trigonometric functions or periodic functions. Radians are always denoted in terms of pi (π), where the value of pi is equivalent to 22/7 or 3.14.
A degree consists of sub-parts also, stated as minutes and seconds. This conversion is the crucial component of Trigonometry applications. Thus, the Degree formula is: - Radians × 180/π = Degrees
Solved Examples on How to Find Radian Measure From Degree
Convert 135° into radian measure
Given = Angle of 135 degrees
Convert 210 degrees to radians.
Solution: Given = Angle of 210 degrees
Angle in radian = Angle in degree x (π/180)
= 210 x (π/180)
Hence, 210 degrees is equal to 7π/6 (3.67) in radian.