Degrees to radians conversion is considered while measuring the angles in Geometry. The measure of the angle is usually denoted by °. An angle can be estimated by two types of units, which are, degree and radian. We can convert one form of representation of angle into another one using simple formulas. A degree has its sub-parts also, stated as minutes and seconds. This conversion is the major part of Trigonometry applications.
| 1 Degree = π/180 Radian |
How to Convert Degrees to Radians?
The value of 180° is equal to π radians. To convert any given angle from the measure of degrees to radians, the value has to be multiplied by π/180.
Where the value of π = 22/7 or 3.14
Degrees to Radians Chart
Let us create the table to convert some of the angles in degree form to radian form.
| Angle in Degrees | Angle in Radians |
|---|---|
|
0° |
0 |
|
30° |
π/6 = 0.524Rad |
|
45° |
π/4 = 0.785Rad |
|
60° |
π/3 = 1.047Rad |
|
90° |
π/2 = 1.571Rad |
|
120° |
2π/3 = 2.094Rad |
|
150° |
5π/6 = 2.618Rad |
|
180° |
Π = 3.14Rad |
|
210° |
7π/6 = 3.665Rad |
|
240° |
3π/2 = 4.189Rad |
|
360° |
2π = 6.283Rad |
Examples Using Degree to Radian Conversion Formula
Question 1: Convert 200 degrees into radians.
Solution: By the formula, we know;
Angle in radian = Angle in degree × π/180
Thus,
200 degrees in radian = 200 × π/180 = 10π/9 = 3.491Rad
Question 2: Convert 450 degrees into radians.
Solution: By the formula, we know;
Angle in radian = Angle in degree × π/180
Thus,
450 degrees in radian = 450 × π/180 = 7.854Rad
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