Degrees to Radians

Degrees to radians conversion is considered while measuring the angles in Geometry. The measure of the angle is usually denoted by degrees (°). An angle can be estimated by two types of units, which are, degree and radian. We can convert one form of representation of any mathematical 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 Radian = π/180 Degrees

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.

Degrees to Radians Formula

Where the value of π = 22/7 or 3.14

Radians to degrees Conversion

As we have already discussed, how to convert degrees to radians for any specific angle. Now, let us see, how we can convert radians to degrees for any specific angle. The formula to convert radians to degrees is given by:

Radians  × 180/π = Degrees

Example: Convert π/6 into degrees.

Solution: Using the formula,

π/6 × 180/π = 180/6 = 30 degrees.

Degrees to Radian Formula

To convert degree to radian, we can use the same formula as given in the above section.

Degree x π/180 = Radian

Let us see some examples:

Example: Convert 15 degrees to radians.

Solution: Using the formula,

15 x π/180 = π/12

Example: Convert 330 degrees to radians.

Solution: Using the formula,

330 x π/180 = 11π/6

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
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

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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