Degrees to Radians

Degrees to radians: In geometry, both degree and radian represent the measure of an angle. One complete anticlockwise revolution can be represented by 2π (in radians) or 360° (in degrees). Therefore, degree and radian can be equated as:

2π = 360°

And

π = 180°

Hence, from the above equation, we can say, 180 degrees is equal to π radian.

Usually, in general geometry, we consider the measure of the angle in degrees (°). Radian is commonly considered while measuring the angles of trigonometric functions or periodic functions. Radians is always represented in terms of pi, where the value of pi is equal to 22/7 or 3.14.

A degree has its sub-parts also, stated as minutes and seconds. This conversion is the major part of Trigonometry applications.

Degree x π/180 = Radian

Radians  × 180/π = 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

Example 1: Convert 90 degrees to radians.

Solution: Given, 90 degrees is the angle

Angle in radian = Angle in degree x (π/180)

= 90 x (π/180)

= π/2

Hence, 90 degrees is equal to π/2 in radian.

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 3: Convert π/6 into degrees.

Solution: Using the formula,

π/6 × (180/π) = 180/6 = 30 degrees

Radian to Degree Equation

As we know already, one complete revolution, counterclockwise, in an XY plane, will be equal to 2π (in radians) or 360° (in degrees). Therefore, both degree and radian can form an equation, such that:

2π = 360°

Or 

π = 180°

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 3: Convert 15 degrees to radians.

Solution: Using the formula,

15 x π/180 = π/12

Example 4: Convert 330 degrees to radians.

Solution: Using the formula,

330 x π/180 = 11π/6

Negative Degrees to Radian

The method to convert a negative degree into radian is same as we have done for positive degrees. Multiply the given value of the angle in degrees by π/180.

Suppose, -180 degrees has to be converted into radian, then,

Radian = (π/180) x  (degrees)

Radian = (π/180) x (-180°)

Angle in radian = – π

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 = 0.524 Rad
45° π/4 = 0.785 Rad
60° π/3 = 1.047 Rad
90° π/2 = 1.571 Rad
120° 2π/3 = 2.094 Rad
150° 5π/6 = 2.618 Rad
180° Π = 3.14 Rad
210° 7π/6 = 3.665 Rad
240° 3π/2 = 4.189 Rad
360° 2π = 6.283 Rad

Solved Examples

Question 1: Convert 200 degrees into radians.

Solution: By the formula, we know;

Angle in radians = Angle in degree × π/180

Thus,

200 degrees in radians = 200 × π/180 = 10π/9 = 3.491 Rad

Question 2: Convert 450 degrees into radians.

Solution: By the formula, we know;

Angle in radians = Angle in degree × π/180

Thus,

450 degrees in radians = 450 × π/180 = 7.854 Rad

Frequently Asked Questions – FAQs

How do we convert degrees to radians?

To convert the value of angle in degree, to its equivalent radians, we need to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.

What is the formula to convert radian into degrees?

To convert the value of angle from radian to degrees, we need to multiply the given value with 180/π. For example, the value of 2π:
2π x 180/π = 360 degrees

How to convert 30 degrees to radians?

Multiply 30 degrees to π/180:
30 x (π/180) = π/6
Hence, 30 degrees is equal to π/6 in radians

How pi radians is equal to 180 degrees?

One complete revolution, counterclockwise, in an XY plane, will be equal to 2π (in radians) or 360° (in degrees). Hence, we can write:
2π = 360°
Or
π = 180°
Therefore, pi is equal to 180 degrees

What is the value of 1 degree?

One degree is equal to 0.0174533 radians.

What is the value of 1 radian?

One radian is equal to 57.2958 degrees.

Convert 3 radians to degrees.

3 radian × 180/π = 171.887Deg

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Quiz on Degrees to Radians

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