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.

Learn about degree measure and radian measure of angles here.

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

In this article, we are going to learn the conversion from degrees to radians, radians to degrees with its conversion procedure and many solved examples in detail.

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

The below steps show the conversion of angle in degree measure to radians.

Step 1: Write the numerical value of the measure of an angle given in degrees

Step 2: Now, multiply the numeral value written in step 1 by π/180

Step 3: Simplify the expression by cancelling the common factors of the numerical

Step 4: The result obtained after the simplification will be the angle measure in radians

Let’s have a look at the examples of conversions of different angle measures.

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 2: 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 Radians Formula

To convert degrees to radians, 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 a radian is the 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 Calculator

To convert the angle value from degrees to radians, the calculator will help in quick results. 

Click here to get the degrees to radians calculator with steps.

Degrees to Radians Chart

Let us create the table to convert some angles in degree form to radian form.

Conversion Of Some Common Angles

Go through the table below to understand the conversion of angles compared to the amount of turns.

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

Question 3: Write 3.25° in degrees, minutes and seconds.
Solution:

3.25° = 3° + 0.25°

= 3° + (25/100).60

= 3° 15′

Question 4: Convert 18°30’42’’ into the degree.

Solution:

18°30’42’’ = 18° + (30/60)° + (42/(60 x 60))°

= 18° + 0.5° + 0.01166°

= 18.51167°

Question 5: Find the value of 1^c in degree minute and second.

Solution: From relation we have,

(π/2)^c = 90°

1^c = 180/π ≈ 57.2957°

≈ 57° + (0.2957 x 60)’

≈ 57° 17.742′

≈ 57° 17′ + (0.742 x 60)”

≈57° 17′ 44″

Note – 1 radian is approximately 57 degrees 17 minutes and 44 seconds.

Practice Questions

1. Transform 700 degrees to radians.
2. How many radians is equal to 100 degrees?
3. Convert 550 degrees to radians.

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