How To Convert To Radians

To Convert to Radians per Second is fairly easy if you have enough information on hand.  The first input is the angle in question, and the second input is how fast do you want your result?  It’s a relatively simple task with a few formulas to remember.  Both formulas are found below so you can decide which one to use. Below you will learn How To Convert To Radians.

Degrees basically state direction and angle size. Facing North means you are facing the direction of 0 degrees. If you turn towards South, you are facing the direction of 90 degrees. If you come back to North after full rotation, you have turned through 360 degrees. Usually, the anticlockwise direction is considered positive. If you turn towards West from North, the angle will be either -90 degrees or +270 degrees.

In geometry, there is another unit for measuring angles, known as the radian (Rad). Now, why do we need radians when we are already comfortable with angles? Most computation in mathematics involves numbers. Since degrees are not actually numbers, then the radians measure is preferred and often required to solve problems. A good example that’s similar to this concept is using decimals when we have percentages. Although a percentage can be shown with a number followed by a % sign, we convert it to a decimal (or fraction).

A circle contains 360 degrees, which is the equivalent of 2π radians, so 360° and 2π radians represent the numerical values for going “once around” a circle. 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.

Degrees x π/180 = Radians

Radians  × 180/π = Degrees

360 Degrees = 2π Radians

180 Degrees = π Radians

Table of Contents

The Conversion Process

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

Sound confusing? Don’t worry, you can easily convert degrees to radians, or from radians to degrees, in just a few easy steps.

Write down the number of degrees you want to convert to radians. Let’s work with a few examples so you really get the concept down. Here are the examples you’ll be working with:

  • Example 1: 120°
  • Example 2: 30°
  • Example 3: 225°

Multiply the number of degrees by π/180. To understand why you have to do this, you should know that 180 degrees constitute π radians. Therefore, 1 degree is equivalent to (π/180) radians. Since you know this, all you have to do is multiply the number of degrees you’re working with by π/180 to convert it to radian terms. You can remove the degree sign since your answer will be in radians anyway. Here’s how to set it up:[4]

  • Example 1: 120 x π/180
  • Example 2: 30 x π/180
  • Example 3: 225 x π/180

Do the math.
 Simply carry out the multiplication process, by multiplying the number of degrees by π/180. Think of it like multiplying two fractions: the first fraction has the number of degrees in the numerator and “1” in the denominator, and the second fraction has π in the numerator and 180 in the denominator. Here’s how you do the math:

  • Example 1: 120 x π/180 = 120π/180
  • Example 2: 30 x π/180 = 30π/180
  • Example 3: 225 x π/180 = 225π/180

 Now, you’ve got to put each fraction in lowest terms to get your final answer. Find the largest number that can evenly divide into the numerator and denominator of each fraction and use it to simplify each fraction. The largest number for the first example is 60; for the second, it’s 30, and for the third, it’s 45. But you don’t have to know that right away; you can just experiment by first trying to divide the numerator and denominator by 5, 2, 3, or whatever works. Here’s how you do it:

  • Example 1: 120 x π/180 = 120π/180 ÷ 60/60 = 2/3π radians
  • Example 2: 30 x π/180 = 30π/180 ÷ 30/30 = 1/6π radians
  • Example 3: 225 x π/180 = 225π/180 ÷ 45/45 = 5/4π radians

Write down your answer. To be clear, you can write down what your original angle measure became when converted to radians. Then, you’re all done! Here’s what you do:

  • Example 1: 120° = 2/3π radians
  • Example 2: 30° = 1/6π radians
  • Example 3: 225° = 5/4π radians

Example 4: 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.

Degrees to Radian Formula

To convert degrees to radian, we can use the formula as given below.

Degree x π/180 = Radian

Let us see some examples:

Example 5: Convert 15 degrees to radians.

Solution: Using the formula,

15 x π/180 = π/12

Example 6: 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 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 Chart

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

Angle in DegreesAngle in Radians
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
270°3π/2 = 4.713 Rad
360°2π = 6.283 Rad

More Examples

Question 7: Convert 200 degrees into radians.

Solution: By the formula, we know;

Angle in radians = Angle in degree × π/180


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

Question 8: Convert 450 degrees into radians.

Solution: By the formula, we know;

Angle in radians = Angle in degree × π/180


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


Converting between radians and degrees is an essential skill for trigonometry, physics, and chemistry. And fortunately it’s not that hard for you to acquire this skill. Following all the tips and tricks you’ve seen here today will make sure of that.

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