How Do You Change Degrees To Radians

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Degrees and radians are two units for measuring angles.^[1] 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.^[2] Sound confusing? Don't worry, you can easily convert degrees to radians, or from radians to degrees, in just a few easy steps.

Practice Problems

Steps

1
Write down the number of degrees you want to convert to radians. ^[3] 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°
2
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
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3
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
4
Simplify. 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
5
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
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Question

How do I derive the formula for the conversion of degrees to radians?

Anan Shah

Community Answer

Simply: π=180 or π=180*1 degree and therefore, 1degree= π/180, thus, degree measure= radian measure * π/180.
Question

What is 63 degree 14 min 51 sec in radian form?

First convert the angle to a decimal. There are 60 seconds in a minute, 60 minutes in a degree, and 3600 seconds (60 x 60) in a degree. 14 minutes 51 seconds equals 891 seconds, which is 891/3600 of a degree or .2475 degree. For simplicity, let's call that ¼ of a degree. Therefore, the angle in question is 63¼ degrees. As shown in the above article, 63¼° multiplied by (π/180) = 1.1 radians.
Question

What is 1085 degrees in radian form?

1085° = 6.0277 radians. 1080° is equivalent to three complete circles, 1085° is the same angle as 5° and 0.0277 radian.
Question

How do I convert radians into degrees?

Multiply the number of radians by 180°. For example, 2 radians equal 360°. 5 radians equal 900°.
Question

What is 22550 degrees in radians form?

In general, multiply degrees by 0.0175 to get radians (1,691.25 radians in this case). If you prefer to treat multiple full circles (as in this case) as less than a full circle, first divide the total degrees by 360 (the number of degrees in a full circle). 22,550 divided by 360 is 62 with a remainder of 230, which is the number of degrees beyond 62 full circles contained in 22,550°. Multiply 230 by 0.0175 to get the radians in one partial circle.
Question

What if the degree is negative?

That just means the angle is being measured in a counter-clockwise direction, but the size of the angle (whether measured in degrees or radians) is the same as if it were positive.
Question

How do I calculate 90 degrees into radians?

Since 90° is ¼ of a circle, it's also ¼ of 2π radians, or (π/2) radians.
Question

Why is pi assumed 22/7?

Because sometimes a fraction is easier to work with than a decimal is, and 22/7 is the fraction that most closely approximates the value of pi.
Question

How do I find the degree measure of 3 pi radian?

Multiply each π radian by 180°. 3 x 180° = 540°. That's 1½ full circles, which for practical purposes is equivalent to one half-circle.
Question

What is 48 degrees converted to radians?

48° × π/180 = 0.8378 rad.

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Article SummaryX

To convert degrees to radians, take the number of degrees to be converted and multiply it by π/180. You can calculate this by converting both numbers into fractions. For example, to convert 120 degrees you would have 120 x π/180 = 120π/180. Once you've gotten your answer, simplify the radians. For more examples of converting degrees to radians, scroll down!

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