October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very essential skill for higher math learners to grasp.

Initially, we need to explain what radians are thereby you can understand how this formula is used in practice. After that we’ll take it one step further by exhibiting some examples of going from radians to degrees quickly!

What Is a Radian?

Radians are units of measurement for angles. It is originated from the Latin word "radix," which suggests nostril or ray, and is a critical theory in mathematics and geometry.

A radian is the SI (standard international) unit for angles, while a degree is a more generally used unit in math.

That being said, radians and degrees are simply two distinct units of measure used for measuring the identical thing: angles.

Note: a radian is not to be mixed with a radius. They are two completely different things. A radius is the distance from the center of a circle to the edge, whereas a radian is a unit of measure for angles.

Association Between Radian and Degrees

There are two manners to think about this question. The initial method is to think about how many radians are present in a full circle. A full circle is equivalent to 360 degrees or two pi radians (precisely). Hence, we can say:

2π radians = 360 degrees

Or easily:

π radians = 180 degrees

The second way to think regarding this question is to think about how many degrees exists in a radian. We know that there are 360 degrees in a complete circle, and we also recognize that there are two pi radians in a complete circle.

If we divide each side by π radians, we’ll see that 1 radian is approximately 57.296 degrees.

π radiansπ radians = 180 degreesπ radians = 57.296 degrees

Both of these conversion factors are useful relying on what you're trying to get.

How to Go From Radians to Degrees?

Now that we've gone through what degrees and radians are, let's practice how to convert them!

The Formula for Converting Radians to Degrees

Proportions are a helpful tool for converting a radian value into degrees.

π radiansx radians = 180 degreesy degrees

Simply plug in your given values to obtain your unknown values. For example, if you wanted to convert .7854 radians into degrees, your proportion will be:

π radians.7854 radians = 180 degreesz degrees

To solve for z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.

This formula works both ways. Let’s recheck our workings by changing 45 degrees back to radians.

π radiansy radians = 180 degrees45 degrees

To work out the value of y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.

Now that we've changed one type, it will always work out with another simple calculation. In this scenario, afterwards converting .785 from its original form back again, following these steps produced precisely what was expected -45°.

The formulas work out like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

Examples of Converting Radians to Degrees

Let's go through a handful of examples, so these theorems become easier to digest.

At the moment, we will change pi/12 rad to degrees. Much like before, we will plug this number into the radians slot of the formula and calculate it like this:

Degrees = (180 * (π/12)) / π

Now, let divide and multiply as you generally would:

Degrees = (180 * (π/12)) / π = 15 degrees.

There you have it! pi/12 radians equals 15 degrees.

Let's try one more general conversion and transform 1.047 rad to degrees. One more time, use the formula to get started:

Degrees = (180 * 1.047) / π

One more time, you multiply and divide as appropriate, and you will wind up with 60 degrees! (59.988 degrees to be exact).

Right away, what happens if you have to convert degrees to radians?

By employing the very same formula, you can do the contrary in a pinch by solving it considering radians as the unknown.

For example, if you want to transform 60 degrees to radians, put in the knowns and work out with the unknowns:

60 degrees = (180 * z radians) / π

(60 * π)/180 = 1.047 radians

If you recollect the formula to find radians, you will get identical answer:

Radians = (π * z degrees) / 180

Radians = (π * 60 degrees) / 180

And there it is! These are just some of the examples of how to change radians to degrees and vice versa. Bear in mind the equation and try solving for yourself the next time you are required to make a transformation between radians and degrees.

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