# Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very essential ability for progressive mathematics learners to comprehend.

Initially, we need to specify what radians are in order that you can understand how this formula works in practice. After that we’ll take it one step further by exhibiting a few examples of converting from radians to degrees with ease!

## What Is a Radian?

Radians are units of measurement for angles. It is originated from the Latin word "radix," which implies ray or nostril, 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 commonly utilized unit in mathematics.

That being said, radians and degrees are just two separate units of measure utilized for measuring the same thing: angles.

Note: a radian is not to be mixed with a radius. They are two absolety different things. A radius is the distance from the middle of a circle to the edge, though a radian is a measuring unit for angles.

### Relationship Between Radian and Degrees

We have two manners to think regarding this question. The first way is to think about how many radians there are in a full circle. A full circle is equal to 360 degrees or two pi radians (exactly). Hence, we can say:

2π radians = 360 degrees

Or simplified:

π radians = 180 degrees

The next way to think about this question is to consider how many degrees there are in a radian. We know that there are 360 degrees in a complete circle, and we also understand that there are two pi radians in a whole circle.

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

π radiansπ radians = 180 degreesπ radians = 57.296 degrees

Both of these conversion factors are helpful depending upon which you're trying to get.

## How to Change Radians to Degrees?

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

### The Formula for Giong From Radians to Degrees

Proportions are a beneficial tool for changing a radian value into degrees.

π radiansx radians = 180 degreesy degrees

With ease plug in your known values to obtain your unknown values. For instance, if you are required to change .7854 radians to degrees, your proportion would 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 can be implemented both ways. Let’s verify our operation by reverting 45 degrees back to radians.

π radiansy radians = 180 degrees45 degrees

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

Now that we've converted one type, it will always work with another straightforward calculation. In this instance, after converting .785 from its first form back again, ensuing these steps produced exactly what was expected -45°.

The formulas work out like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

### Examples of Going From Radians to Degrees

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

Now, we will transform pi/12 rad to degrees. Much like before, we will place this value in the radians slot of the formula and solve it like this:

Degrees = (180 * (π/12)) / π

Now, let divide and multiply as you normally do:

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

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

Let's try another common conversion and transform 1.047 rad to degrees. Yet again, utilize the formula to get started:

Degrees = (180 * 1.047) / π

Once again, you multiply and divide as suitable, and you will find yourself with 60 degrees! (59.988 degrees to be almost exact).

Right away, what happens if you want to change degrees to radians?

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

For example, if you have to change 60 degrees to radians, plug 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 the same thing:

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. Keep in mind the formula and see for yourself the next time you are required to make a conversion from or to radians and degrees.

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