October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very essential ability for progressive arithmetic students to grasp.

Initially, we are required to explain what radians are so that you can see how this formula works in practice. Then we’ll take it one step further by exhibiting some examples of going from radians to degrees with ease!

What Is a Radian?

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

A radian is the SI (standard international) unit of measurement for angles, while a degree is a more generally utilized unit in mathematics.

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

Note: a radian is not to be confused with a radius. They are two absolety distinct concepts. A radius is the distance from the center of a circle to the perimeter, though a radian is a measuring unit for angles.

Correlation Between Radian and Degrees

There are two manners to go about regarding this question. The initial method is to figure out about how many radians are present in a full circle. A full circle is equal to 360 degrees or two pi radians (precisely). So, we can state:

2π radians = 360 degrees

Or simplified:

π radians = 180 degrees

The second way to figure out about this question is to think about how many degrees there are in a radian. We all know that there are 360 degrees in a complete circle, and we also understand that there are two pi radians in a full circle.

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

π radiansπ radians = 180 degreesπ radians = 57.296 degrees

Both of these conversion factors are useful depending upon which you're trying to do.

How to Convert Radians to Degrees?

Since we've gone through what degrees and radians are, let's find out how to convert them!

The Formula for Converting Radians to Degrees

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

π radiansx radians = 180 degreesy degrees

Simply plug in your given values to obtain your unknown values. For instance, if you wished to turn .7854 radians into degrees, your proportion will be:

π radians.7854 radians = 180 degreesz degrees

To find out the value of z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.

This formula implied both ways. Let’s verify our operation by changing 45 degrees back to radians.

π radiansy radians = 180 degrees45 degrees

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

Once we've transformed one type, it will always work with different unsophisticated calculation. In this instance, after changing .785 from its original form back again, ensuing these steps made exactly what was predicted -45°.

The formulas solves like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

Examples of Changing Radians to Degrees

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

Now, we will convert pi/12 rad to degrees. Just the same as before, we will plug this number into the radians slot of the formula and work it out 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 equivalents 15 degrees.

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

Degrees = (180 * 1.047) / π

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

Now, what happens if you have to change degrees to radians?

By employing the very same formula, you can do the converse 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 solve for the unknowns:

60 degrees = (180 * z radians) / π

(60 * π)/180 = 1.047 radians

If you remember the formula to solve for radians, you will get identical answer:

Radians = (π * z degrees) / 180

Radians = (π * 60 degrees) / 180

And there it is! These are just a few examples of how to change radians to degrees and conversely. Bear in mind the formula and try solving for yourself the next time you have to make a transformation between radians and degrees.

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