October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very crucial ability for higher arithmetic learners to comprehend.

First, we are required to specify what radians are thereby you can understand how this formula is used in practice. Thereafter we’ll take this a step further by showing some examples of converting from radians to degrees quickly!

What Is a Radian?

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

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

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

Note: a radian is not to be confused with a radius. They are two absolety different things. A radius is the length from the middle of a circle to the border, though a radian is a unit of measure for angles.

Relationship Between Radian and Degrees

There are two manners to go about about this question. The initial way is to contemplate about how many radians exists in a full circle. A full circle is equivalent to 360 degrees or two pi radians (exactly). So, we can say:

2π radians = 360 degrees

Or simplified:

π radians = 180 degrees

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

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

π radiansπ radians = 180 degreesπ radians = 57.296 degrees

Both of these conversion factors are helpful relying upon which 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 find out how to convert them!

The Formula for Converting Radians to Degrees

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

π radiansx radians = 180 degreesy degrees

With ease plug in your given values to get your unknown values. For instance, if you are required to change .7854 radians into degrees, your proportion will be:

π radians.7854 radians = 180 degreesz degrees

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

This formula implied both ways. Let’s double-check our workings by converting 45 degrees back to radians.

π radiansy radians = 180 degrees45 degrees

To solve for 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 straightforward calculation. In this case, afterwards changing .785 from its first form back again, after these steps produced precisely what was predicted -45°.

The formulas plays out 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.

At the moment, we will convert pi/12 rad into degrees. Just 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 normally would:

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

There you have the answer! pi/12 radians equivalents 15 degrees.

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

Degrees = (180 * 1.047) / π

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

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

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

For example, if you want to change 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 remember the equation to solve for radians, you will get identical answer:

Radians = (π * z degrees) / 180

Radians = (π * 60 degrees) / 180

And there you have it! These are just a few examples of how to change radians to degrees and vice versa. Remember the equation and see for yourself the next time you need to make a transformation between radians and degrees.

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