October 28, 2022

Radians to Degrees - Conversion, Formula, Examples

Radians and degrees conversion is a very crucial ability for higher math learners to understand.

First, we need to explain what radians are thereby you can perceive how this theorem works in practice. After that we’ll take it one step further by looking at some examples of changing from radians to degrees quickly!

What Is a Radian?

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

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

Simply put, radians and degrees are simply 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 completely distinct things. A radius is the length from the center of a circle to the border, whereas a radian is a unit of measure for angles.

Correlation Between Radian and Degrees

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

2π radians = 360 degrees

Or simplified:

π radians = 180 degrees

The next way to figure out regarding this question is to consider how many degrees exists in a radian. We know that there are 360 degrees in a whole 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 about 57.296 degrees.

π radiansπ radians = 180 degreesπ radians = 57.296 degrees

Both of these conversion factors are beneficial depending on what you're trying to get.

How to Convert Radians to Degrees?

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

The Formula for Converting Radians to Degrees

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

π radiansx radians = 180 degreesy degrees

Just put in your known values to get your unknown values. For example, if you are required to turn .7854 radians to degrees, your proportion would 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 works 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 by 3.14 (pi) and divide by 180: .785 radians.

Once we've converted one type, it will always work with another unsophisticated calculation. In this case, afterwards converting .785 from its original form back again, after these steps produced exactly what was expected -45°.

The formulas plays out like this:

Degrees = (180 * z radians) / π

Radians = (π * z degrees) / 180

Examples of Going From Radians to Degrees

Let's try a handful of examples, so these ideas become easier to digest.

Now, we will change pi/12 rad into degrees. Much like before, we will put this value into the radians slot of the formula and solve 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 result! pi/12 radians equivalents 15 degrees.

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

Degrees = (180 * 1.047) / π

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

Right away, what to do if you want to transform degrees to radians?

By utilizing the very same formula, you can do the contrary in a pinch by work out with radians as the unknown.

For example, if you want to convert 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 remember the formula to find radians, you will get the exact result:

Radians = (π * z degrees) / 180

Radians = (π * 60 degrees) / 180

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

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