Q&A for How to Convert Radians to Degrees

We know from working with the numbers in the article above that one radian is equivalent to approximately 57.3 degrees. Therefore, you would multiply 57.3 by 1.03 to find the number of degrees you're looking for.

The easiest way to do it is to recognize that 180° equals π radians, or 3.14 radians. Then determine what fraction (or percentage) of 180° the angle you're concerned with is, and multiply that fraction by 3.14 radians. For example, to convert 60° to radians, divide 60° by 180°. That's 1/3. Then multiply 1/3 by 3.14: that's 1.05 radians.

Since 1 radian is approximately 57.3 degrees, 11/16 of a radian is (11/16)(57.3°) = 39.39°.

Because π radians = 3.14 radians = 180°, π radians / π = 1 radian = 180°/3.14 = 57.32°. Therefore, 1/4 radian = 57.32° / 4 = 14.33°.

The length arc of a circle can be found by multiplying the angle measurement (theta) by the radius r.

Yes, the degree/radian relationship can be used to convert in either direction.

As with any other radians-to-degrees conversion, multiply the radians value by 180/π. In this case, (π/3)(180/π) = 180/3 = 60°.

The process is the same as with positive degrees. Just insert a negative sign in front of the final radians value.

If you're given an angle in a diagram, you can find the reference angle and then convert into radians from there. But an angle is generally given in degrees, so unless you're given an angle in radians, it should already be in degrees. Anything with theta is already in degrees, while values with a given 'x' are in radians. To convert to degrees, you multiply by 180/pi. But in most cases, you can find the measure of the angle by looking at a diagram or, if you're talking about geometry, there's different ways there to find the measures of the angles.

1 revolution is equivalent to 2π radians, so simply multiply 2 revolutions by 2π radians/1 revolution. The revolutions cancel, and you are left with 4π radians.