How to convert degrees to radians or radians to degrees.
What are 'radians' ?
One radian is the angle of an arc created by wrapping the radius of a circle around its circumference.
In this diagram, the radius has been wrapped around the circumference to create an angle of 1 radian. The pink lines show the radius being moved from the inside of the circle to the outside:
circumference = 2pr
So there are 2p radians in a complete circle, and p radians in a half circle.
Converting radians to degrees:
To convert radians to degrees, we make use of the fact that p radians equals one half circle, or 180º.
This means that if we divide radians by p, the answer is the number of half circles. Multiplying this by 180º will tell us the answer in degrees.
So, to convert radians to degrees, multiply by 180/p, like this:
Converting degrees to radians:
To convert degrees to radians, first find the number of half circles in the answer by dividing by 180º. But each half circle equals p radians, so multiply the number of half circles by p.
So, to convert degrees to radians, multiply by p/180, like this:
Maths Helper Plus can show you the
working steps for converting your angles between radians and degrees. It also
draws the angle as an arc of a circle.
Step 2 Enter the angle to convert
Press the F5 key to display the parameters box:
The number in the 'X' edit box changes the type of conversion performed.
If necessary, click on the 'X' edit box and set the value to 1 or 2, depending on the type of conversion you want to perform.
Click on the 'A' edit box and enter the angle to convert. For degrees, just type a number. For radians, you can type a number, or you can enter a value in terms of p by using 'pi' for p.
Click the 'Update' button to update the calculations.