Radians

This is a very basic explanation of Radians, if you have never been taught Radians before.

Radians are another way of describing angles, as opposed to using degrees. Something similar to Radians is used in everyday life, when we use fractions. We say, "I want a third of a piece of cake," not, "I want 120 degrees worth of cake."

For a basic idea of Radians to how much "cake" or "circle" you have, divide the radians by "2 pi". To convert how much "cake" or "circle" you have to Radians, multiply the "cake" (or circle) by "2 pi":

2pi => one whole circle
pi => one-half circle
2pi/3 => one-third circle
pi/2 => one fourth circle
2pi/5 => one-fifth circle
pi/3 => one-sixth circle
2pi/7 => one-seventh circle
pi/4 => one-eighth circle
2pi/9 => one-ninth circle
pi/5 => one-tenth circle
2pi/11 => one-eleventh circle
pi/6 radians => one-twelfth circle
0 radians => No circle

Sometimes finer measurements are needed than simple fractions. Degrees slice a circle into 360 parts -- and sometimes degrees need to be converted into Radians. To convert from degrees to radians, divide by 180/pi. To convert from radians to degrees, multiply by 180/pi.

For example:
360 Degrees => 2pi radians
270 Degrees => 3pi/2 radians
180 Degrees => pi radians
90 Degrees => pi/2 radians
60 Degrees => pi/3 radians
45 Degrees => pi/4 radians
30 Degrees => pi/6 radians
0 Degrees => 0 radians

See Also

Radians

Radian Degree Converter