Radians

This article is about an advanced topic.

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

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

Advanced

The above examples have used whole numbers and rather clean fractions. Unfortunately, if you want to make something like a "spiralling staircase", you will need to work with much finer "pie slices" than the ones above, and you will get decimals. However, the principle and the computation is the same:

For example:

0 Degrees => 0 radians
1 Degree => 0.017453292519943295769236907684886 Radians
2 Degrees => 0.034906585039886591538473815369772 Radians
3 Degrees => 0.052359877559829887307710723054658 Radians
4 Degrees => 0.069813170079773183076947630739545 Radians

And the reverse:
1 Radian => 57.295779513082320876798154814105 Degrees
2 Radians => 114.59155902616464175359630962821 Degrees
3 Radians => 171.88733853924696263039446444232 Degrees
4 Radians => 229.18311805232928350719261925642 Degrees

And so on. You can convert Degrees to Radians and Radians to Degrees using online conversion tools, with your calculator, or with the following functions:

math.pi
Roblox reads this as Pi, which is 3.141592654.

math.rad (x)
Converts x (in degrees) into Radians. Example: math.rad(90) results in 1.5707963267.

math.deg (x)
Converts x (in Radians) into degrees. Example: math.deg(3.141592654) results in 180.

See Also

Radians

Degrees

Radian Degree Converter

Table of polyhedron dihedral angles