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."

In this sense, we are using the concept of "turns". There is one turn in a full circle, so 1 turn is 360°. It follows that 180° is half a turn, 90° is a quarter turn, and so on.

Conversion

One turn is equal to 2π radians. Therefore, 2π radians = 360°. From this, formulae for converting degrees to radians, and vice versa, can be found:

File:Radians to Degrees.png

In Lua terms, these can be written as:

local radians = degrees * math.pi / 180
local degrees = radians * 180 / math.pi

However, there is a cleaner way of doing this. Lua provides functions to do these conversions for you in the math library:

local inRadians = math.rad(degrees)
local inDegrees = math.deg(radians)

Radians and Degrees

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":

Angle in radians	represents
2π	one whole circle
π	one-half circle
2π/3	one-third circle
π/2	one fourth circle
2π/5	one-fifth circle
π/3	one-sixth circle
2π/7	one-seventh circle
π/4	one-eighth circle
2π/9	one-ninth circle
π/5	one-tenth circle
2π/11	one-eleventh circle
π/6	one-twelfth circle
0	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/π).

For example:

360°|| 2π radians 270°|| 3π/2 radians 180°|| π radians 90°|| π/2 radians 60°|| π/3 radians 45°|| π/4 radians 30°|| π/6 radians 0°|| 0 radians

Angle in degrees	represents

More info

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