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Using Radians to Measure Angles

Using Radians to Measure Angles

Jul 02 2018, 6:01 PM PST 5 min

This is a very basic explanation of Radians, a mathematical concept used for measuring angles.

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,” rather than, “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.


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



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
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/pi).

For example:

Angle in degrees Represents
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 radians

More info

You can convert Degrees to Radians and vice versa using online conversion tools, with your calculator, or with the following members of the Lua math library:

  • math.rad(x)
    Converts x (in degrees) into Radians. Example: math.rad(90) results in 1.5707963267948966.

  • math.deg(x)
    Converts x (in Radians) into degrees. Example: math.deg(3.141592653589793) results in 180.

  • math.pi
    Roblox reads this as Pi, which is 3.141592653589793.

See Also

  • math
  • lua
  • coding
  • concept