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Ok I've found another source and it makes a lot more sense.

You want L, the arc length.
You have C, which is the chord.
edit - I see you know the diameter (and hence radius), which is awesome and makes things simpler.
You'll need to know the angle of the sector that the arc is relative to. With C and R, you can do this by using this formula...

Now you have the angle, it's simple...
We essentially calculate the entire circumference, then multiply it by the angle (angle being a fraction of a whole, for example 90 degrees is 90/360, or 1/4, 0.25, one quarter... a 90 degree angle is one quarter of a circle)
2r*pi * a/360
That was a fun start to the day.
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