Coiled Cord Retracted Length and Stretched Length

A lot of people always ask how we calculate coiled cord stretched (extended) length from a known retracted length, or how long of straight cable do we need to make a coil cord based on our desired retracted length. I cannot find any related articles on calculating those retracted length and stretched length.
Actually, there is no any fix formula for us to accurately calculate the retracted and stretched length of coil cord, because the coiling is formed by heating wire jacket, during this process, the wire become deformed and effect originally length.
Ideally and assume there is no any distortion to the wire, we can get the retracted length and stretched length as below formula.

source from telephone cord