Crimp and Take-up Conversion

Crimp and take-up describe the same physical fact — yarn waving in cloth — and differ only in what the excess length is divided by. Crimp measures it against the fabric length; take-up measures it against the yarn length. So for the same cloth,

$$c = \frac{L_y - L_f}{L_f}, \qquad TU = \frac{L_y - L_f}{L_y} = \frac{c}{1+c}, \qquad c = \frac{TU}{1-TU}.$$

Take-up is therefore always the smaller number, by exactly the factor $1/(1+c)$. In percentage form, which is how mills write it: $TU = 100C/(100+C)$.

The reason the confusion survives is that at small crimps it is nearly harmless. Seven per cent crimp is 6.54% take-up — half a point apart, which looks like somebody's rounding. It stops being harmless as soon as the construction gets crimpy: 25% crimp is 20% take-up, and 50% crimp is 33.3% take-up. A woven pile, a seersucker or a crepe can sit in that range, and treating the two figures as interchangeable there loses a third of the yarn.

There is a structural asymmetry worth carrying around, because it doubles as a sanity check. Crimp is unbounded — a yarn can be four times the length of the cloth it sits in, giving 300% crimp — while take-up can never reach 100%, because it is a fraction of the yarn and the yarn cannot contribute more than all of itself. So any figure above 100 is a crimp, and any figure that a source calls take-up and puts above 100 is a mislabelled crimp.

Which one a specification uses is local habit and nothing more, so when a sheet says only "6%", the question to ask is what it was divided by. Fabric length gives crimp; yarn length gives take-up. Then convert before feeding it into a weight or a consumption calculation, both of which are written in crimp.