Dye Exhaustion Rate Calculator

Under the Beer-Lambert law, absorbance at a dye's characteristic wavelength is directly proportional to its concentration, so the ratio of before-and-after absorbance readings gives the same exhaustion percentage as a ratio of before-and-after concentrations would, without needing a calibration curve or a known extinction coefficient. That's why only two absorbance values — initial and final — are required as inputs, rather than a measured concentration in grams per liter.

Exhaustion rate only tells you how much dye left the bath and attached to the fiber, but some of that exhausted dye is loosely held and will wash or rub off later rather than being permanently bonded. Overall fixation multiplies exhaustion by your fixation rate input to estimate what fraction of the original dye charge ends up permanently fixed — so a bath can show 95% exhaustion but, with a 70% fixation rate typical of some reactive dyes, only about 66% overall fixation actually stays on the fabric through washing.

In theory, final absorbance should always be lower than initial absorbance since dye is leaving the bath, but a stale spectrophotometer baseline, a dirty cuvette, or reading noise can occasionally produce a final absorbance that's higher than expected relative to the initial reading, which would otherwise compute a negative or over-100% exhaustion. The clamp catches that and floors or caps the result, but it's a sign to recheck your readings rather than trust the clamped number as accurate.

Fabric weight only enters the % OWF (on weight of fiber) calculation, which expresses the dye actually fixed as a percentage of your fabric's dry weight — a standard way dyers compare recipes across different batch sizes. It has no effect on exhaustion percentage, dye-on-fiber grams, or residual dye grams, all of which depend only on the absorbance readings, total dye charge, and fixation rate.