Hop Utilisation (Tinseth)

Alpha acids are not bitter. The humulones in a hop cone are only sparingly soluble and nearly tasteless; what bitters beer is their isomers, the iso-alpha acids, and converting one to the other takes heat and time in the boil. Utilisation is the fraction of the alpha acids added that make it through that conversion and stay dissolved in the finished beer — and it is remarkably low. A sixty-minute addition to ordinary-strength wort utilises about 23% of what went in. The other three-quarters is thrown away with the trub.

Glenn Tinseth published his correlation in 1997 after measuring his own beers, and it factors cleanly into two independent effects. The time factor, $(1 - e^{-0.04t})/4.15$, is first-order isomerisation kinetics: the rate is proportional to how much un-isomerised acid remains, so the curve rises steeply at first and flattens toward an asymptote. Past about sixty minutes there is very little left to gain, which is exactly why nobody boils hops for two hours. The gravity factor, $1.65 \times 0.000125^{G_b - 1}$, is the empirical part — the "bigness factor" — and it says that dense wort suppresses isomerisation. Raising boil gravity from 1.040 to 1.080 cuts utilisation by roughly a quarter, which is why a strong beer needs disproportionately more hops to taste as bitter.

Both constants are unit-bound and neither announces it. The 0.04 is per MINUTE; hand it a time in seconds or hours and the exponential returns a confidently wrong number with no warning. The 0.000125 base wants boil gravity as a SPECIFIC GRAVITY — 1.050, not 50 points and not 12.4 °P — because $G_b - 1$ is meant to be the small decimal 0.050. These two substitutions are the most common way this equation gets misused, and both fail silently.

Tinseth is one of three widely used models and they disagree. Rager's tables generally predict higher utilisation, Garetz's lower with an additional correction for altitude, and none of them was measured on your kettle. Real utilisation depends on boil vigour, kettle geometry, whether the hops were whole or pelletised, wort pH, how much break material is present, and how long the wort sat hot after flameout. The right way to use any of them is as an internally consistent yardstick: pick one model, brew the same recipe repeatedly, and calibrate to what your own system produces. The absolute number matters far less than the fact that it is the same number every time.