Tinseth
Glenn Tinseth's model splits utilisation into two independent factors — one for how much sugar is in the boil, one for how long the hops are in it — and multiplies them.
The bigness factor falls as boil gravity rises: thick wort extracts less bitterness from the same hops. The boil time factor is an exponential approach to a ceiling, which is why a 90 minute addition is barely more bitter than a 60 minute one.
Rager
Jackie Rager's model uses a hyperbolic tangent for utilisation and applies a gravity correction only above 1.050.
Why they disagree
Rager runs consistently higher than Tinseth — often by 30% or more. One ounce of 14% alpha hops, 60 minutes, 5 gallons at 1.050 gives roughly 48 IBU on Tinseth and 65 on Rager.
Neither is measuring your beer. Both are curve fits to somebody else's data, from systems with different boil vigour, different hop forms and different equipment. The useful move is to pick one model and never switch, so that your numbers stay comparable to your own previous batches. Most modern recipes and commercial clone recipes are quoted in Tinseth.
What this calculator does not cover
- Multiple hop additions — run each one and add the IBUs together
- Whirlpool and hop stand additions, where temperature rather than time governs isomerisation
- Dry hopping, which adds aroma and almost no measurable bitterness
- Pellet versus whole cone, which differ in utilisation by roughly 10%
For a recipe with several additions, calculate each separately and sum. Bitterness from separate additions is additive; utilisation is not.