How do you calculate IBUs?
An IBU is a milligram of isomerized alpha acid per liter of beer. You know how much alpha acid you added (weight × AA%); what you don't know is what fraction of it isomerized in the kettle — the utilization — and that's what the formulas estimate. Tinseth's (1997), the default in nearly every piece of brewing software:
IBU = (mg/L of alpha acid) × utilization
utilization = 1.65 × 0.000125(boil gravity − 1) × (1 − e−0.04 × minutes) ÷ 4.15 — a gravity factor times a time factor
One ounce of 14% Magnum boiled 60 minutes in 5 gallons of 1.050 wort: alpha acid 14% × 28.35 g = 3.97 g in 18.9 L = 210 mg/L; utilization at 60 minutes and 1.050 is 23.1%; so 48 IBU. Utilization tops out around 25–30% however long you boil, falls as the wort gets denser (the same 60-minute addition gives 30% less bitterness at 1.080 than at 1.040), and is nearly nothing under five minutes — which is the entire logic of a hop schedule.
Tinseth vs Rager: why do recipes disagree?
Rager's formula (1990) predates Tinseth's, and a lot of recipes — and some calculators — still use it. It swaps in a different utilization curve (a hyperbolic tangent of boil time) and only corrects for gravity above 1.050. Everyone repeats that "Rager reads 20–30% higher"; the truth is more useful than that, because the disagreement depends on when the hop went in:
The Brewer's Friend IBU reference provides another implementation of the common utilization models. Compare formula, hop form, gravity, and volume before interpreting a difference between calculators.
| Boil time | Tinseth util. (1.050) | Rager util. | Rager ÷ Tinseth |
|---|---|---|---|
| 90 min | 24.7% | 31.9% | 1.29× |
| 60 min | 23.1% | 30.8% | 1.33× |
| 45 min | 21.2% | 26.9% | 1.27× |
| 30 min | 17.7% | 17.1% | 0.96× |
| 20 min | 14.0% | 10.5% | 0.75× |
| 15 min | 11.4% | 8.2% | 0.72× |
| 10 min | 8.4% | 6.7% | 0.80× |
| 5 min | 4.6% | 5.7% | 1.24× |
| 1 min | 1.0% | 5.2% | 5.23× |
Same addition, 5 gal at 1.050, from this page's engine. Shaded where the two differ by more than a quarter.
So on a bittering charge Rager reads a third higher; on a 15–20 minute flavor addition it reads a quarter lower; and on flameout hops its curve never drops below about 5%, so it credits bitterness Tinseth says isn't there. Add up a normal pale-ale schedule and Rager comes out about 21% higher (73 vs 60) — but a late-hopped IPA can come out lower. That's why the calculator shows both per addition: if a recipe's IBU number doesn't match your Tinseth total, look at which additions carry the gap before you change anything.
| Addition | Tinseth | Rager |
|---|---|---|
| 1 oz Magnum 12 % · 60 min | 41.5 | 55.2 |
| 1 oz Cascade 6 % · 15 min | 10.3 | 7.4 |
| 2 oz Cascade 6 % · 5 min | 8.3 | 10.2 |
| Total (5 gal, 1.050) | 60 | 73 |
Tinseth is this calculator’s default and a widely used recipe-planning model. If you are reproducing a recipe, use the model the author specified so the estimates are comparable. Neither Tinseth nor Rager is a laboratory measurement, and agreement with a particular brewery depends on its ingredients and process.
Tinseth utilization table
Percent of alpha acid that isomerizes, by boil time and boil gravity. Multiply your mg/L of alpha acid by the cell to get IBUs by hand.
| Boil time ↓ · gravity → | 1.030 | 1.040 | 1.050 | 1.060 | 1.070 | 1.080 | 1.090 | 1.100 |
|---|---|---|---|---|---|---|---|---|
| 90 min | 29.5 | 27.0 | 24.7 | 22.6 | 20.6 | 18.8 | 17.2 | 15.7 |
| 75 min | 28.9 | 26.4 | 24.1 | 22.0 | 20.1 | 18.4 | 16.8 | 15.4 |
| 60 min | 27.6 | 25.2 | 23.1 | 21.1 | 19.3 | 17.6 | 16.1 | 14.7 |
| 45 min | 25.3 | 23.2 | 21.2 | 19.4 | 17.7 | 16.2 | 14.8 | 13.5 |
| 30 min | 21.2 | 19.4 | 17.7 | 16.2 | 14.8 | 13.5 | 12.4 | 11.3 |
| 20 min | 16.7 | 15.3 | 14.0 | 12.8 | 11.7 | 10.7 | 9.8 | 8.9 |
| 15 min | 13.7 | 12.5 | 11.4 | 10.5 | 9.6 | 8.7 | 8.0 | 7.3 |
| 10 min | 10.0 | 9.1 | 8.4 | 7.6 | 7.0 | 6.4 | 5.8 | 5.3 |
| 5 min | 5.5 | 5.0 | 4.6 | 4.2 | 3.8 | 3.5 | 3.2 | 2.9 |
| 0 min | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
Tinseth (1997), pellet or whole (he made no distinction; many brewers add ~10% for pellets). mg/L of alpha acid = grams × AA% × 1000 ÷ liters, or oz × AA% × 7,490 ÷ gallons. From this page's engine.
Whirlpool, hop stand and dry hop
Hops added after flameout still isomerize while the wort is hot — a 170°F (77°C) hop stand for 20 minutes contributes real bitterness, and a whirlpool at 200°F more still. No formula was fitted to this; the calculator scales Tinseth's utilization down as the temperature falls (halving roughly every 10°C below boiling, zero below 60°C / 140°F), which is the common approximation and about as good as anyone's. Treat whirlpool IBUs as a rough add-on: they can be 5–15 IBU on a heavily hopped IPA, and they're the main reason such beers taste more bitter than their "60-minute" number suggests. Dry hops add no IBUs by these formulas; in practice they add a little perceived bitterness and a lot of aroma, and the number can't see either.
Both formulas are curve fits to other people's kettles. Your alpha acid is a lot number that's been degrading in a freezer; your kettle geometry, boil vigor and trub all move utilization; and the same 40 IBU tastes soft in a 1.070 malty beer and sharp in a 1.040 one — which is what BU:GU (IBU per gravity point) is for: about 0.5 reads balanced, 0.3 malty, 0.8+ hop-forward. Use IBUs to keep your own recipes consistent and to compare against a style range, and don't chase the second digit.