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:
| 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, unless the recipe tells you otherwise. It tracks measured beers more closely (its author fitted it to lab IBU data), it's what Brewfather, BeerSmith and Brewer's Friend default to, and it's what this page leads with. Use Rager only to read an old recipe: if a 1990s pale ale says "35 IBU" and your Tinseth total says 28, that's the formula talking, not your hops. Garetz and Daniels exist; nobody writes recipes in them any more.
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.