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Bitterness

Bitterness is the number brewers argue about most, and the one no two calculators agree on. We work it out with Tinseth’s model by default, convert every whirlpool addition into the boil minutes it is really worth, and show you what the other two published models would have said about the same hops. This page is the arithmetic behind that, with a real recipe in it.

Why three models, and why Tinseth

Section titled “Why three models, and why Tinseth”

All three do the same thing in the same shape. They work out how many milligrams of alpha acid per liter went into the kettle, then multiply by a utilization fraction, and they differ only in how they get the fraction.

Tinseth’s is a curve fitted to measured utilization, with a gravity term that suppresses it in heavy wort and a time term that flattens out after about sixty minutes. It is what almost every modern calculator uses, so it is the model that makes your recipe comparable with the one you are reading about somewhere else. Rager’s numbers run higher, and Rager himself said they suit full-wort boils. Garetz applies three separate penalties to raw utilization and runs lower than either. The gap between them on the same beer is wider than most brewers expect, and that gap is the honest measure of how much any one of the numbers is worth.

The app calculates with Tinseth. The engine knows all three, which is how this page shows them side by side on the same schedule, and the IBU figure’s explanation names the model it used.

Whirlpool additions

Section titled “Whirlpool additions”

A curve fitted to boiling wort has nothing to say about eighty degrees, which is where these models originally fell over. We convert a hop stand into the boil minutes it is actually worth by integrating the isomerisation rate along a cooling curve, the approach the mIBU work took. That drops into all three models without special-casing any of them. A thirty-minute stand at 80 °C comes out worth about five boil minutes, and setting the stand temperature on the row is what makes that right for your kettle. Telling the row what the kettle read when the stand ended narrows it further: we fit the cooling curve to your two temperatures instead of ours, and a whirlpool you held at one temperature is the case where that curve comes out flat.

The IBU figure’s explain popover shows the working for every stand in the recipe: the hop, how long it stood, between which temperatures, and what that came to in boil minutes and IBU.

What the number cannot know

Section titled “What the number cannot know”

Dry hops are zero IBU by definition. They add no measurable iso-alpha acid however bitter they taste. And no model here has measured your kettle. They are fits to somebody else’s, which is why the figure is worth reading as a range with your beer somewhere in it.

The beer these numbers come from

Section titled “The beer these numbers come from”

Reference pale ale — 20 L into the fermenter, a 60 minute boil.

Grist Amount Color
Crisp Maris Otter Pale Ale Malt 4.5 kg 2.8 °L
Thomas Fawcett Caramalt 0.35 kg 9.9 °L
Hops Amount Alpha Addition
Magnum 15 g 13.5 % 60 min boil
Cascade 30 g 6.8 % 10 min boil
Citra 40 g 13 % 20 min stand at 80 °C
It comes out at
Original gravity 1.0507
Final gravity 1.0094
Alcohol 5.52 %
Bitterness 35.66 IBU
Color 5.14 SRM (10.12 EBC)
Into the fermenter 20 L

The numbers

Section titled “The numbers”

Bitterness (tinseth-1997)

35.66 IBU, from tinseth-1997.

IBU = 1.65 × 0.000125^(Gb−1) × (1 − e^(−0.04t))/4.15 × (AA% × g × 1000 / L)
⇒ Bitterness = 35.66 IBU
Input Value Unit
Volume 22.11 L
Volume basis post-boil —
Boil gravity 1.0507 SG
Gravity basis post-boil —
Whirlpool model mibu —
Hop count 3 —

What it assumes:

  • Citra, 20 min from 80 °C cooling: worth 1.6 boil minutes, 4.1 IBU.
  • Dry hops contribute 0 IBU.

Sources:

Bitterness (rager-1990)

51.33 IBU, from rager-1990.

IBU = (18.11 + 13.86 tanh((t−31.32)/18.27))/100 × (AA% × g × 1000 / L) / (1 + GA)
⇒ Bitterness = 51.33 IBU
Input Value Unit
Volume 22.11 L
Volume basis post-boil —
Boil gravity 1.0507 SG
Gravity basis post-boil —
Whirlpool model mibu —
Hop count 3 —

What it assumes:

  • Citra, 20 min from 80 °C cooling: worth 1.6 boil minutes, 13.6 IBU.
  • Dry hops contribute 0 IBU.

Sources:

Bitterness (garetz-1994)

20.15 IBU, from garetz-1994.

IBU = U(t) × (AA% × g × 1000 / L) / (GF × HF × TF)
⇒ Bitterness = 20.15 IBU
Input Value Unit
Volume 22.11 L
Volume basis post-boil —
Boil gravity 1.0507 SG
Gravity basis post-boil —
Whirlpool model mibu —
Hop count 3 —

What it assumes:

  • Citra, 20 min from 80 °C cooling: worth 1.6 boil minutes, 0.0 IBU.
  • Dry hops contribute 0 IBU.

Sources:

BU:GU

0.703 ratio, from bu-gu-ratio.

BU:GU = IBU / ((OG − 1) × 1000)
⇒ BU:GU = 0.703 ratio
Input Value Unit
Bitterness 35.7 IBU
Original gravity 1.0507 SG

Sources:

  • Designing Great Beers — Ray Daniels, 1996

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