IBU — Tinseth formula
Predict the bitterness (International Bitterness Units) of beer given hop additions and boil characteristics.
Formula
Utilisation = (1.65 × 0.000125^(SG−1)) × (1 − e^(−0.04 × time)) ÷ 4.15 IBU per addition = (grams × α% × Utilisation × 10) ÷ batch_L
Inputs
| Name | Unit | Description |
|---|---|---|
| SG | - | Pre-boil specific gravity (uses for boil-gravity utilisation factor) |
| t | minutes | Hop addition boil time |
| α | % | Hop alpha acid percentage |
| W | grams | Weight of hop addition |
| V | L | Post-boil batch volume |
Outputs
| Name | Unit | Description |
|---|---|---|
| IBU | mg/L iso-α | International Bitterness Units (additive across all hop additions) |
Worked example
Inputs:
- hop = Centennial 30 g
- alpha = 10
- time_min = 60
- SG = 1.062
- batch_L = 19
Calculation:
U = (1.65 × 0.000125^(0.062)) × (1 − e^(−0.04 × 60)) ÷ 4.15 = (1.65 × 0.659) × 0.909 ÷ 4.15 = 0.238 (i.e. 23.8% utilisation) IBU = 30 × 10 × 0.238 × 10 ÷ 19 = 37.6
Result:
~38 IBU from this single 60-min addition
Sample values
| Time (min) | Utilisation (1.050 wort) | Utilisation (1.080 wort) |
|---|---|---|
| 0 | 0 | 0 |
| 5 | 0.045 | 0.038 |
| 15 | 0.115 | 0.097 |
| 30 | 0.193 | 0.163 |
| 45 | 0.232 | 0.196 |
| 60 | 0.252 | 0.213 |
| 90 | 0.27 | 0.228 |
What this formula assumes
Tinseth’s model assumes whole-cone or pellet hops added directly to a boiling wort, with isomerisation efficiency decreasing as gravity rises (more sugar = less hop oil contact with water). It is a prediction, not a measurement. Actual IBU varies ±15% from prediction due to hop freshness, kettle geometry, boil vigour and trub absorption.
When to use which utilisation
- Pre-boil SG is the right gravity to plug in — the wort spends more boil time at pre-boil than post-boil concentration.
- For 90-minute boils, take the 60-min utilisation and add a small bonus (~5%) for the extra time at the high-utilisation plateau.
- Whirlpool/hop-stand additions at 80-90 °C give measurable IBU — roughly 1/3 of what the same hop would give at 0-min flame-out. Most calculators have a whirlpool override.
Sanity checks
- 60-min bittering hop at 1.050 wort yields ~25% utilisation.
- IBU above ~80 is increasingly hard to perceive — physiology caps perception.
- Cohumulone-heavy hops (Cluster, Galena) give a harsher bitterness at the same IBU than low-cohumulone hops (Saaz, Hallertau).