Diluting and boiling off wort
How much water to add or boil off to reach the target gravity.
If gravity came out above target after the boil, the wort is diluted with water; if below, it is boiled down. Both problems are solved by the same proportion, because the extract is conserved through dilution and boil-off.
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Why a proportion is enough
Gravity points are proportional to the extract concentration. If you add water, the extract mass does not change while the volume grows — so the concentration falls by exactly the factor by which the volume grew. Hence a simple proportion: the volume is multiplied by the ratio of current points to target points.
The same calculation runs in reverse for boil-off: the volume shrinks and the concentration rises.
Vtarget = Vcurrent · (SGcurrent − 1) / (SGtarget − 1) water to add = Vtarget − Vcurrent
Example
You collected 20 litres of wort at 1.052, but the recipe calls for 1.050. Target volume: 20 · 52 / 50 = 20.8 litres, so you need to add 0.8 litres of water. The reverse case: 20 litres at 1.048, target 1.052 — target volume 20 · 48 / 52 = 18.5 litres, so you need to boil off 1.5 litres.
Caveats
- The water must be clean and preferably boiled and cooled: it should introduce neither minerals beyond the recipe nor infection.
- Mixing water and wort gives a volume slightly smaller than the sum — by roughly 0.5–1 %. The calculation ignores this, and at homebrew volumes the error is insignificant.
- Boiling off changes more than gravity: aroma is lost, bitterness rises through reduction, and the colour shifts. If the gravity needs a significant lift, adding malt extract is the better move than boiling down.
- Measure gravity at 20 °C or apply the hydrometer correction, otherwise the calculation drifts off.