A brew day

brewing calculationshomebrew formulasmash and boil mathsrecipe to kettle

Strike temperature to knockout: heating the mash, the gravity a grain bill gives, the colour it makes and the bitterness the hops add.

Mash Strike Water Temperature

T_w = \frac{0.2}{R}\,(T_2 - T_1) + T_2

How hot the water must be so that grain at room temperature and water together settle at the mash temperature you want. Palmer's form, from a heat balance between grain and water.

Infusion Volume for a Mash Step

W = \frac{(T_2 - T_1)\,(0.2\,G + W_m)}{T_w - T_2}

How much hot water to add to a mash already sitting at one temperature to bring it to the next rest. The heat balance behind every step-mash schedule.

Gravity Points from a Grain Bill

P = \frac{PPG \times W \times E}{V}

The gravity a grain bill should produce, from each malt's potential, the weight used, the brewhouse efficiency and the batch volume. The forecast every recipe is built on.

Brewhouse Efficiency

E = \frac{m_a}{m_p}

The share of the extract locked in the grain that actually reached the kettle. The definitional form — extract recovered over extract available — from which every working efficiency figure descends.

Dilution to a Target Gravity

V_2 = \frac{V_1 P_1}{P_2}

The volume a wort reaches once it is diluted to a lower gravity, worked in gravity points. The fix for a batch that came out stronger than the recipe asked for.

Malt Colour Units

MCU = \frac{L \times W}{V}

The colour a grain bill contributes, weighted by how much of it there is and how far it is diluted — the raw input to every beer-colour correlation.

Beer Colour (Morey's Equation)

SRM = 1.4922 \times MCU^{0.6859}

Turns malt colour units into a predicted beer colour on the SRM scale. Morey's power law is the correlation most recipe software uses, and it exists because colour does not add up linearly.

Hop Utilisation (Tinseth)

U = \frac{1.65 \times 0.000125^{\,G_b - 1}\left(1 - e^{-0.04\,t}\right)}{4.15}

The fraction of a hop addition's alpha acids that actually isomerise into the beer, as a function of boil gravity and boil time. Glenn Tinseth's 1997 correlation, still the industry default.

IBU from Utilisation

IBU = \frac{U \times m_\alpha}{V}

The bitterness a hop addition delivers: the mass of alpha acids that isomerised, divided by the volume it ended up in. One IBU is one milligram of iso-alpha acid per litre.

How they fit together

A brew day is one long calculation with the kettle as its last line, and it starts before any water is hot. Strike water temperature comes first because the grain is a heat sink: pour water at mash temperature onto room-temperature malt and you land eight to twelve degrees low, with no way back that does not involve boiling more water. The water-to-grain ratio in that equation is doing real work, so a thick mash needs a hotter strike than a thin one for the same target. Infusion volume is the same heat balance asked in reverse, for a mash that already exists and has to be stepped up, and each infusion thins the mash a little further, which is worth watching if you are running three steps.

Then the sugar. Gravity points from a grain bill is the prediction — malt potential times weight times efficiency, divided by volume — and brewhouse efficiency is the measurement that tells you whether the prediction was honest. Use the second to calibrate the first. A recipe written at 75% and brewed on a system that gets 65% comes out four gravity points light every single time, and the fix is to edit the E in the equation rather than to add more malt. When the wort comes out the other way, too strong rather than too weak, dilution to target gravity is the correction, and the thing it will not remind you of is that diluting the wort dilutes the bitterness in exactly the same proportion.

Colour and bitterness run off the same grain bill and the same batch volume, which is why they belong on the same page rather than in separate lookups. Malt colour units is the raw sum, and it is wrong on its own — MCU rises without limit while a beer can only get so black, so a stout that computes to 90 MCU is not 90 SRM. Morey's equation is the correction, and above about 10 MCU the two answers separate sharply. On the hop side, Tinseth utilisation depends on boil gravity, not original gravity and certainly not final gravity, and the difference matters most in the beers where bitterness matters most: a high-gravity boil extracts less from the same hops, so an imperial recipe scaled up by weight alone comes out softer than the arithmetic promised. Feed that fraction into IBU with the alpha acid mass and the batch volume, and the recipe is finished.