BakersMath

Methodology

How BakersMath calculators work

One canonical page covering the math behind every calculator on the site. Each section states the formula in standard notation, the data sources it pulls from, and the edge cases where the model breaks. If you want to verify a number, this is where to start.

Editorial posture

  • Flour is always 100%. Every other ingredient is a percentage of flour weight (baker's percentage, per AACC International).
  • Ranges, not magic numbers. Where baking allows a range, the range is what's published.
  • Math is unit-tested. Each calculator's core function has Vitest coverage against cited reference values.
  • No credentials claimed. Calculators are written by a math-trained home baker; sources are named so readers can verify.
  • Updates are dated. Significant changes to ranges or formulas appear on the changelog.

How I use AI

BakersMath is drafted with AI assistance and reviewed by hand before anything goes live. I use AI the way a working writer uses a research assistant: it speeds up the labor, it does not replace the judgment.

What AI does

  • Produces first drafts and rephrasing options from the cited sources.
  • Suggests candidate sources. I read and verify each one before it is cited.
  • Helps keep voice, structure, and terminology consistent across pages.
  • Flags edge cases and ambiguous wording worth documenting.

What AI does not do

  • Get a source cited without me checking it against the original.
  • Set the published formulas, ranges, or defaults.
  • Push anything live without a human review pass against the cited source.

The math does not depend on trusting either of us. Every calculator's core function is unit-tested against the cited reference values, and every formula is published on this page so you can check it yourself. If a sentence reads as off, or a number does not trace to its cited source, that is a bug. Tell me and it gets fixed.

Cited authorities

Sources are grouped by what they govern. Trade bodies define convention; data sources provide measured numbers; practitioner literature provides cross-checks against working bakery practice.

Baker's percentage convention
AACC International (Cereals & Grains Association)
Neapolitan pizza specification
Associazione Verace Pizza Napoletana (AVPN)
Sourdough definition
Real Bread Campaign
Artisan bread practice
Bread Bakers Guild of America
Ingredient densities
USDA FoodData Central, King Arthur Baking
Yeast equivalence
Lallemand, Fleischmann's
High-altitude baking
Colorado State University Extension
Practitioner literature
Hamelman, Reinhart, Forkish, Suas, Modernist Bread

Sourdough Hydration Calculator

Formula

total flour=recipe flour+starter1+hs/100\text{total flour} = \text{recipe flour} + \frac{\text{starter}}{1 + h_s/100}
total water=H100⋅total flour\text{total water} = \frac{H}{100} \cdot \text{total flour}
water to add=total water  −  starter⋅hs/1001+hs/100\text{water to add} = \text{total water} \;-\; \text{starter} \cdot \frac{h_s/100}{1 + h_s/100}
salt=salt %100⋅total flour\text{salt} = \frac{\text{salt}\,\%}{100} \cdot \text{total flour}

H is the target hydration and hₛ the starter hydration, both in percent.

Sources

  • AACC International (Cereals & Grains Association) — baker's percentage convention (flour = 100%).
  • King Arthur Baking technical library — hydration ranges by loaf style.
  • Hamelman, Bread (2nd ed.), Chapter 6 — sourdough hydration practice.
  • Forkish, Flour Water Salt Yeast — open-crumb hydration table.
  • Bread Bakers Guild of America — artisan bread practice norms.
  • Real Bread Campaign — definition of sourdough (no commercial yeast).

Edge cases and limitations

  • Stiff starters (50–60% hydration) require recomputing the flour/water split inside the starter; the calculator does this automatically.
  • Whole-grain flours absorb 5–10% more water than white at the same hydration percentage; treat ranges as starting points.
  • Above 85% hydration the dough behaves more like batter; shaping technique dominates outcome over math.

Sourdough Starter Feeding Scheduler

Formula

tpeak=tbase×Q10(24−T)/10,Q10=2t_{\text{peak}} = t_{\text{base}} \times Q_{10}^{(24 - T)/10}, \qquad Q_{10} = 2

T is the kitchen temperature in °C, clamped to the 10–34 °C range. Base peak times at 24 °C: 5 h (1:1:1), 7 h (1:2:2), 10 h (1:5:5), 14 h (1:10:10).

Sources

  • Q10 temperature coefficient for biological systems (standard biochemistry).
  • King Arthur Baking — starter maintenance practice.
  • Real Bread Campaign — starter terminology and feeding ratios.

Edge cases and limitations

  • Below 18°C the model overestimates speed; the population transitions to a slower fermentation regime.
  • Above 28°C acetic acid bacteria outpace yeast and the starter sours before it peaks.
  • Refrigerated starters need warming time before the peak clock starts; not modeled.

Yeast Conversion Calculator

Formula

fresh:active dry:instant=3:1:0.75(by weight)\text{fresh} : \text{active dry} : \text{instant} = 3 : 1 : 0.75 \quad \text{(by weight)}

All conversions go through active dry as the reference unit: 1 g active dry ≈ 3 g fresh ≈ 0.75 g instant.

Sourdough substitution: ~120 g of 100%-hydration starter per 1 g active dry (range 100–150 g), with the starter's flour and water subtracted from the recipe totals.

Sources

  • Lallemand technical bulletin on baker's yeast equivalence.
  • Fleischmann's Yeast professional baking guide.
  • AACC International — yeast activity definition.

Edge cases and limitations

  • Sourdough conversion is approximate; starter activity varies day-to-day.
  • Old active dry yeast loses ~10% activity per year past the production date.
  • Cold-retard schedules favor instant or sourdough; fresh yeast loses activity faster in the fridge.

Pizza Dough Calculator

Formula

total dough=ball weight×ball count\text{total dough} = \text{ball weight} \times \text{ball count}
flour=total dough1+(h+s+o+y)/100\text{flour} = \frac{\text{total dough}}{1 + (h + s + o + y)/100}
ingredienti=flour×pi100\text{ingredient}_i = \text{flour} \times \frac{p_i}{100}
yeast %=Kt×2(T−24)/10\text{yeast}\,\% = \frac{K}{t \times 2^{(T - 24)/10}}

h, s, o, and y are hydration, salt, oil, and yeast as baker's percentages; pᵢ is any ingredient's percentage of flour weight.

The yeast percentage comes from a Q10 model over the fermentation time t (hours) and temperature T (°C, clamped 10–34): K = 2.5 for fresh yeast (active dry = fresh ÷ 3, instant = fresh ÷ 4) and K = 160 for sourdough starter.

Sources

  • Associazione Verace Pizza Napoletana (AVPN) — Neapolitan specification.
  • Tony Gemignani, The Pizza Bible — NY, Detroit, Roman style ranges.
  • Forkish, The Elements of Pizza — fermentation schedules.
  • Bread Bakers Guild of America — high-temperature baking practice.

Edge cases and limitations

  • Neapolitan dough at 55–58% hydration baked below 800°F will be tough; the math is right but the oven dominates.
  • Doughs with 0% oil dehydrate faster during proofing; cover them.
  • 00 flour absorbs less water than American bread flour at the same hydration percentage.

Bread Fermentation Time Calculator

Formula

tferment=Kpeff×2(Tdough−24)/10t_{\text{ferment}} = \frac{K}{p_{\text{eff}} \times 2^{(T_{\text{dough}} - 24)/10}}
peff=p×(instant=1, active dry=0.75, fresh=0.25)p_{\text{eff}} = p \times \big(\text{instant} {=} 1,\ \text{active dry} {=} 0.75,\ \text{fresh} {=} 0.25\big)

A Q10 model with a 24 °C reference temperature (dough temp clamped 10–40 °C). K is a per-dough calibration constant — larger for slow ferments (lean, enriched, pizza, sourdough). p is the leaven percentage, converted to an instant-yeast-equivalent p_eff before the rate is applied.

Sources

  • Q10 temperature coefficient (biochemistry standard).
  • AACC International — dough rheology and fermentation rate literature.
  • Hamelman, Bread — desired dough temperature targets and fermentation timing.

Edge cases and limitations

  • Below 4°C and above 32°C the Q10 model breaks; yeast activity becomes nonlinear.
  • High-sugar enriched doughs ferment slower than the model suggests because osmotic pressure inhibits yeast.
  • Starters and commercial yeast respond similarly to temperature but at different baselines; calibrate to your starter.

Enriched Dough Calculator (brioche, challah, milk bread)

Formula

flour=total dough1+e+b+o+s+sa+m+w+y100\text{flour} = \frac{\text{total dough}}{1 + \dfrac{e + b + o + s + \text{sa} + m + w + y}{100}}
ingredienti=flour×pi100\text{ingredient}_i = \text{flour} \times \frac{p_i}{100}

Every enrichment is a baker's percentage of flour: e eggs, b butter, o oil, s sugar, sa salt, m milk, w water, y yeast. Flour is back-solved from the total, then each ingredient is flour × its percentage.

Eggs are counted at 50 g each. Default yeast is 1.5% — enriched doughs ferment slowly, so fat and sugar are offset with more yeast and 1.5–2× the time of a lean dough.

Sources

  • Hamelman, Bread — enriched dough chapter.
  • Reinhart, The Bread Baker's Apprentice — brioche commune/moyenne/riche definitions.
  • AACC International — enriched dough rheology.

Edge cases and limitations

  • Brioche riche (50%+ butter) requires laminated technique; straight-mix yields a greasy crumb.
  • Sugar above 15% inhibits yeast even at higher yeast percentages; cold ferment helps.
  • Egg solids contribute structure as well as water; do not substitute pure water for egg.

Bagel Dough Calculator

Formula

yeast %=Kt×2(T−24)/10\text{yeast}\,\% = \frac{K}{t \times 2^{(T - 24)/10}}

Standard baker's percentage. Malt syrup goes in the dough (~1.5% of flour) and in the boil water (about 1 tbsp per litre).

Style presets: New York ~57% hydration with 1.5% malt, Montreal ~50% hydration with honey. Yeast is set by the same Q10 model as the pizza calculator (K = 2.5 commercial, 160 sourdough; time t in hours, temp T in °C clamped 10–34).

Sources

  • Reinhart, Bread Baker's Apprentice — bagel chapter.
  • Marc Vetri, Mastering Bread — bagel section.
  • Bread Bakers Guild of America — bagel formula tradition.

Edge cases and limitations

  • Boil time longer than 90 s per side leaves a leathery crust.
  • Skipping cold retard gives the bagel a yeasty rather than malty flavour profile.
  • Sugar substitution for malt syrup loses the characteristic crust browning.

Laminated Dough Calculator (croissant, danish, pain au chocolat)

Formula

L=∏i=1nfi,fletter=3,fbook=4L = \prod_{i=1}^{n} f_i, \qquad f_{\text{letter}} = 3, \quad f_{\text{book}} = 4

L is the number of butter layers after n folds; the default croissant uses three letter folds (3³ = 27 layers). Beurrage (butter block) as a percentage of détrempe flour: croissant and pain au chocolat 27%, danish 30%, kouign-amann 35%.

Sources

  • Hamelman, Bread — laminated dough section.
  • Suas, Advanced Bread and Pastry — viennoiserie chapter.
  • Bread Bakers Guild of America — viennoiserie practice.

Edge cases and limitations

  • Butter temperature outside 15–18°C either tears (too cold) or smears (too warm).
  • Room temperature above 22°C requires a refrigerated workspace or shorter rolling sessions.
  • More than 4 letter folds compresses layers and reduces flake.

Poolish & Preferment Calculator

Formula

preferment flour=preferment %100×total flour\text{preferment flour} = \frac{\text{preferment}\,\%}{100} \times \text{total flour}
preferment water=preferment flour×hp\text{preferment water} = \text{preferment flour} \times h_p
poolish yeast %=r(t)2(T ⁣F−70)/17\text{poolish yeast}\,\% = \frac{r(t)}{2^{(T_{\!F} - 70)/17}}

hₚ is the preferment's hydration ratio: poolish 100%, biga user-set (~55%), pâte fermentée 63%. Whatever flour, water, salt, and yeast the preferment carries is subtracted from the final-dough totals.

Poolish yeast is interpolated from a time table r(t) — 0.5% of preferment flour at 6 h down to 0.025% at 24 h — then adjusted for temperature (halving every 17 °F above a 70 °F reference).

Sources

  • Hamelman, Bread — preferment chapter (poolish, biga, pâte fermentée).
  • Reinhart, Bread Baker's Apprentice — preferment theory.
  • AACC International — flavour development through extended fermentation.

Edge cases and limitations

  • Poolish past 16 h at 22°C collapses and loses leavening power; refrigerate or use sooner.
  • Biga at 50% hydration needs more force to incorporate into the final dough.
  • Pâte fermentée brings in salt; reduce final dough salt accordingly.

Yeast to Sourdough Converter

Formula

starter=i×recipe flour,i∈{12%,20%,30%}\text{starter} = i \times \text{recipe flour}, \qquad i \in \{12\%, 20\%, 30\%\}
flour in starter=starter1+hs/100\text{flour in starter} = \frac{\text{starter}}{1 + h_s/100}

The inoculation i is set by target sourness: 12% (mild), 20% (balanced), 30% (tangy). hₛ is the starter hydration. Subtract the starter's flour and water from the recipe totals to hold the target hydration.

Sources

  • Real Bread Campaign — sourdough conversion guidance.
  • King Arthur Baking — yeast-to-sourdough substitution.
  • Hamelman, Bread — levain conversion examples.

Edge cases and limitations

  • Recipes relying on rapid rise (< 90 min) do not convert cleanly to sourdough; rework the schedule.
  • Stiff starters (60%) shift the recipe water more than the calculator's default 100% assumption.
  • Salt and sugar percentages are unchanged on conversion.

Sourdough Starter From Scratch (calculator + day-by-day)

Formula

Day 1: mix 50 g flour + 50 g lukewarm water (~30 °C).

Days 2–5: discard down to 50 g, feed 50 g flour + 50 g water (1:1:1) every 24 h.

Days 6+: discard to 50 g, feed 100 g flour + 100 g water (1:2:2) twice a day until active.

Baseline is ~12 days; cool kitchens (< 18 °C) add ~2 days, warm (> 26 °C) subtract ~1, and rye/whole wheat establish ~2 days faster than white.

Sources

  • Real Bread Campaign — starter creation protocol.
  • King Arthur Baking — starter from scratch guide.
  • Modernist Bread (vol 3) — wild yeast establishment timing.

Edge cases and limitations

  • Chlorinated tap water can stall fermentation in the first 3 days; use filtered or rested water.
  • Whole rye accelerates establishment by 2–4 days versus white flour.
  • Cool kitchens (under 20°C) extend the timeline by ~50%.

Baking Weight Converter

Formula

weight (g)=volume (cups)×density (g/cup)\text{weight (g)} = \text{volume (cups)} \times \text{density (g/cup)}

Densities are maintained per ingredient.

Sources

  • USDA FoodData Central — ingredient densities.
  • King Arthur Baking — ingredient weight chart.
  • Bob's Red Mill — packaged ingredient weights.

Edge cases and limitations

  • Spooned-and-leveled flour (125 g/cup) versus dipped flour (150 g/cup) is a 20% difference.
  • Brown sugar density depends on packing pressure; calculator assumes packed.
  • Honey and molasses density varies by water content and temperature.

Yeast Conversion (cross-listed with active dry, instant, fresh)

Formula

fresh:active dry:instant=3:1:0.75\text{fresh} : \text{active dry} : \text{instant} = 3 : 1 : 0.75

The standard ratios apply uniformly.

Sources

  • Lallemand baker's yeast equivalence chart.
  • Fleischmann's professional baking guide.

Edge cases and limitations

  • Bread machine yeast equals instant yeast for math purposes.
  • Some labels state SAF Gold (osmotolerant); use it for high-sugar enriched dough but treat as standard instant for conversion.

Oven Temperature Converter

Formula

∘F=∘C×95+32{}^{\circ}\mathrm{F} = {}^{\circ}\mathrm{C} \times \tfrac{9}{5} + 32
∘C=(∘F−32)×59{}^{\circ}\mathrm{C} = ({}^{\circ}\mathrm{F} - 32) \times \tfrac{5}{9}

Fan/convection offset: subtract 20 °C from the set temperature (then converted to °F), or reduce the bake time by roughly 10–15%.

Sources

  • ASTM standard temperature conversion.
  • Manufacturer literature (Wolf, GE, Miele) on convection compensation.

Edge cases and limitations

  • Domestic oven calibration drift of ±10–30°C is typical; an oven thermometer is the cheapest fix.
  • Fan offset assumes recipe was written for conventional baking; some modern recipes already factor in convection.

Bread Recipe Scaler

Formula

scaled ingredient=ingredient×target flouroriginal flour\text{scaled ingredient} = \text{ingredient} \times \frac{\text{target flour}}{\text{original flour}}

Baker's percentages scale at any ratio; absolute weights do not without renormalizing.

Sources

  • AACC International — baker's percentage formal definition.
  • Hamelman, Bread — scaling appendix.

Edge cases and limitations

  • Mixers have a working capacity ceiling around 2 kg of dough; above that, knead by hand or in batches.
  • Salt at <10 g totals should be measured to 0.1 g; rounding error at small batch sizes is meaningful.
  • Yeast at <1 g totals needs a 0.01 g jeweler's scale.

Pan Size Calculator

Formula

scale factor=Vtarget panVoriginal pan\text{scale factor} = \frac{V_{\text{target pan}}}{V_{\text{original pan}}}

Multiply every ingredient by the scale factor. Bake time adjustment: a larger volume runs +10–20%, a smaller volume −10–15%, and a similar volume stays about the same.

Sources

  • Standard pan dimensions (USA Pan, Nordic Ware, Williams Sonoma reference).
  • America's Test Kitchen — pan substitution guide.

Edge cases and limitations

  • Round-to-square conversion at the same area changes corner-to-center heat path; expect uneven browning.
  • Bundt pans transfer more heat than tube pans of the same capacity; reduce temperature 25°F.
  • Glass pans bake hotter than metal at the same set temperature.

High-Altitude Baking Calculator

Formula

yeast reduction=clamp⁡ ⁣(A−300014000,  0,  0.5)\text{yeast reduction} = \operatorname{clamp}\!\left(\frac{A - 3000}{14000},\; 0,\; 0.5\right)
chemical leavener reduction=clamp⁡ ⁣(A−300021000,  0,  0.33)\text{chemical leavener reduction} = \operatorname{clamp}\!\left(\frac{A - 3000}{21000},\; 0,\; 0.33\right)
rise-time reduction=clamp⁡ ⁣(A−300020000,  0,  0.45)\text{rise-time reduction} = \operatorname{clamp}\!\left(\frac{A - 3000}{20000},\; 0,\; 0.45\right)

Adjustments scale continuously with elevation A (in feet) above a 3,000 ft threshold, rather than in discrete bands.

Liquid: +1 tbsp per 1,000 ft above 3,000 (capped at 5 tbsp). Sugar: −1 tbsp per 2,000 ft (capped at 3 tbsp). Oven: +15 °F, or +25 °F at/above 7,000 ft. Cake flour: +1 tbsp (≥ 5,000 ft: +2; ≥ 7,000 ft: +3).

Sources

  • Colorado State University Extension — high-altitude baking guidelines.
  • USDA — altitude adjustment principles.

Edge cases and limitations

  • Dramatic elevation changes (sea level to 7,500 ft within hours) require longer dough rest before baking.
  • Sourdough is more forgiving at altitude than commercial yeast; reduce starter percentage less aggressively.
  • Pressure cooker and steam-oven baking compresses these adjustments.

Butter to Oil Converter

Formula

substitute=amount×fsourceftarget\text{substitute} = \text{amount} \times \frac{f_{\text{source}}}{f_{\text{target}}}
Δwater=amount×wsource−substitute×wtarget\Delta\text{water} = \text{amount} \times w_{\text{source}} - \text{substitute} \times w_{\text{target}}

f and w are each fat's fat and water fractions. Butter is modelled at 80% fat / 16% water (US) and 82% / 15% (European-style); oils, shortening, lard, and ghee at 100% fat.

Salt correction for salted butter: 1.6% of butter weight.

Sources

  • USDA FoodData Central — butter and oil composition.
  • 21 U.S.C. 321a — US standard of identity for butter (80% milkfat minimum).
  • King Arthur Baking ingredient weight chart — volume densities.

Edge cases and limitations

  • The conversion matches fat content, not function. Creaming, cookie spread, flake, and lamination depend on solid fat and do not survive a swap to liquid oil.
  • Milk solids (~4% of butter) drive browning and flavour; no substitution recovers them.
  • Salted butter runs 1.2–2% salt by brand; the 1.6% correction is an industry average, not a guarantee.

Spot an error in a formula or a source? Get in touch via the About page. Dated changes to ranges, formulas, and citations appear on the changelog.