Methodology
How BakersMath calculators work
One canonical page covering the math behind every calculator on the site. Each section names the formula in plain 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.
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 + starter × (1 / (1 + starter_hydration/100)). total_water = target_hydration × total_flour − starter × (starter_hydration/100) / (1 + starter_hydration/100). Salt is salt_pct × total_flour.
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
peak_time = base_time × Q10^((22 − kitchen_temp_C) / 10), where base_time is 5 h for 1:1:1 and 10 h for 1:5:5 at 22°C, Q10 = 2.
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 : 1.25 : 1 (by weight). Sourdough substitution: starter at ~20% of flour weight, with starter flour and water subtracted from 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
ball_weight × ball_count = total_dough. flour = total_dough / (1 + hydration% + salt% + oil% + yeast%). Other ingredients = flour × their respective percentages.
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
ferment_time = base_time × Q10^((reference_temp − dough_temp) / 10), with Q10 = 2.
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
Hydration accounts for water in eggs (~75%) and butter (~16%). Yeast scales up 1.0–2.0% to overcome osmotic pressure from sugar and fat.
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.
Open the enriched dough calculator (brioche, challah, milk bread) →
Bagel Dough Calculator
Formula
Standard baker's percentage with malt syrup added in dough (1–3%) and in boil water (15–25 g/gal). Hydration ranges by style: NY 58–62%, Montreal 55–60%.
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
Layers per turn: letter fold = 3, book fold = 4. Total layers after n folds = product of fold types. Beurrage as percentage of détrempe flour: croissant 50–60%, danish 40–50%.
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.
Open the laminated dough calculator (croissant, danish, pain au chocolat) →
Poolish & Preferment Calculator
Formula
Preferment flour = preferment_pct × total_flour. Yeast in poolish: 0.05–0.2% of preferment flour. Final dough = total_flour × hydration − water_already_in_preferment − salt − final yeast.
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
Replace commercial yeast with starter at 15–25% of recipe flour. Subtract starter_flour and starter_water from recipe totals to maintain 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: 50 g flour + 50 g water. Days 2–4: feed 1:1:1 every 24 h. Day 5+: feed 1:2:2 every 12 h once activity is consistent.
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%.
Open the sourdough starter from scratch (calculator + day-by-day) →
Baking Weight Converter
Formula
weight_g = volume_cups × density_g_per_cup, with densities 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
Standard ratios apply uniformly: Fresh : ADY : Instant = 3 : 1.25 : 1.
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.
Open the yeast conversion (cross-listed with active dry, instant, fresh) →
Oven Temperature Converter
Formula
°F = °C × 9/5 + 32. °C = (°F − 32) × 5/9. Fan/convection offset: subtract 20°C (35°F) from the set temperature, or reduce bake time by 25%.
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
Each ingredient × (target_flour / 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 = target_pan_volume / original_pan_volume. Multiply every ingredient by the scale factor. Bake time adjustment: shallower −10–20%, deeper +10–20%.
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
Adjustments scale with elevation in three bands. Above 3,500 ft: yeast −25%, hydration +1–2%, oven +25°F. Above 5,000 ft: yeast −40%, hydration +2–4%. Above 7,500 ft: yeast −50%, hydration +3–5%, bake time −10%.
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.
Found a number that doesn't match your experience? Email hello@bakersmath.co with the calculator and the value you'd expect. Most discrepancies trace back to different measurement standards (spooned vs dipped flour is the most common). The changelog lists every reference-range update with the date and reason.