- Calculation purpose
- Express ingredient share
- Numerator
- Ingredient mass m, in g
- Denominator
- Total initial mix mass M, in g
- Equation
- Percentage = 100 × m ÷ M
- Conditions
- Count each weighed ingredient once
CHEFSQUIRE
Formula Basis & Mass Balance
Calculate ingredient and component contributions with explicit mass denominators. Match Ice Cream & Sorbet Calculator inputs to the ingredient composition and coefficient conventions.
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| Concept | Calculation purpose | Numerator | Denominator | Equation | Conditions | Sources |
|---|---|---|---|---|---|---|
| Express ingredient share | Ingredient mass m, in g | Total initial mix mass M, in g | Percentage = 100 × m ÷ M | Count each weighed ingredient once | [1] | |
| Calculate fat, sugar or another component | Sum of ingredient grams × component fraction | Total formula grams M | Component % = 100 × Σ(mᵢ × xᵢ) ÷ M | xᵢ is g component per g ingredient as sold | [1] | |
| Close a compatible composition balance | Water mass or total solids mass | Same ingredient or formula mass | Water % + total solids % = 100% | Use a defined analytical partition | [1][2] | |
| Track dairy nonfat material | Dairy-origin MSNF grams | Total formula grams M | MSNF % = 100 × MSNF grams ÷ M | Lactose, milk proteins and minerals sit inside MSNF | [1][2] | |
| Convert compatible dry-matter assay | Component mass in dry matter | As-sold ingredient mass | x(as sold) = D × x(dry basis) | D is g defined dry matter per g as sold | [1][2] | |
| Supply a target solids mass | Required grams of named solids | Grams named solids per gram syrup | Syrup grams = target solids grams ÷ solids fraction | Obtain total solids separately if targeting one sugar | [1][2] | |
| Calculate ideal anhydrous equivalent | Anhydrous formula mass A, in g/mol | Hydrate formula mass H, in g/mol | Equivalent grams = hydrate grams × A ÷ H | Exact hydrate and assay basis required | [1][2][3] | |
| Express overall flour-based ratios | Ingredient grams m | Total flour grams F, including preferments | Baker’s % = 100 × m ÷ F | Declare which ingredients count as flour | [1] | |
| Preserve initial ingredient proportions | Target initial batch mass | Original initial batch mass | Scale factor = target ÷ original; new m = old m × factor | Composition and processing need separate checks | [1][2] | |
| Convert with matched density | Mass m, in g | Volume V, in mL | Density ρ = m ÷ V; mass = ρ × V | Product, temperature and physical state must match | [1][2] | |
| Compare sweetness on a declared scale | Sum of component grams × coefficient r | Total mix grams M | Index = 100 × Σ(mᵢ × rᵢ) ÷ M | Choose sucrose = 1 for r; coefficients must share basis | [1][2] | |
| Compare model freezing effects | Sum of dissolved-solute grams × model factor q | Total mix grams M | Index = 100 × Σ(mᵢ × qᵢ) ÷ M | Choose sucrose = 1 for q; state included solutes | [1][2][3][4] | |
| Describe reducing power of a starch hydrolysate | Reducing sugars expressed as dextrose mass | Total dry sample mass | DE = 100 × dextrose-equivalent reducing mass ÷ dry mass | Use the named product’s assay method | [1][2] | |
| Read a sucrose-calibrated optical value | Grams sucrose in the pure-sucrose reference solution | 100 g reference sucrose solution | Pure sucrose solution: °Bx = g sucrose per 100 g solution | Mixed foods give apparent Brix | [1] |
Mass fractions use grams per gram; percentages use grams per 100 g. Hypothetical examples illustrate arithmetic only. A complete mass balance counts every component once and preserves unknown values.
- Calculation purpose
- Calculate fat, sugar or another component
- Numerator
- Sum of ingredient grams × component fraction
- Denominator
- Total formula grams M
- Equation
- Component % = 100 × Σ(mᵢ × xᵢ) ÷ M
- Conditions
- xᵢ is g component per g ingredient as sold
- Calculation purpose
- Close a compatible composition balance
- Numerator
- Water mass or total solids mass
- Denominator
- Same ingredient or formula mass
- Equation
- Water % + total solids % = 100%
- Conditions
- Use a defined analytical partition
- Calculation purpose
- Track dairy nonfat material
- Numerator
- Dairy-origin MSNF grams
- Denominator
- Total formula grams M
- Equation
- MSNF % = 100 × MSNF grams ÷ M
- Conditions
- Lactose, milk proteins and minerals sit inside MSNF
- Calculation purpose
- Convert compatible dry-matter assay
- Numerator
- Component mass in dry matter
- Denominator
- As-sold ingredient mass
- Equation
- x(as sold) = D × x(dry basis)
- Conditions
- D is g defined dry matter per g as sold
- Calculation purpose
- Supply a target solids mass
- Numerator
- Required grams of named solids
- Denominator
- Grams named solids per gram syrup
- Equation
- Syrup grams = target solids grams ÷ solids fraction
- Conditions
- Obtain total solids separately if targeting one sugar
- Calculation purpose
- Calculate ideal anhydrous equivalent
- Numerator
- Anhydrous formula mass A, in g/mol
- Denominator
- Hydrate formula mass H, in g/mol
- Equation
- Equivalent grams = hydrate grams × A ÷ H
- Conditions
- Exact hydrate and assay basis required
- Calculation purpose
- Express overall flour-based ratios
- Numerator
- Ingredient grams m
- Denominator
- Total flour grams F, including preferments
- Equation
- Baker’s % = 100 × m ÷ F
- Conditions
- Declare which ingredients count as flour
- Calculation purpose
- Preserve initial ingredient proportions
- Numerator
- Target initial batch mass
- Denominator
- Original initial batch mass
- Equation
- Scale factor = target ÷ original; new m = old m × factor
- Conditions
- Composition and processing need separate checks
- Calculation purpose
- Convert with matched density
- Numerator
- Mass m, in g
- Denominator
- Volume V, in mL
- Equation
- Density ρ = m ÷ V; mass = ρ × V
- Conditions
- Product, temperature and physical state must match
- Calculation purpose
- Compare sweetness on a declared scale
- Numerator
- Sum of component grams × coefficient r
- Denominator
- Total mix grams M
- Equation
- Index = 100 × Σ(mᵢ × rᵢ) ÷ M
- Conditions
- Choose sucrose = 1 for r; coefficients must share basis
- Calculation purpose
- Compare model freezing effects
- Numerator
- Sum of dissolved-solute grams × model factor q
- Denominator
- Total mix grams M
- Equation
- Index = 100 × Σ(mᵢ × qᵢ) ÷ M
- Conditions
- Choose sucrose = 1 for q; state included solutes
- Calculation purpose
- Describe reducing power of a starch hydrolysate
- Numerator
- Reducing sugars expressed as dextrose mass
- Denominator
- Total dry sample mass
- Equation
- DE = 100 × dextrose-equivalent reducing mass ÷ dry mass
- Conditions
- Use the named product’s assay method
- Calculation purpose
- Read a sucrose-calibrated optical value
- Numerator
- Grams sucrose in the pure-sucrose reference solution
- Denominator
- 100 g reference sucrose solution
- Equation
- Pure sucrose solution: °Bx = g sucrose per 100 g solution
- Conditions
- Mixed foods give apparent Brix
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Total-formula mass percentage
- Calculation purpose
- Express ingredient share
- Numerator
- Ingredient mass m, in g
- Denominator
- Total initial mix mass M, in g
- Equation
- Percentage = 100 × m ÷ M
- Conditions
- Count each weighed ingredient once
- Definition
- M is the sum of all ingredient masses at the stated formulation stage. An ingredient’s mass percentage uses that complete mass as its denominator.
- Illustration
- Hypothetical arithmetic: 150 g ingredient in a 1,000 g initial mix contributes 15% of the mix mass. Heating losses require a new final-mass denominator.
Component contribution
- Calculation purpose
- Calculate fat, sugar or another component
- Numerator
- Sum of ingredient grams × component fraction
- Denominator
- Total formula grams M
- Equation
- Component % = 100 × Σ(mᵢ × xᵢ) ÷ M
- Conditions
- xᵢ is g component per g ingredient as sold
- Compound ingredients
- Cream, sweetened condensed milk and syrup each supply several components. Count the ingredient once in the weighing list, then allocate its component masses using compatible as-sold composition.
- Illustration
- Hypothetical ingredient: 200 g at 8 g fat per 100 g as sold supplies 200 × 0.08 = 16 g fat. In a 1,000 g mix, that contribution is 1.6% fat. The ingredient composition is hypothetical and identifies no commercial product.
Water and total solids
- Calculation purpose
- Close a compatible composition balance
- Numerator
- Water mass or total solids mass
- Denominator
- Same ingredient or formula mass
- Equation
- Water % + total solids % = 100%
- Conditions
- Use a defined analytical partition
- Component hierarchy
- Total solids include fat, dairy nonfat solids, added sweetener solids and other non-water material. Sum mutually exclusive categories. Missing composition leaves the balance unresolved; keep unknown component amounts separate from zero.
- Method boundary
- Drying and moisture methods define the water/solids partition. Apply water = 100 − total solids only for the same material and compatible basis; volatile ingredients and crystal-water conventions can require a separate account.
Milk solids-not-fat
- Calculation purpose
- Track dairy nonfat material
- Numerator
- Dairy-origin MSNF grams
- Denominator
- Total formula grams M
- Equation
- MSNF % = 100 × MSNF grams ÷ M
- Conditions
- Lactose, milk proteins and minerals sit inside MSNF
- Nested components
- Milk solids-not-fat contains lactose, caseins, whey proteins and milk minerals. Report their individual contributions when known, while counting their parent MSNF only once in the total-solids balance.
- Sweetened dairy
- Added sucrose in sweetened condensed milk belongs in a separate sugar account. Total solids minus fat yields MSNF only when the remaining solids consist entirely of dairy nonfat material.
- Illustration
- Hypothetical complete ingredient: 8 g fat + 20 g MSNF + 45 g added sugar + 27 g water = 100 g. Total solids are 73 g; adding lactose and milk protein again would double-count portions of the 20 g MSNF.
Dry-basis to as-sold composition
- Calculation purpose
- Convert compatible dry-matter assay
- Numerator
- Component mass in dry matter
- Denominator
- As-sold ingredient mass
- Equation
- x(as sold) = D × x(dry basis)
- Conditions
- D is g defined dry matter per g as sold
- Required basis
- The dry-matter definition must match the assay denominator. For ingredient mass m, component grams = m × D × x(dry basis). A dry residue can contain several substances, so dry matter and analyte purity need separate values.
- Illustration
- Hypothetical ingredient with D = 0.96 and a component fraction of 0.50 on that dry basis has 0.48 g component per gram as sold. A 100 g portion contributes 48 g. Specification endpoints describe allowable composition bounds; lot measurements establish actual results.
Syrup solids and water
- Calculation purpose
- Supply a target solids mass
- Numerator
- Required grams of named solids
- Denominator
- Grams named solids per gram syrup
- Equation
- Syrup grams = target solids grams ÷ solids fraction
- Conditions
- Obtain total solids separately if targeting one sugar
- Illustration
- Hypothetical syrup at 80% total solids: 100 g syrup supplies 80 g solids and 20 g water on a compatible mass basis. A target of 160 g total solids requires 200 g syrup and introduces 40 g water.
- Sugar identity
- Total solids establishes the total dry fraction. A sucrose or glucose target additionally needs that sugar’s fraction; apparent Brix alone cannot provide it in an arbitrary mixture.
Hydrated crystals
- Calculation purpose
- Calculate ideal anhydrous equivalent
- Numerator
- Anhydrous formula mass A, in g/mol
- Denominator
- Hydrate formula mass H, in g/mol
- Equation
- Equivalent grams = hydrate grams × A ÷ H
- Conditions
- Exact hydrate and assay basis required
- Crystal water
- A named hydrate includes stoichiometric water in its formula mass. Use the exact form and supplier assay basis before assigning an anhydrous equivalent; avoid a second water correction when the stated assay already accounts for it.
- Citrate example
- Ideal pure trisodium citrate dihydrate: A = 258.07 g/mol and H = 294.10 g/mol. Thus 10 g × 258.07 ÷ 294.10 ≈ 8.775 g anhydrous equivalent. Actual product composition requires its assay and water data.
- Dairy convention
- Codex milk-powder accounting places lactose water of crystallization within MSNF and excludes it from the stated water limit. Preserve that definition alongside any separate chemical-water calculation.
Baker’s percentage
- Calculation purpose
- Express overall flour-based ratios
- Numerator
- Ingredient grams m
- Denominator
- Total flour grams F, including preferments
- Equation
- Baker’s % = 100 × m ÷ F
- Conditions
- Declare which ingredients count as flour
- Preferment accounting
- For overall flour and water totals, break a preferment into its component masses. Its assembled mass can remain one weighing instruction; its flour and water belong in the overall ratios.
- Illustration
- Hypothetical flour-and-water mixture: 1,000 g flour + 650 g water = 1,650 g. Water is 65% of flour mass and approximately 39.39% of total mix mass. The flour-basis percentages sum to 165%.
Proportional batch scaling
- Calculation purpose
- Preserve initial ingredient proportions
- Numerator
- Target initial batch mass
- Denominator
- Original initial batch mass
- Equation
- Scale factor = target ÷ original; new m = old m × factor
- Conditions
- Composition and processing need separate checks
- Illustration
- Scale the hypothetical 1,650 g flour-and-water mixture to 2,475 g: factor = 1.5. Flour becomes 1,500 g and water 975 g; the new masses sum to 2,475 g.
- Process
- The mass factor preserves starting ingredient proportions. Mixing, heating, evaporation, aeration and cooling have their own equipment- and batch-dependent conditions; measure final yield separately.
Mass and volume basis
- Calculation purpose
- Convert with matched density
- Numerator
- Mass m, in g
- Denominator
- Volume V, in mL
- Equation
- Density ρ = m ÷ V; mass = ρ × V
- Conditions
- Product, temperature and physical state must match
- Ingredient data
- A nutrient value per 100 mL needs a compatible density to become a value per 100 g. If density or a measured serving mass is unavailable, keep the original volume denominator.
- Frozen desserts
- Aeration changes volume and density. Gram-based composition uses ingredient and product masses; serving volume requires its own density or overrun measurement.
Relative sweetness and POD
- Calculation purpose
- Compare sweetness on a declared scale
- Numerator
- Sum of component grams × coefficient r
- Denominator
- Total mix grams M
- Equation
- Index = 100 × Σ(mᵢ × rᵢ) ÷ M
- Conditions
- Choose sucrose = 1 for r; coefficients must share basis
- Convention
- For a mass-normalized POD convention, calculate sucrose-equivalent grams per 100 g mix. Convert a sucrose = 100 coefficient to r by dividing by 100; declare whether lactose and other sweeteners enter the sum.
- Sensory basis
- Aqueous relative sweetness compares a sweetener with sucrose at equal concentration. Temperature, concentration and viscosity affect the comparison. A calculated mix index carries those coefficient limits; finished-dessert sweetness requires sensory evaluation.
- Syrups
- Use component or compatible dry-solids grams when the coefficient describes dry material. Applying that coefficient to the entire syrup mass would include its water as sweetener.
Freezing index and PAC
- Calculation purpose
- Compare model freezing effects
- Numerator
- Sum of dissolved-solute grams × model factor q
- Denominator
- Total mix grams M
- Equation
- Index = 100 × Σ(mᵢ × qᵢ) ÷ M
- Conditions
- Choose sucrose = 1 for q; state included solutes
- Model basis
- A mass-normalized PAC index expresses one formulation convention for comparative freezing effects; it gives no temperature in degrees Celsius. Ingredient form, water content and model solute treatment govern eligible factors.
- Physical distinction
- Ideal dilute freezing-point depression uses solute molality: moles of dissolved solute per kilogram of solvent water. During freezing, ice formation concentrates the unfrozen phase. A PAC total alone determines neither a freezing curve nor a serving-hardness measurement.
- Input compatibility
- Match ingredient masses, composition and coefficients to the Ice Cream & Sorbet Calculators’ input definitions. Keep ingredient composition, sweetness, freezing estimates and observed texture as separate quantities.
Dextrose equivalent
- Calculation purpose
- Describe reducing power of a starch hydrolysate
- Numerator
- Reducing sugars expressed as dextrose mass
- Denominator
- Total dry sample mass
- Equation
- DE = 100 × dextrose-equivalent reducing mass ÷ dry mass
- Conditions
- Use the named product’s assay method
- Interpretation
- DE describes reducing power on a dry basis. Different saccharide mixtures can share one DE. DE alone determines neither glucose composition nor a complete sweetness or freezing coefficient.
- Product basis
- Identify a DE value as a lot measurement, typical value or specification range. A syrup also requires its as-sold solids fraction for gram-based component accounting.
Refractometric Brix
- Calculation purpose
- Read a sucrose-calibrated optical value
- Numerator
- Grams sucrose in the pure-sucrose reference solution
- Denominator
- 100 g reference sucrose solution
- Equation
- Pure sucrose solution: °Bx = g sucrose per 100 g solution
- Conditions
- Mixed foods give apparent Brix
- Measurement
- A refractometer measures refractive index and converts it through a sucrose scale. Temperature, calibration and liquid composition affect interpretation.
- Mixed foods
- Acids, salts and other solutes affect the reading. Treat a mixed-food result as apparent Brix unless a product-specific relationship supports conversion to sugar or solids mass. Fat and insoluble material further separate whole-food solids from the optical liquid-phase measurement.