Theoretical Yield Calculator

Limiting{{ resultsReady ? computation.values.limiting_reactant_names : '—' }} Product amount{{ resultsReady ? formatMoles(computation.values.theoretical_product_moles) : '—' }} Actual yield{{ formatNumber(computation.values.percent_yield) }}%

Balanced reaction:

Enter the approved balanced reaction and make every identity and coefficient below agree with it.

Balanced reaction verified:

Required after changing the reaction basis or reactant set. The calculator cannot verify conservation, identity, selectivity, conditions, or safety.

Product identity:

Name the product whose theoretical yield you need.

Product coefficient:

Use the coefficient for the selected product, not a formula subscript.

Product molar mass source:

Use a manual value when the simple formula is not the approved material basis.

Product formula:

Charges, isotope notation, and fractional stoichiometry are not inferred.

Product molar mass:

g/mol

Use the protocol, label, or certificate value for the exact material.

Reactants:

Enter 2–8 reactants. Each row is normalized to pure moles before comparing n / coefficient.

Reactant	Coefficient	Amount	Purity	Mass source	Formula / molar mass	Remove
Reactant {{ index + 1 }} identity	Reactant {{ index + 1 }} coefficient	Reactant {{ index + 1 }} amountReactant {{ index + 1 }} amount unit	Reactant {{ index + 1 }} purity%	Reactant {{ index + 1 }} molar mass source

Actual yield comparison:

The neutral default does not change theoretical yield.

Measured product amount:

Use the same product identity and material-form basis as the theoretical result.

Yield audit

Reaction extent: {{ formatMoles(computation.values.reaction_extent) }}
Theoretical product: {{ formatMass(computation.values.theoretical_product_mass_g) }}
Product molar mass: {{ formatNumber(computation.values.product_molar_mass_g_mol) }} g/mol

Calculation path

xi = min(n_i / nu_i); n(product) = xi x nu(product)

{{ row.label }}: {{ row.value }}{{ row.note }}

Scope: Calculation only. Verify identities, material forms, coefficients, units, purity, conditions, and protocol assumptions before practical use.

Species	Role	Pure amount	Coefficient	Extent	Consumed	Remaining / yield	Copy
{{ row.label }}	{{ row.role }}	{{ row.available }}	{{ row.coefficient }}	{{ row.extent }}	{{ row.consumed }}	{{ row.remaining }}

A balanced chemical equation is also a quantity map. Its coefficients state how many moles of each reactant are consumed for every mole-scale progress of the reaction and how many moles of product that progress can form. Theoretical yield is the maximum product amount predicted by that stoichiometric map when the supplied reactants follow the stated reaction completely.

When two or more reactants are supplied, the limiting reagent determines how far the reaction can proceed. Dividing each pure reactant amount in moles by its coefficient puts all reactants on a common basis. The smallest quotient is the reaction extent; any reactant with a larger quotient is in excess. If two quotients agree within calculation tolerance, the reactants are co-limiting.

Theoretical yield terms and practical meaning
Term	Meaning	Common source of error
Limiting reagent	Reactant with the smallest available moles per stoichiometric coefficient	Comparing masses directly instead of converting to moles
Theoretical yield	Product amount predicted from the limiting reaction extent	Using an unbalanced equation or the wrong product coefficient
Actual yield	Product amount measured after the real procedure	Comparing different chemical forms, hydration states, or purity bases
Percent yield	Actual yield divided by theoretical yield, expressed as a percentage	Treating a value above 100% as impossible instead of checking moisture, impurities, basis, or measurement

Mass entries need the molar mass of the exact material. Formula-based molar masses are convenient for ordinary neutral formulas, but a protocol may use a hydrate, salt form, solution basis, isotope-labelled material, or certified assay that needs a manual value. Purity also changes the available amount: 10 g at 80% purity contributes the same modeled reactant mass as 8 g of pure material.

Theoretical yield is a stoichiometric ceiling, not a prediction of isolated product. Equilibrium, incomplete conversion, side reactions, work-up losses, solvent or water retention, and analytical error can all separate actual yield from the calculation. Reaction identity, coefficients, conditions, material form, hazards, and protocol suitability must be verified independently before practical use.

How to Use This Tool:

Start from an approved balanced reaction and keep every identity, coefficient, and material basis consistent with it.

Enter the Balanced reaction, verify it outside the calculator, then select Balanced reaction verified. The text is a record of your basis, not an automatic equation check.
Name the selected product and enter its equation coefficient. Choose a formula-derived molar mass only when the simple formula represents the exact product form; otherwise enter the approved manual molar mass.
Add between two and eight reactants. For each one, enter its distinct identity, coefficient, supplied amount, unit, purity, and molar-mass basis.
Correct any identity, formula, amount, purity, or coefficient warning before using the result. Purity must be greater than 0% and no more than 100%.
Use Actual yield comparison only when the measured product uses the same identity and material-form basis as the theoretical result.
Review the limiting reagent, reaction extent, theoretical moles and mass, remaining excess, and optional percent yield together. A plausible number does not replace reaction and protocol verification.

Interpreting Results:

The limiting reagent is the reactant whose pure moles permit the smallest reaction extent. The theoretical product is calculated from that extent, while excess remaining is the unconsumed amount predicted for every non-limiting reactant. Zero remaining does not prove complete real-world consumption; it describes the balanced-equation model.

Percent yield compares measured product with that theoretical basis. Values below 100% are common, but the number alone does not identify the cause. A result above 100% calls for a basis check: wet or impure product, residual solvent, an incorrect molar mass, a different product form, an unbalanced equation, or measurement error can all raise the measured mass.

Technical Details:

Stoichiometric coefficients provide the conversion between reactant amount and reaction extent. Each entered mass is first converted to moles using the selected molar mass, then multiplied by its purity fraction. Amounts already entered in moles or millimoles do not require a molar-mass conversion, although the molar mass is still needed for remaining-mass and product-mass results.

Formula Core:

For reactant i, nᵢ is its gross amount in moles, qᵢ is purity in percent, and νᵢ is its positive stoichiometric coefficient. The smallest available extent ξ controls the product amount.

n_{pure,i} = n_{i} \times \frac{q_{i}}{100}

ξ = \min_{i} (\frac{n_{pure,i}}{ν_{i}})

n_{product} = ξ \times ν_{product}

m_{theoretical} = n_{product} \times M_{product}

percent yield = \frac{m_{actual}}{m_{theoretical}} \times 100 %

M is molar mass in g/mol. Mass units are normalized to grams and amount units to moles. Remaining moles equal pure supplied moles minus ξνᵢ; tiny residuals within the calculation tolerance are reported as zero. Reactants whose extents differ from the minimum by no more than the larger of 10⁻¹² mol and one-billionth of the extent are treated as co-limiting.

Material and Formula Rules:

Molar mass and amount handling rules
Input basis	Conversion	Important limit
mol	Used directly	Purity still scales the available moles
mmol	Divide by 1000	Keep coefficients dimensionless
kg, g, or mg	Convert to grams, then divide by molar mass	Molar mass must match the exact material form
Formula molar mass	Sum 2024 CIAAW abridged atomic weights from element counts	Charges, isotope notation, fractional stoichiometry, and non-simple material bases are not inferred
Manual molar mass	Use the entered positive g/mol value	Prefer the protocol, label, or certificate basis for hydrates, salts, formulations, or certified materials

The balanced-reaction text is not parsed to prove atom or charge conservation. Coefficients entered for the product and reactants are the numeric authority for the ledger, so they must be copied from the verified reaction without substituting formula subscripts.

Limitations and Safety:

The result is a calculation aid, not a reaction validator, procedure, hazard assessment, or guarantee of conversion and selectivity.

Verify the balanced equation, identities, coefficients, physical forms, purity values, conditions, and approved protocol before practical use.
Formula-derived molar masses use abridged standard atomic weights for normal materials; isotope-enriched or specially certified materials may need a different value.
The model does not include equilibrium, kinetics, side reactions, solvent, catalysts, recovery losses, analytical uncertainty, or scale-up hazards.
Use suitable chemical training, safety data, engineering controls, and institutional procedures for laboratory or process work.

Worked Examples:

Hydrogen-limited water calculation

For 2 H₂ + O₂ → 2 H₂O, enter 4 g H₂ and 32 g O₂ at 100% purity. Using formula molar masses, hydrogen permits an extent of about 0.99206 mol and is limiting. The theoretical water yield is about 1.98413 mol or 35.7440 g. A measured 30 g product on the same basis gives about 83.93% yield.

Co-limiting ammonia reactants

For N₂ + 3 H₂ → 2 NH₃, 1 mol N₂ and 3 mol H₂ both allow an extent of 1 mol. They are reported as co-limiting, and the equation predicts 2 mol NH₃, about 34.062 g on the formula-mass basis.

References:

Extent of reaction, IUPAC Compendium of Chemical Terminology, 5th edition, 2025.
Abridged Standard Atomic Weights 2024, Commission on Isotopic Abundances and Atomic Weights.
Reaction Yields, OpenStax Chemistry 2e.

Theoretical Yield Calculator

{{ summaryTitle }}

Reactants:

Yield audit

Calculation path

Introduction:

How to Use This Tool:

Interpreting Results:

Technical Details:

Formula Core:

Material and Formula Rules:

Limitations and Safety:

Worked Examples:

Hydrogen-limited water calculation

Co-limiting ammonia reactants

References: