Theoretical Yield Calculator

Background.

Drop zinc into a blue solution of copper(II) sulfate and the colour fades as a reddish-brown powder of copper metal settles out. Start with 1.274 g of copper sulfate and add zinc in excess, and the most copper that can possibly form is 0.5072 g. That ceiling is the theoretical yield, and it is fixed before you touch a beaker: by how much of the limiting reactant you used, by the coefficients of the balanced equation, and by the molar masses of the two substances.

The calculation is a chain of three conversions. Grams of reactant become moles by dividing by its molar mass. Moles of reactant become moles of product through the mole ratio, the product's coefficient divided by the reactant's. Moles of product become grams by multiplying by the product's molar mass. Only the middle step involves the chemistry of the reaction; the other two are bookkeeping between mass and amount of substance. Molar masses are worked out from the formulas you type, using the current IUPAC standard atomic weights, and every intermediate value is shown so that a wrong formula or a forgotten coefficient is visible rather than buried in the answer.

What you recover at the bench will be less. Reactions stop short of completion, side reactions divert some reactant elsewhere, and product is lost on the filter paper, in the washings and on the walls of the flask. In OpenStax's version of the copper experiment, 0.392 g was isolated against the 0.5072 g ceiling, a percent yield of about 77.3%, which is an ordinary result rather than a failure.

What is theoretical yield calculator?

Theoretical yield is the amount of product a reaction could produce from the amount of limiting reactant present, calculated from the stoichiometry of the balanced chemical equation. It is a calculated quantity, never a measured one. Formally it rests on the extent of reaction, ξ: for a balanced equation a A → p P, using up all of the limiting reactant A sets ξ = n(A) ⁄ a, and the product formed is n(P) = p × ξ = n(A) × p ⁄ a. Three assumptions are built in: every mole of the limiting reactant reacts, all of it goes to the product you named rather than to side products, and none of the product is lost in isolation. The measured mass divided by the theoretical yield, times 100, is the percent yield.

How to use this calculator.

1. 01Balance the equation on paper and decide which reactant runs out first. If two reactants could be limiting, settle it with the limiting reagent calculator; a reactant added in deliberate excess is never the limiting one.
2. 02Type the limiting reactant's formula in ordinary notation, minding capitals: Co is cobalt and CO is carbon monoxide. Parentheses are allowed, as in Al2(SO4)3, but dots, charges and state labels are not, so write a hydrate such as CuSO4·5H2O as CuSO4(H2O)5.
3. 03Enter that reactant's coefficient from the balanced equation and its mass in grams. For amounts below about a milligram, enter milligrams in the mass field and read every mass result as milligrams; the calculation is proportional, so the answer scales exactly.
4. 04Type the product's formula and its own coefficient. For 2 H2 + O2 → 2 H2O the water coefficient is 2.
5. 05Before trusting the theoretical yield, glance at the two molar masses and the mole ratio. A molar mass that disagrees with your own working points to a mistyped formula, and a mole ratio that is not p ⁄ a points to a coefficient error.
6. 06Report the theoretical yield to the significant figures of your balance reading, then take it with the mass you actually isolated to the percent yield calculator.

The formula.

For a balanced equation a A → p P with m(A) grams of limiting reactant, the three steps are n(A) = m(A) ⁄ M(A), then n(P) = n(A) × p ⁄ a, then m(P) = n(P) × M(P). The units run g ÷ g/mol = mol, then mol × a pure number = mol, then mol × g/mol = g. Collapsed into one line, m(P) = m(A) × (p ⁄ a) × M(P) ⁄ M(A).

The mole ratio p ⁄ a follows from the IUPAC definition of the extent of reaction. Every species changes by its stoichiometric number times the same extent ξ, negative for reactants and positive for products, so when A is used up, ξ = n(A) ⁄ a, and the product formed is p times that. The ratio is exact because both coefficients are pure numbers, and since the 2019 SI redefinition fixed the Avogadro constant at exactly 6.02214076 × 10²³ per mole, the mole itself is an exactly defined count.

The factor (p ⁄ a) × M(P) ⁄ M(A) is given separately as the mass ratio: grams of product per gram of reactant. For copper from copper(II) sulfate it is 0.3982, so every gram of the salt can give at most 0.3982 g of copper. Below 1 means the product is lighter than the reactant it came from, above 1 heavier, and once you know it, any starting mass times the ratio is the theoretical yield.

Molar masses are summed from the CIAAW abridged standard atomic weights, 2024 revision, so Cu is 63.546, S 32.06, O 15.999 and H 1.008. Elements without a standard atomic weight, such as technetium, radon and the elements beyond uranium, have no natural-abundance molar mass and are rejected. Coefficients need not be whole numbers, which allows equations written per mole of fuel.

Two things are taken on trust. The calculator does not know the rest of your equation, so it cannot check that it balances, and it does not know whether another reactant would run out sooner. Temperature and pressure play no part, because a mole balance holds under any conditions; that is why gases are entered as masses here.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Flowers, P., Theopold, K., Langley, R. & Robinson, W. R. (2019). Chemistry 2e, Section 4.4 'Reaction Yields'. OpenStax, Rice University. Peer-reviewed, CC BY 4.0. PRIMARY SOURCE: defines theoretical yield as 'the amount of product that may be produced by a reaction under specified conditions, as calculated per the stoichiometry of an appropriate balanced chemical equation', and works Example 4.13 (1.274 g CuSO4 -> 0.5072 g Cu), which is this page's worked example, plus Example 4.12 (2.00 g Si in 3 Si + 2 N2 -> Si3N4), used as an independent check. Retrieved 2026-07-29. Open access.
2. [2]IUPAC. Compendium of Chemical Terminology (the Gold Book), 'stoichiometric number, ν' (S06025). Sourced there to Pure Appl. Chem. 1996, 68, 149 ('A glossary of terms used in chemical kinetics, including reaction dynamics', IUPAC Recommendations 1996) at p. 187 and to the Green Book 2nd ed. p. 42: stoichiometric numbers are positive for products and negative for reactants, with dξ = dn_B / ν_B. It agrees with the textbook mass–mole–mass rule and shows the mole ratio p/a to be a consequence of a single extent of reaction rather than an independent postulate. Retrieved 2026-07-29 via the legacy IUPAC host (the current goldbook.iupac.org returns HTTP 403 to automated retrieval). Open access.
3. [3]IUPAC (2007). Quantities, Units and Symbols in Physical Chemistry ('the Green Book'), 3rd edition (2nd printing 2008), section 2.12 'Chemical reactions' — formal definitions of stoichiometric number, extent of reaction and amount of substance underpinning the mole-ratio step. International Union of Pure and Applied Chemistry / RSC Publishing. Retrieved 2026-07-29. Bibliographic reference: print and PDF edition rather than a live web page.
4. [4]Meija, J. et al. (2021). 'Atomic weights of the elements 2021 (IUPAC Technical Report)'. Pure and Applied Chemistry 93(5), 573–600, doi:10.1515/pac-2019-0603, as maintained in the CIAAW table 'Abridged Standard Atomic Weights 2024' (named revision: 2024, incorporating the Gd, Lu and Zr revisions on the Atomic Weights 2021 base). The named, versioned source of every molar mass this calculator computes — Cu 63.546, S 32.06, O 15.999, Si 28.085, N 14.007, H 1.0080. Retrieved 2026-07-29. Open access.
5. [5]BIPM (2019). The International System of Units (SI), 9th edition — the 2019 redefinition fixing the Avogadro constant at exactly 6.02214076 × 10^23 mol⁻¹, which is what makes 'amount of substance' an exactly defined base quantity and the mole ratio an exact rather than measured conversion. Bureau International des Poids et Mesures. Retrieved 2026-07-29. Open access.
6. [6]Constable, D. J. C., Curzons, A. D. & Cunningham, V. L. (2002). 'Metrics to "green" chemistry — which are the best?' Green Chemistry 4(6), 521–527, doi:10.1039/B206169B. Royal Society of Chemistry, peer-reviewed. Table 1 records measured yields across twenty-eight industrial reaction classes (71–96 %), the evidence for this page's statement that a theoretical yield is a ceiling routinely missed by 10–30 % even in optimised manufacturing. Retrieved 2026-07-29. Publisher page paywalled; an open copy was consulted.