Atom Economy Calculator

Background.

Atom economy asks a question percent yield cannot: of all the atoms you put into a reaction, what fraction ends up in the molecule you actually wanted? A reaction can give a 99 percent yield and still be grotesquely wasteful, if the stoichiometry throws most of the reactants' mass away as by-product. Barry Trost introduced the metric in Science in 1991 to make that waste visible at the point where it is decided — the choice of route — rather than at the point where it is measured.

The calculation is one division. Take the molar mass of the desired product multiplied by its coefficient in the balanced equation, divide by the sum of coefficient times molar mass over every reactant, and multiply by 100. Nothing else is needed, and in particular no experiment is needed: as Sheldon puts it, the strength of atom economy is that 'it can be applied without the need for experimentation', which makes it a route-selection tool rather than a report card.

WHAT IT DELIBERATELY IGNORES — state this whenever you quote the number. Atom economy assumes exact stoichiometric quantities of starting materials and a theoretical chemical yield, and it disregards substances such as solvents and auxiliary chemicals that do not appear in the stoichiometric equation. So it says nothing about yield, nothing about the molar excess you actually charged, nothing about the fifty volumes of DMF, nothing about the aqueous work-up, and nothing about energy. A 100 percent atom-economical reaction run at 20 percent yield in a solvent-heavy process is not a green process. Atom economy and percent yield are complementary, not alternatives, and the mass-efficiency metrics that combine them — reaction mass efficiency, process mass intensity, Sheldon's E factor — exist precisely because neither is sufficient alone.

UNITS AND CONVENTIONS. Molar masses are in g/mol and the two mass outputs are quoted per one equation as written, hence 'g/mol-eq'. Atom economy is a percentage and the stoichiometric E factor is a dimensionless mass ratio quoted as kg of by-product per kg of product. There is no temperature or pressure basis: atom economy is fixed by the balanced equation alone. Catalysts are excluded because they are not consumed and do not appear in the stoichiometric equation; reagents used in stoichiometric quantities are included, even when a paper calls them catalysts. Molar masses come from the CIAAW Abridged Standard Atomic Weights 2024 table.

TWO PHRASINGS OF THE SAME DEFINITION, both correct, recorded here because they look different. Trost, and Constable, Curzons and Cunningham after him, define atom economy against the REACTANTS — 'a calculation of how much of the reactants remain in the final product'. Sheldon defines it against the PRODUCTS — 'dividing the molecular weight of the desired product by the sum of the molecular weights of all substances produced in the stoichiometric equation'. For a balanced equation these are identical, because mass is conserved and the two sums are equal. This calculator uses the reactant sum, which needs only the reactants you already know.

HOW TO READ THE RESULT. Only addition and rearrangement reactions can reach 100 percent; substitution and elimination cannot, because they necessarily expel a leaving group. In the GSK survey of industrial fine-chemicals reactions, individual reaction classes run from about 64 percent for an N-dealkylation up to 100 percent for a salt formation, and across 38 multi-stage pharmaceutical processes the overall atom economy averaged 43 percent with a range of 21 to 86 percent. So a figure in the 40s is normal for real synthesis rather than a failure. The lever that moves it most is replacing a stoichiometric reagent with a catalyst: a catalyst is not consumed, so its entire mass leaves the denominator.

AN IMPOSSIBLE RESULT IS INFORMATION. A value above 100 percent cannot happen for a balanced equation, because the product cannot outweigh everything that made it. The calculator reports it anyway, with a negative by-product mass, and tells you what it means — almost always a missing reactant or a wrong coefficient. Clamping it at 100 would hide the diagnosis.

What is atom economy calculator?

Atom economy — also called atom efficiency or atom utilisation — is a green-chemistry metric introduced by Barry Trost in Science in 1991 and now enshrined as the second of the twelve Principles of Green Chemistry: 'design syntheses so that the final product contains the maximum proportion of the starting materials; waste few or no atoms.' Formally, percentage atom economy is the molar mass of the desired product (times its stoichiometric coefficient) divided by the sum of the molar masses of all reactants (each times its coefficient), expressed as a percentage. It is a property of the EQUATION, not of a run: two chemists using the same route get the same atom economy no matter how skilfully either of them works. That is its point. Percent yield measures how well you executed a route; atom economy measures whether the route was worth executing. A Wittig olefination has an excellent yield and a poor atom economy, because triphenylphosphine oxide — heavier than the alkene you wanted — leaves the reaction as waste every single time, and no amount of technique can change that. The metric also has a natural companion. If a fraction AE of the reactant mass reaches the product, the remainder becomes by-product, so the theoretical minimum waste per unit of product is (100 − AE)/AE. That is the stoichiometric floor of Sheldon's E factor, the kilograms of waste per kilogram of product that has become the standard industrial measure. The real E factor is always larger, because it counts solvent losses, water, work-up chemicals and yield losses — in pharmaceuticals manufacture, solvents and water alone account for the great majority of process waste.

How to use this calculator.

1. 01Balance your equation on paper first, and decide which single product you actually want. Everything else it produces is by-product by definition.
2. 02Enter the desired product's formula and — this is the step people skip — its coefficient from the balanced equation.
3. 03List every reactant as 'coefficient formula', separated by commas or new lines. Leave the coefficient out and 1 is assumed.
4. 04Include reagents that are consumed in stoichiometric quantities, even ones a paper loosely calls catalysts. Exclude true catalysts and all solvents: they do not appear in the stoichiometric equation.
5. 05Read the atom economy at the top and the by-product mass below it. The by-product figure is often the more actionable one — it is the mass a route change would have to eliminate.
6. 06Check the 'reactants counted' output against how many you meant to enter, in case a separator typo swallowed one.
7. 07If the answer comes out above 100 percent, the equation is not balanced. Recheck the coefficients and make sure no reactant is missing.
8. 08Quote the number with its caveats: atom economy assumes exact stoichiometry and a theoretical yield, and ignores solvent, work-up and energy. Pair it with percent yield, never substitute it.

The formula.

For a balanced equation Σ ν_i A_i → ν_P P + by-products,

AE = ( ν_P × M_P ) / Σ_i ( ν_i × M_i ) × 100 %

The numerator is the mass of the desired product formed by one equation as written; the denominator is the mass of everything charged to make it. Both are in grams per mole of equation, so AE is dimensionless and is quoted in percent.

THE PRODUCT COEFFICIENT MATTERS AND IS EASY TO DROP. For 2 H₂ + O₂ → 2 H₂O, one equation makes TWO moles of water: 2 × 18.015 = 36.030 against a reactant sum of 2 × 2.016 + 31.998 = 36.030, giving exactly 100 percent. Enter the product coefficient as 1 and the answer halves to 50 percent, with nothing on screen to warn you.

WHY MASS CONSERVATION MAKES THE TWO PUBLISHED PHRASINGS EQUIVALENT. Trost and Constable et al. define the denominator as the sum over reactants; Sheldon defines it as the sum over all substances produced. For a balanced equation Σ(reactant masses) = Σ(product masses) exactly, so the two give the same number. In the worked example below, the reactants sum to 173.046 g/mol-eq and the products — C₂H₄O 44.053, CaCl₂ 110.978, H₂O 18.015 — also sum to 173.046. This calculator uses the reactant form because it needs only what you already know, and because it is the phrasing of the originating paper.

THE STOICHIOMETRIC E FACTOR. If a fraction AE/100 of the input mass reaches the product, the rest becomes by-product, so by-product per unit product is (100 − AE)/AE. That is reported as the stoichiometric E factor in kg/kg. It is a FLOOR, not an estimate: Sheldon's E factor is the actual waste produced and includes solvent losses, water, work-up chemicals and everything lost to less-than-quantitative yield. The real figure for a pharmaceutical process is routinely one to two orders of magnitude above this floor.

WHAT COUNTS AS A REACTANT. Constable et al. state the convention: a reactant is a substance of which some part is incorporated into a reaction product, and 'catalysts' used in stoichiometric quantities, or an acid or base used for hydrolysis, are counted as reactants. True catalysts, which are not consumed, and solvents, which do not appear in the stoichiometric equation, are excluded. Judgement calls here move the number substantially, so state your inclusions whenever you quote an atom economy.

ROUNDING STAGE. No intermediate rounding. Every molar mass, the reactant sum, the ratio and the E factor are carried at arbitrary decimal precision and each returned value is rounded once, at the return boundary, to ten decimal places. The assessment band is selected from the unrounded percentage, so the label can never disagree with the number at a boundary.

INVALID DOMAIN. A zero or negative product coefficient, an empty or unreadable reactant list, a reactant coefficient of zero or less, an unknown element symbol, an unbalanced parenthesis, and elements with no IUPAC standard atomic weight each raise a field error naming the fault. A result above 100 percent is NOT refused: it is reported, with a negative by-product mass, because the only way to get one is an unbalanced equation and saying so is more useful than hiding it.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Trost, B. M. (1991). 'The Atom Economy — A Search for Synthetic Efficiency'. Science 254(5037), 1471–1477, doi:10.1126/science.1962206. PRIMARY SOURCE: the paper that introduced the metric, defining it as the fraction of reactant atoms appearing in the product and arguing that methods combining building blocks with any additional reagent needed only catalytically represent the highest atom economy. Retrieved 2026-07-29. Publisher page paywalled; the record, abstract and DOI are open, and the definition is independently restated in the two open sources below.
2. [2]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. SECOND, INDEPENDENT AUTHORITY consulted for this page. States the definition against the REACTANTS ('atom economy is a calculation of how much of the reactants remain in the final product'), states the assumptions ('kept deliberately simple by making certain key assumptions, ignoring reaction yield and molar excesses of reactants... does not account for solvents and reagents'), gives the inclusion rule for stoichiometric reagents versus catalysts, and supplies both the reference figures used in this page's assessment bands — Table 1 (atom economy by reaction class, 64–100%) and Table 2 (38 multi-stage processes, overall AE averaging 43%, range 21–86%). Its worked example (benzyl alcohol FW 108.1 + tosyl chloride FW 190.65 → sulfonate ester FW 262.29 + HCl) is this calculator's independent test case. Retrieved 2026-07-29. Publisher page paywalled; an open copy was consulted.
3. [3]Sheldon, R. A. (2018). 'Metrics of Green Chemistry and Sustainability: Past, Present, and Future'. ACS Sustainable Chemistry & Engineering 6(1), 32–48, doi:10.1021/acssuschemeng.7b03505. Peer-reviewed; the author's TU Delft repository copy is open access. RECORDED SOURCE VARIATION: Sheldon phrases the denominator as the sum of the molecular weights of all substances PRODUCED in the stoichiometric equation, where Trost and Constable phrase it as the reactants. For a balanced equation the two are identical by conservation of mass, and this page demonstrates that identity in its worked example. Sheldon is also the source for the statement that 'AE is a theoretical number which assumes the use of exact stoichiometric quantities of starting materials and a theoretical chemical yield and disregards substances, such as solvents and auxiliary chemicals which do not appear in the stoichiometric equation', and for the E-factor definition and its solvent-dominated composition. Retrieved 2026-07-29.
4. [4]US Environmental Protection Agency, 'Basics of Green Chemistry' — the 12 Principles of Green Chemistry of Anastas and Warner, of which Principle 2 is 'Maximize Atom Economy: design syntheses so that the final product contains the maximum proportion of the starting materials. Waste few or no atoms.' Page last updated 29 January 2026; retrieved 2026-07-29. Open access, US government publication.
5. [5]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 — C 12.011, H 1.0080, O 15.999, Cl 35.45, Ca 40.078, S 32.06. Retrieved 2026-07-29. Open access.