Atom Economy Calculator

Background.

Make styrene by a Wittig reaction, benzaldehyde plus the phosphorus ylide Ph₃P=CH₂, and even a perfect 100% yield sends 278.291 g of triphenylphosphine oxide to waste for every 104.152 g of styrene. No improvement in technique can change that; it is written into the equation. Atom economy is the number that exposes it. Barry Trost proposed the measure in Science in 1991: the share of the reactants' mass that ends up in the product you actually want. For the Wittig step above it is 27.23%.

The calculation needs only a balanced equation and a table of atomic weights, so it can be done before anyone goes near a flask. That is its use: comparing routes to the same molecule at the planning stage, when swapping a stoichiometric reagent for a catalyst or an addition for a substitution is still cheap. It became the second of Anastas and Warner's twelve Principles of Green Chemistry, which the US EPA phrases as designing syntheses so the final product contains the maximum proportion of the starting materials.

What atom economy leaves out matters as much as what it measures. It assumes exact stoichiometric amounts and a theoretical yield, and it ignores solvents, work-up chemicals, excess reagent and energy. A route with 100% atom economy run at low yield in a large volume of solvent is not a clean process, which is why chemists report atom economy alongside percent yield and Sheldon's E factor rather than instead of them.

What is atom economy calculator?

Atom economy, also called atom efficiency, is the mass of the desired product formed by one balanced equation divided by the total mass of the reactants that equation consumes, expressed as a percentage. It describes the route rather than any particular run of it: two chemists following the same equation get the same figure however well either of them works. Trost and later Constable, Curzons and Cunningham write the denominator as the sum of the reactants; Sheldon writes it as the sum of everything produced. For a balanced equation the two sums are equal, because mass is conserved, so the definitions agree.

How to use this calculator.

1. 01Balance the equation first and decide which single product you want. Every other product counts as by-product, even if it is useful elsewhere.
2. 02Type the desired product's formula in Hill-style notation (C2H4O, Ca(OH)2; symbols are case sensitive) and enter its coefficient from the balanced equation. Leaving the coefficient at 1 when the equation says 2 halves the answer.
3. 03List every reactant as a coefficient followed by a formula, separated by commas or new lines, such as 1 C2H4, 0.5 O2. A reactant written without a coefficient is taken as 1.
4. 04Include reagents consumed in stoichiometric amounts, including acids or bases used for hydrolysis. Leave out true catalysts and solvents, which do not appear in the stoichiometric equation.
5. 05Check that the reactants-counted figure matches the number you meant to enter, then read the atom economy, the by-product mass and the stoichiometric E factor together.

The formula.

AE = (ν_P × M_P) ÷ Σ(ν_i × M_i) × 100, where ν_P and M_P are the coefficient and molar mass of the desired product and each ν_i, M_i pair belongs to one reactant. Molar masses are built from the CIAAW Abridged Standard Atomic Weights 2024 (C 12.011, H 1.008, O 15.999, Cl 35.45, Ca 40.078, S 32.06). Both sums are grams per one equation as written, so the ratio is dimensionless. Scaling every coefficient by the same factor leaves the result unchanged, which is why fractional coefficients such as ½O₂ work. The coefficient on the product is where mistakes creep in: 2 H₂ + O₂ → 2 H₂O gives 36.03 g of water from 36.03 g of reactants, exactly 100%, but entering the product coefficient as 1 gives 50%. By-product mass is the reactant total minus the product mass. The stoichiometric E factor, (100 − AE) ÷ AE, is that by-product expressed per kilogram of product, the smallest waste figure the equation allows before solvent, work-up or yield losses are added. A value above 100% cannot happen for a balanced equation, so it is reported rather than capped: it means a reactant is missing or a coefficient is wrong, and the by-product mass turns negative at the same time.

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. 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 reproduced by this calculator. 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.