Atom economy calculator.
Calculate the theoretical atom economy of any chemical reaction from molecular weights and stoichiometry.
What is atom economy — and why does it matter?
Atom economy (AE), introduced by Barry Trost in 1991, measures what fraction of the atoms in your starting materials end up in the desired product, and is the second principle of green chemistry. A reaction with high AE generates little intrinsic waste, regardless of how much product you actually isolate. It is a design-stage metric, calculated directly from the balanced equation before any experiment is run.
The formula
| Symbol | Term | Units |
|---|---|---|
| $\text{AE}$ | Atom Economy | % (dimensionless; ideal = 100%) |
| $\sum MW_{\text{desired}}$ | Sum of molar masses of desired product(s) × stoichiometric coefficients | g mol−1 |
| $\sum MW_{\text{reactants}}$ | Sum of molar masses of all consumed reactants × stoichiometric coefficients | g mol−1 |
Catalysts are excluded from the denominator — they are not consumed by the reaction. Stoichiometric coefficients are taken directly from the balanced equation, written in its simplest whole-number ratio. By-products reduce AE but are listed for mass-balance context.
AE by reaction type
| Reaction type | Comment |
|---|---|
| Addition / Cycloaddition (e.g. Diels–Alder) | ~100% AE as all reactant atoms incorporated into product |
| Rearrangement | ~100% AE as only bond rearrangement; no atoms lost |
| Substitution (SN2, SNAr) | Leaving group expelled as waste; AE is highly variable depending on the leaving group |
| Condensation (e.g. esterification) | Small molecule (H₂O etc.) lost as by-product; AE varies with the size of that by-product relative to the product |
| Elimination | HX or H₂O by-product generated; AE is highly variable |
| Oxidation / Reduction (stoichiometric) | Heavy oxidant/reductant becomes waste; AE is often low and highly variable |
Strengths and limitations
Strengths
- Calculable at the design stage before any experiment is performed
- Predictive: flags reactions where most atoms will become waste by design
- Drives innovation as AE encourages catalytic, addition, and rearrangement chemistry
- Aligns environmental and economic goals (less inherent waste = lower costs)
- Widely accepted; easy to communicate to non-specialists
Limitations
- Theoretical only as AE ignores actual yield and side-reaction by-products
- Does not account for solvents, excess reagents, or workup materials
- Treats all non-product atoms equally, regardless of toxicity or fate
- A 100% AE reaction can still have a poor E-factor if large solvent volumes are used
- Does not capture energy consumption or life-cycle impacts
AE in context: complementary green metrics
| Metric | What it measures | Stage |
|---|---|---|
| Atom Economy (AE) | Theoretical fraction of reactant mass incorporated into the desired product (from balanced equation) | Design |
| % Yield | Fraction of theoretical product actually isolated | Experimental |
| E-factor | Mass of all waste per mass of product (all inputs, real scale) | Experimental |
| PMI (Process Mass Intensity) | Total mass of all inputs per mass of product; PMI = E-factor + 1 | Experimental |
| RME (Reaction Mass Efficiency) | AE × yield × stoichiometric factor — combined practical efficiency | Both |
In the RME expression, the stoichiometric factor compensates for any reactant used in excess of the balanced equation as it corrects RME back down towards the reaction's true mass efficiency when reagents aren't used in exact stoichiometric ratio.
Experiment details
Reactants
Enter each consumed reactant with its molar mass and stoichiometric coefficient. Do not include catalysts — they are not consumed and should not appear in the AE denominator.
| Compound name | Formula (optional) | MW (g mol−1) | Coeff. | MW × n |
|---|
Products
Add the desired product(s) first, then any by-products. Only desired-product MW contributes to the AE numerator; by-products are shown for mass-balance context. Use the Role dropdown to switch between desired and by-product.
| Compound name | Formula (optional) | MW (g mol−1) | Coeff. | Role | MW × n |
|---|
Results (updates live)
Reactant mass contributions
Product vs. by-product / waste
Detailed breakdown & interpretation
| Compound | Role | Formula | MW (g mol−1) | Coeff. | MW × n | % of Σ reactants | Visual |
|---|---|---|---|---|---|---|---|
| Enter reactants and at least one desired product above to see breakdown. | |||||||
Interpretation & recommendations
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Export
Export your atom economy calculation as a PDF report or CSV data file. PDF opens in a new tab and uses your browser's print function. CSV downloads directly.
Where can I read more?
References are sorted alphabetically by first author.
- P. T. Anastas and J. C. Warner, Green Chemistry: Theory and Practice, Oxford University Press, 1998. ISBN 978-0-19-850698-0. — Original statement of the 12 Principles; atom economy is Principle 2.
- C. Jiménez-González et al., Org. Process Res. Dev., 2011, 15, 912–917. DOI. — Defines PMI and places AE in the broader context of green metrics.
- R. A. Sheldon, Pure Appl. Chem., 2000, 72, 1233–1246. DOI. — Atom efficiency and catalysis in organic synthesis; compares AE with E-factor.
- B. M. Trost, Science, 1991, 254, 1471–1477. DOI. — The original paper introducing atom economy.
- B. M. Trost, Angew. Chem. Int. Ed., 1995, 34, 259–281. DOI. — Atom economy as a challenge for organic synthesis; reaction-type analysis.
Contributors
Roles follow the CRediT taxonomy (Contributor Roles Taxonomy), adapted for educational software. Hover a contributor's name for a summary, or a column header for the definition of that role.
| Contributor |
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