Calculate the theoretical atom economy of any chemical reaction from molecular weights and stoichiometry.
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.
| 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.
| 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 |
| 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.
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 |
|---|
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 |
|---|
| 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. | |||||||
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References are sorted alphabetically by first author.
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.
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