Atom Economy Calculator – How Much of Your Reactants Ends Up in the Product?
This atom economy calculator balances your chemical equation, lets you pick the product you want and reports the share of reactant mass that ends up in it. If you also enter the masses you actually used, it adds the real-world green chemistry metrics: reaction mass efficiency (RME), E-factor, process mass intensity (PMI) and carbon efficiency.
Atom economy: Trost's definition
Barry Trost introduced atom economy in 1991 as a way to judge a reaction by what it builds rather than by its yield alone. For a balanced equation the formula is:
AE = (νp · Mp) / Σ(νi · Mi) × 100
Here ν is the balanced coefficient and M the molar mass. Because mass is conserved, the reactant total equals the product total, and the tool shows both as a check. Scaling every coefficient by the same factor does not change the answer.
Atom economy versus yield
Yield tells you how well an experiment performed against its theoretical maximum. Atom economy tells you how high that maximum can ever be. A substitution such as making 1-bromobutane from butanol, sodium bromide and sulfuric acid can give a 100% yield and still have an atom economy below 50%, because sodium hydrogen sulfate and water are built into the equation as by-products. Addition, cycloaddition and rearrangement reactions reach 100% because every atom is kept.
From atom economy to RME
In practice you rarely use exact stoichiometric amounts. The experimental section breaks the final efficiency into three factors:
RME = ε × AE / SF
ε is the fractional yield, AE the atom economy and SF the stoichiometric factor, which is the mass of reactants you weighed divided by the mass the limiting reagent actually needed. SF is always at least 1, and it grows when you use an excess of a reagent. The waterfall chart shows how much each factor removes, in percentage points.
E-factor, PMI and carbon efficiency
Roger Sheldon's E-factor is the mass of waste per mass of product. The simple E-factor counts only unconverted reactant mass, while the complete E-factor adds solvents, water, catalysts and work-up chemicals. PMI, used by the ACS Green Chemistry Institute Pharmaceutical Roundtable, is the total input mass per mass of product, so PMI = complete E-factor + 1. Carbon efficiency is the fraction of carbon atoms in the reactants that ends up in the product.
Industry benchmarks
Sheldon's sector table (Green Chem. 2007, 9, 1273) gives order-of-magnitude E-factors: oil refining below 0.1, bulk chemicals about 1 to 5, fine chemicals 5 to 50 and pharmaceuticals 25 to 100 or more. The gauge places your simple and complete E-factors on this scale. The simple and complete split follows Roschangar and co-workers (Green Chem. 2015).
A classic case study
The Boots and BHC syntheses of ibuprofen are the standard teaching example. The older six-step Boots route is commonly quoted at an overall atom economy of about 40%, while the three-step BHC route reaches about 77%, and recovers its acetic acid by-product to go higher still. The gap is entirely a matter of route design, not yield.
How to use the calculator
- Type the equation, balanced or not, or load one of the examples.
- Choose the desired product. Tick co-products only if they are genuinely sold or reused.
- Read the atom economy, the mass-flow strip and the element chart that shows where the waste atoms sit.
- Switch on "I ran this reaction", enter masses, purity and auxiliaries, and read RME, E-factors and PMI.