Atom Economy Calculator

Atom economy, introduced by Barry Trost in 1991, measures what fraction of the atoms in the reactants end up in the desired product rather than in waste byproducts. It is one of the twelve principles of green chemistry and a key metric for sustainable chemical process design.

Atom Economy = (MW of desired product / sum of MW of all products) × 100%

Trost wrote it the other way around, as the desired product over the total mass of the reactants. For a balanced equation the two totals are identical, since mass is conserved, so both forms give the same number. This page uses the products form because the byproducts are usually the easier side to write down.

A reaction that produces only the desired product and no byproducts has 100% atom economy. An addition reaction (A + B → AB) always achieves 100% atom economy because all atoms go into one product.

A substitution reaction is typically worse. For example, a Grignard reaction that produces the target alcohol plus magnesium halide byproduct might show 60-70% atom economy, since a significant portion of the atomic mass ends up in the salt that gets washed away.

Common atom economy ranges by reaction type:

• Addition reactions: 100% (no byproducts by definition)
• Rearrangement reactions: 100%
• Substitution reactions: 10-80%, depending on byproduct mass
• Elimination reactions: often low, because a small molecule is thrown away
• Condensation reactions: variable, often 85-95%

Worked example, chlorination of methane

CH₄ + 2Cl₂ → CH₂Cl₂ + 2HCl

Dichloromethane is the target at 84.93 g/mol. Hydrogen chloride is the byproduct, and there are two of them: 2 × 36.46 = 72.92 g/mol.

Atom economy = 84.93 / (84.93 + 72.92) × 100 = 53.8%

So even a reaction running at a perfect 100% yield throws away almost half the mass it consumed. Enter 84.93 and 72.92 above and you should see that figure.

Watch the coefficients. This is where most people get a wrong answer. If a byproduct comes out of the balanced equation with a coefficient in front of it, enter the coefficient times its molecular weight, not the bare molecular weight. Enter 36.46 for the example above and the calculator reports 70.0%, which makes the reaction look far greener than it is.

Atom economy is not the same as yield. A reaction with 100% atom economy but 50% yield still wastes half the material, and the two multiply: our worked example at a realistic 80% yield delivers 0.538 × 0.80 = 43% of the input mass as useful product. Industrial chemists optimize both together, and the combined figure is sometimes called reaction mass efficiency.

Barry Trost won the Presidential Green Chemistry Challenge Award partly for developing palladium-catalyzed reactions with high atom economy that replaced older, wasteful syntheses of pharmaceutical intermediates.