The atom economy formula

The atom economy formula is percentage atom economy = (Mr of desired product ÷ sum of Mr of all reactants) × 100, using the balanced equation. It tells you what percentage of the mass of the starting materials ends up in the product you want, rather than in waste by-products. A reaction with only one product has an atom economy of 100%.

What is atom economy?

Atom economy, also called atom utilisation, measures how much of the starting materials end up as useful products. Atoms are never destroyed in a reaction, but they can end up in a product nobody wants. Making lime by heating limestone, for example, also gives off carbon dioxide: nearly half the mass of the limestone leaves as gas.

Reactions with a high atom economy waste less, use up fewer raw materials and create less to dispose of, which matters for sustainable development and for cost. That is why chemists comparing two ways of making the same product look at atom economy alongside yield, rate and energy use.

The atom economy formula

Both sides use the balancing numbers in the equation. If the equation makes 2 molecules of the product you want, use 2 × its Mr on the top. If it uses 3 molecules of a reactant, count 3 × that reactant's Mr on the bottom.

Because mass is conserved, the sum of the Mr of all reactants equals the sum of the Mr of all products. So you can also write the bottom line as the total Mr of all the products, which is a handy check.

How to calculate atom economy

1. Write the balanced equation.
2. Work out the Mr of each substance from the relative atomic masses on the periodic table. Our guide to relative formula mass shows how.
3. Multiply by the balancing numbers.
4. Divide the total Mr of the desired product by the total Mr of all the reactants.
5. Multiply by 100 to get a percentage.

Example 1: making lime from limestone

Calcium oxide (lime) is made by heating calcium carbonate: CaCO₃ → CaO + CO₂. Find the atom economy for making calcium oxide.

Mr values: CaCO₃ = 40 + 12 + 48 = 100, and CaO = 40 + 16 = 56.

So 56% of the mass of the limestone ends up as lime. The other 44% leaves as carbon dioxide.

Example 2: extracting iron

In a blast furnace, Fe₂O₃ + 3CO → 2Fe + 3CO₂. Find the atom economy for making iron. Use Fe = 56, C = 12, O = 16.

Reactants: Fe₂O₃ = 112 + 48 = 160, and 3CO = 3 × 28 = 84, so the total is 244. The desired product is 2Fe = 2 × 56 = 112.

Check: the products are 112 + 3 × 44 = 244, the same as the reactants.

Example 3: making hydrogen from methane

Most industrial hydrogen starts with methane and steam: CH₄ + H₂O → CO + 3H₂. Find the atom economy for hydrogen.

Reactants: 16 + 18 = 34. Desired product: 3H₂ = 3 × 2 = 6.

Very low, because most of the mass ends up in the carbon monoxide. If the carbon monoxide can be used or sold, the process wastes much less than the figure suggests: atom economy only counts the one product you name as desired.

Example 4: comparing two ways to make ethanol

Ethanol can be made by fermenting glucose, or by reacting ethene with steam.

Hydration of ethene has the higher atom economy, because ethanol is the only product. Fermentation wastes almost half the mass as carbon dioxide. But fermentation uses a renewable raw material, sugar, while ethene comes from crude oil, which is why atom economy alone never decides which method is best.

Here is a quick check.

Atom economy and percentage yield

Atom economy and percentage yield are both percentages and both measure efficiency, but they measure different things.

For example, if a reaction could make 5.6 g of calcium oxide but only 4.2 g is collected, the percentage yield is 4.2 ÷ 5.6 × 100 = 75%. The atom economy is still 56%, because that depends only on the equation. A good industrial process wants both to be high.

Common mistakes

• Ignoring the balancing numbers. In Fe₂O₃ + 3CO, the CO counts three times on the bottom, and 2Fe counts twice on the top.
• Putting the sum of the products on top. The top is only the desired product.
• Mixing up atom economy and percentage yield. Atom economy comes from the equation; yield comes from what you actually collect.
• Using masses from an experiment. Atom economy uses relative formula masses from the equation, not grams weighed in the lab.
• Using the wrong Ar. Use the values on your periodic table, such as 35.5 for chlorine and 63.5 for copper.
• Forgetting the units. Give the answer as a percentage.

Atom economy at GCSE

In AQA's GCSE Chemistry specification, checked in November 2026, you need to calculate the atom economy of a reaction to form a desired product from the balanced equation, and the specification gives the formula in the same form as above. Higher tier students also need to explain why a particular reaction pathway is chosen, given information about atom economy, yield, rate, equilibrium position and usefulness of by-products. Percentage yield is in the same section. The Stoichiometry Calculator works out masses from balanced equations, which helps when you need the theoretical yield.

Practise in a short timed paper

GCSE Chemistry Higher and A-level Chemistry: Year 1 each give you a short timed paper every day, with 8 questions worth 25 to 35 marks across the course. Atom economy and yield questions often come with a choice between two industrial methods.

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