To calculate the atom economy, first write the balanced equation and pick out the desired product. Work out the relative formula mass (Mr) of the desired product, multiplying by the big number in front if there is one. Then work out the total Mr of all the reactants in the same way. Finally use: atom economy = (Mr of desired product / total Mr of reactants) x 100.
Example: heating calcium carbonate, CaCO3 → CaO + CO2, to make calcium oxide. With Ar values Ca = 40, C = 12 and O = 16, the Mr of CaCO3 is 100 and the Mr of CaO is 56. Atom economy = 56 / 100 x 100 = 56%. The other 44% of the mass is the carbon dioxide waste.
Example with a big number: Fe2O3 + 3CO → 2Fe + 3CO2, where iron is the desired product. The Mr of the two iron atoms is 2 x 56 = 112. The Mr of the reactants is 160 + (3 x 28) = 244. Atom economy = 112 / 244 x 100 = 45.9%, which is 46% to two significant figures. Check that your answer is between 0 and 100%.