Moles Calculator with Working

The relative formula mass of a substance, written Mr, is what you get when you add up the relative atomic masses (Ar) of every atom in its formula. To do it by hand, count the atoms of each element, multiply each count by that element’s Ar, and add the results. The calculator shows this as a table so you can see where every number comes from.

Two things catch people out. A small number after a bracket multiplies everything inside it, so Ca(OH)2 has one calcium, two oxygens and two hydrogens. And in a hydrate such as CuSO4.5H2O, the number after the dot multiplies the whole water part, so there are five lots of H2O to add in. The number in front of a formula in an equation, such as the 2 in 2MgO, is not part of its Mr: you use it later, as part of the ratio.

A mole is an amount of substance. The useful fact is that the mass of one mole of a substance, in grams, is the same number as its Mr. That is why one relationship does all the work: moles = mass ÷ Mr. Turn it round and you get mass = moles × Mr, and Mr = mass ÷ moles. If you cover up the thing you want in a triangle of m, n and Mr, the other two show you whether to multiply or divide, and the calculator does the same job and then shows the arithmetic.

Moles are worked out from a mass in grams. If your question gives kilograms, multiply by 1,000 first, and if it gives milligrams, divide by 1,000. The calculator has a unit box for this and shows the conversion as a separate step, because a missed conversion is one of the most common reasons for an answer that is a thousand times too big or too small.

A balanced equation has the same number of atoms of every element on both sides, because atoms are not made or destroyed in a reaction. The big numbers in front of the formulae then tell you the ratio of moles. In 4Al + 3O2 → 2Al2O3, four moles of aluminium go with two moles of aluminium oxide, a ratio of 4 : 2, which is 2 : 1.

To find the mass of one substance from the mass of another, work in moles in the middle. Turn the known mass into moles, use the ratio to find the moles of the substance you want, then turn those moles into a mass. The calculator checks the equation by atom count first. If it does not balance, it tells you which element is out and, when there is only one way to fix it, offers the balanced version. Balancing means changing the big numbers in front, never the small numbers inside a formula.

The boards print their own periodic tables. AQA and Edexcel give whole numbers for most elements, apart from chlorine at 35.5 and copper at 63.5. OCR gives every element to one decimal place, so magnesium is 24.3 and iron is 55.8. Because of this, the same question can give slightly different answers on different tables. Use the table that comes with your exam, and pick the same one in the calculator’s settings. If your question lists its own Ar values, type them in and they will be used instead.

The calculator keeps every value exactly and rounds only once, at the very end, so rounding part-way through never creeps into the answer. It starts at 3 significant figures because that is a common choice, but the specifications of all three boards list using an appropriate number of significant figures as a skill, so always give the accuracy your question asks for.

At Foundation tier, the part of this topic to know is the relative formula mass. You should be able to work out the Mr of a substance from its formula and the Ar values you are given, including formulae with brackets. On AQA and Edexcel you also use it to find the percentage by mass of an element in a compound. Writing and balancing equations, and the idea that mass is conserved, are also in every tier. Calculations with moles are not part of Foundation tier on any of the three boards, so on Foundation you can use the Mr table and the equation check, and leave the moles steps.

At Higher tier you also need moles: turning a mass into moles and back using the Mr. All three boards mark these calculations as Higher tier. Masses of reactants and products from a balanced equation are Higher tier on AQA and OCR, and Edexcel does not mark them as Higher, although the method uses moles, which it does. Showing each step is good practice: it makes your method clear, and it makes a slip much easier to find. Limiting reactants are a further Higher topic, and concentration in mol/dm³, gas volumes and percentage yield belong to separate Chemistry. None of those is in this calculator. Combined Science courses were not checked for this tool, so read your own specification or ask your teacher which tier you are entered for.