Percent Yield Calculator

The percent yield formula

Percent yield = Actual ÷ Theoretical × 100(1)

The actual yield is what you collected and weighed at the end of the experiment. The theoretical yield is the most the balanced equation allows from the limiting reactant — the amount you would get if nothing were lost. Both must be in the same unit: grams with grams, or moles with moles. Mixing them (or mg with g) is the classic way to get a yield far over 100%. To convert, 1 g = 1000 mg, 1 kg = 1000 g and 1 tonne = 1000 kg. You can type the unit after each number (4.2 g) as long as both boxes use the same one; if they differ, the calculator shows the conversion instead of an answer.

Collecting 2.45 g of product against a theoretical 3.10 g: 2.45 ÷ 3.10 ≈ 0.7903, so the percent yield is 79.03%. Report it to the precision of your measurements, usually as many significant figures as the least precise mass: 4.20 g of 5.00 g is 84.0%, three significant figures. The calculator drops trailing zeros (84%) until you choose a Decimals setting inside “Show steps”; then it prints exactly that many places (84.0% at 1).

A worked example

Type 4.9 and 5.6 into the calculator — the first example chip — to see the same working, with the 12.5% that was not recovered.

Theoretical yield: where it comes from

The theoretical yield is worked out from the balanced equation, before the experiment:

1. Balance the equation.
2. Convert the mass of each reactant to moles (mass ÷ molar mass).
3. Find the limiting reactant: divide each reactant’s moles by its coefficient in the equation — the smallest result runs out first.
4. Use the mole ratio to get the moles of product the limiting reactant can make.
5. Multiply by the product’s molar mass to get the theoretical yield in grams.

This calculator takes the theoretical yield as an input; it does not do the stoichiometry. Work it out first, then enter it beside the mass you collected.

Finding actual or theoretical yield from a percent

Rearrange the formula. To find the actual yield, multiply the theoretical yield by the percent ÷ 100: an 80% yield of a theoretical 9.00 g is 0.80 × 9.00 = 7.20 g, and 85% of 15 g is 12.75 g. Enter 7.2 and 9 above and the calculator gives back 80%.

To find the theoretical yield from the actual yield and a percent, divide: 7.20 ÷ 0.80 = 9.00 g. That is the question “7.2 is 80% of what number?”, which the X is Y% of what number calculator answers exactly.

When percent yield is over 100%

It is a real result, and the calculator never caps it. A product cannot contain more of itself than the reactants allow, so a yield over 100% means the mass you weighed includes something else: water or solvent that was not dried off, impurities or unreacted starting material, or a slip in weighing or transferring — or, in a calculator, the two amounts typed into each other’s boxes. Collecting 5.40 g against a theoretical 5.00 g is 108% — dry the product and weigh it again.

Far over 100% — 150%, 1000% — usually means the two numbers are in different units (mg and g, or grams against moles) or the theoretical yield itself is wrong. Exactly 100% is rare, not impossible.

Why yields are below 100%

• The reaction does not go to completion, or it is reversible.
• Side reactions turn some of the reactants into other products.
• Product is lost when it is transferred, filtered or crystallised.
• Some product stays dissolved in the solution.

Each of these lowers the mass you collect; the theoretical yield assumes none of them happen. That gap is what the calculator reports as “not recovered”.

Percentage yield at GCSE

“Percentage yield” is the UK name for the same quantity, and UK specifications write it in terms of mass: the mass of product actually made, divided by the maximum theoretical mass, times 100. The calculator works the same way for either name.

It is often asked beside atom economy, and the two answer different questions: atom economy is decided by the equation, before anything is weighed; percentage yield is decided by the experiment.

Percent yield, percent error and atom economy

Below 100%, the percent error of your yield against the theoretical yield is simply 100 minus the percent yield: 2.45 g against 3.10 g is a 79.03% yield and a 20.97% error, which the percent error calculator gives directly. Atom economy is fixed by the equation — for calcium oxide from calcium carbonate it is 56 ÷ 100 × 100 = 56%. For how a percentage change differs from a percentage difference, see the percentage difference calculator.

Percent yield in Excel or Google Sheets

With the actual yield in A1 and the theoretical yield in B1, enter =A1/B1 and format the cell as a percentage, or =A1/B1*100 for a plain number. Fill it down a column to get the yield of every run at once.