The percent yield calculator above compares the amount of product a reaction actually delivered with the maximum the balanced equation allows. You can enter a theoretical yield directly if you already have it, or let the tool derive it from the mass of the limiting reactant, the two molar masses and the mole ratio taken from the balanced equation. Either way the headline number is the percentage, and the grid shows the shortfall in grams and the amount of product formed in moles.
Arb Digital builds free calculators that answer the question behind the question. Percent yield itself is a one-line division; the part that goes wrong is the theoretical yield, which depends on identifying the limiting reactant correctly and using the mole ratio rather than the mass ratio. This page keeps that derivation on screen so the final percentage is traceable rather than assumed.
What This Percent Yield Calculator Does
In direct mode it divides an actual yield by a theoretical yield and multiplies by a hundred. In stoichiometric mode it first converts the limiting reactant mass to moles, applies the mole ratio from the balanced equation, converts back to grams of product, and only then does the division. The second route is the one most homework problems and most laboratory reports need.
The grid reports the theoretical yield in grams, the shortfall between theoretical and actual, the moles of product formed, and the mass you would need to isolate in order to hit a percentage you specify. That last figure is genuinely useful when planning: if you need 5 g of product and you know the reaction typically runs at 70 percent, it tells you how much starting material to put in.
The defaults model the thermal decomposition of calcium carbonate to calcium oxide, a one-to-one reaction with a 100.09 g/mol reactant and a 56.08 g/mol product. Ten grams of the carbonate gives a theoretical 5.60 g of the oxide, so recovering 4.8 g is a percent yield of 85.7.
How to Use It
- Identify the limiting reactant first. Convert each reactant mass to moles, divide by its coefficient, and the smallest result is the one that runs out.
- Enter the coefficients from the balanced equation — the reactant's and the product's. If the equation is not balanced, balance it before you start.
- Supply both molar masses. They come from the formulae, not from the masses you weighed.
- Enter the actual yield as the dry, purified mass you weighed at the end.
- Use the target percentage box when you are planning a run rather than reporting one.
The Formula and How It Is Calculated
Percent yield is (actual / theoretical) × 100. The theoretical yield comes from a three-step conversion: moles of limiting reactant = mass / molar mass, moles of product = moles of reactant × (product coefficient / reactant coefficient), and theoretical mass = moles of product × product molar mass.
Working the default: 10 g divided by 100.09 g/mol is 0.09991 mol of calcium carbonate. The one-to-one ratio makes that 0.09991 mol of calcium oxide, which at 56.08 g/mol is 5.603 g. An actual yield of 4.8 g divided by 5.603 and multiplied by a hundred gives 85.7 percent. The molar masses are sums of standard atomic weights from the IUPAC Commission on Isotopic Abundances and Atomic Weights table, the same conventional values distributed in the NIST atomic weights and isotopic compositions database.
Why the Limiting Reactant Is Not the Smallest Mass
This is the error that costs the most marks and produces the most silently wrong laboratory reports. The limiting reactant is the one that runs out first in molar terms after the coefficients are applied, and mass says almost nothing about that directly.
Consider hydrogen reacting with oxygen to make water, where two moles of hydrogen need one mole of oxygen. Two grams of hydrogen is 0.99 mol; sixteen grams of oxygen is 0.50 mol. The oxygen weighs eight times more and is still very nearly the limiting reactant, because hydrogen molecules are so light that a small mass is a large amount. Comparing 2 g against 16 g and concluding that hydrogen limits the reaction gives an answer that is wrong by a factor of two.
The reliable method is to divide each reactant's moles by its coefficient and take the smallest quotient. Dividing by the coefficient is the step people skip. In a reaction needing three moles of one reagent for every one of another, having equal moles of both does not mean neither limits — the one with the coefficient of three runs out first.
What a Percent Yield Above 100 Really Means
Conservation of mass is not negotiable, so a genuine yield above the theoretical maximum is impossible. When the number comes out above 100, one of a small set of explanations applies, and all of them are worth checking before the figure goes into a report.
The most common is residual solvent. A product that has not been dried to constant mass carries water or organic solvent, and both weigh something. Drying to constant mass — weighing, drying again, reweighing until the reading stops changing — exists precisely to catch this. The second is contamination with unreacted starting material or an inorganic salt that co-precipitated, which is why a melting point or a spectrum accompanies a yield in any serious write-up.
Third is an arithmetic error in the theoretical yield, usually a wrong molar mass or an unbalanced equation. Fourth, and rarer, is a mistaken limiting reactant: if you used the wrong one, the theoretical yield is too low and the percentage inflates accordingly. A yield of 105 percent is a signal to recheck the calculation, not a result.
Theoretical, Actual and Atom Economy Are Three Different Measures
Percent yield tells you how much of the possible product you recovered. It says nothing about how much of the starting material ended up in the product rather than in by-products, and that is a separate and often more revealing measure called atom economy.
Atom economy is the mass of the desired product divided by the total mass of everything on the reactant side, expressed as a percentage. A reaction can have a percent yield of 95 and an atom economy of 30, meaning almost all of the achievable product was recovered but most of the mass fed in left as waste. An addition reaction where every atom of the reactants appears in the product has an atom economy of 100 percent by design; an elimination reaction never can.
The two numbers answer different questions. Percent yield measures how well the process was executed. Atom economy measures how well the reaction was chosen. Reporting only the first, which is the norm in teaching laboratories, hides the second entirely.
Where Yield Calculations Sit in a Workflow
Everything upstream of this page is stoichiometry. The chemical equation balancer gives the coefficients, the molar mass calculator gives the two g/mol figures, and the moles to grams calculator handles the conversions if you would rather do them one at a time and see each step.
If the reaction happens in solution, the amount of limiting reactant usually comes from a concentration and a volume rather than from a balance, which is the molarity calculator's job, and the titration calculator covers the case where the amount is determined by titration. For comparing a measured value against an accepted one in a report, the percent error calculator is the right tool — percent yield and percent error are different quantities and should not be swapped.
Arb Digital publishes hundreds of free calculators across chemistry, maths, finance and marketing — no sign-up, no limits. If something you need is missing, tell us and we will look at building it.
Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Choosing the limiting reactant by mass — convert to moles and divide by the coefficient first, or a light reagent will fool you.
- Using an unbalanced equation — the mole ratio comes from the coefficients, so an unbalanced equation gives a wrong theoretical yield with no visible symptom.
- Weighing a wet product — residual solvent inflates the actual yield and is the usual cause of a result above 100 percent.
- Applying the mass ratio instead of the mole ratio — coefficients count particles, not grams, and the two ratios coincide only by accident.
- Confusing percent yield with percent error — one compares output to a theoretical maximum, the other compares a measurement to an accepted value.
Related Free Tools From Arb Digital
Balance the reaction first with the chemical equation balancer, get molar masses from the molar mass calculator, and convert amounts with the moles to grams calculator. For solution-phase work the molarity calculator supplies the amount of limiting reactant, and the percentage calculator covers general percentage arithmetic outside chemistry. The full free online tools hub lists everything else.
Frequently Asked Questions
Divide the actual yield by the theoretical yield and multiply by one hundred. Both masses must be for the same product and in the same unit. Recovering 4.8 g when the equation allows 5.60 g is a percent yield of 85.7.
It is the maximum mass of product the balanced equation permits from the limiting reactant, assuming the reaction goes to completion and nothing is lost. It is calculated by converting the reactant mass to moles, applying the mole ratio, and converting back to grams.
Convert each reactant mass to moles, divide each result by that reactant's coefficient in the balanced equation, and the smallest quotient identifies the limiting reactant. Comparing masses directly is unreliable because molar masses differ widely.
Not genuinely. A figure above 100 means the product was still wet, contained unreacted starting material or impurities, or the theoretical yield was miscalculated. Drying to constant mass removes the most common cause.
It depends entirely on the reaction. Simple precipitations often exceed 90 percent, while multi-step organic syntheses may be considered successful at 40. The useful comparison is against published results for the same transformation, not against a universal benchmark.
Percent yield measures how much of the achievable product you recovered. Atom economy measures what fraction of the reactant mass ends up in the desired product rather than in by-products. A reaction can score well on one and poorly on the other.
Either, as long as both figures use the same one. Since actual and theoretical refer to the same product with the same molar mass, the molar mass cancels and the ratio is identical whichever quantity you use.
This calculator is provided for education and general reference. It describes how yield is computed and is not laboratory, safety or handling guidance; follow the procedures and risk assessments issued by your own institution.
