Actual Yield and Theoretical Yield Formulas

Theoretical yield is the maximum amount of product predicted by a balanced chemical equation: theoretical yield = moles of limiting reactant × product-to-reactant mole ratio × product molar mass. Actual yield is the amount of product obtained in an experiment, measured and usually expressed in grams or moles; percent yield = (actual yield ÷ theoretical yield) × 100% compares the two.

Formula

The calculator reports percent yield, which relates the measured actual yield to the calculated theoretical yield:

Percent yield (%) = (actual yield ÷ theoretical yield) × 100%

• Actual yield, A: the mass of product collected or measured, in grams (g), entered as ar.
• Theoretical yield, T: the maximum product mass predicted from the reaction stoichiometry, in grams (g), entered as tr.
• Percent yield: actual yield divided by theoretical yield and multiplied by 100; it is a percentage, not a mass.

For a reaction calculation, the theoretical yield follows from the limiting reactant:

Theoretical yield (g) = moles of limiting reactant (mol) × (product coefficient ÷ limiting-reactant coefficient) × product molar mass (g/mol)

The coefficients come from the balanced equation. If starting material is given as a mass, first convert it to moles by dividing by its molar mass. When multiple reactants are supplied, calculate the possible product from each reactant; the reactant predicting the least product is limiting. This calculator takes the resulting actual and theoretical product masses as inputs rather than deriving stoichiometry from a reaction.

Worked Example

Using the calculator’s default inputs, actual yield is 8.50 g and theoretical yield is 10.00 g.

1. Divide actual yield by theoretical yield: 8.50 g ÷ 10.00 g = 0.85000.
2. Convert the ratio to a percentage: 0.85000 × 100 = 85.000%.
3. Rounded to the calculator’s two decimal places, the percent yield is 85.00%.

The gram units cancel in the division, leaving a dimensionless ratio. Multiplying by 100 expresses that ratio as a percentage.

Assumptions

• Actual and theoretical yields refer to the same product and use the same mass units.
• The theoretical yield was calculated from a correctly balanced equation and the true limiting reactant.
• Theoretical yield is greater than zero; the calculator accepts nonnegative input values, but a zero theoretical yield makes percent yield undefined.
• The calculator does not determine product purity, identify side reactions, or correct measurements for moisture or contamination.

How to Calculate Theoretical Yield

Theoretical yield is a stoichiometric prediction, not a measurement of what the experiment produced. To find it from reactant quantities:

1. Balance the chemical equation. Its coefficients establish the mole ratios between reactants and products.
2. Convert each known reactant amount to moles. For a mass, use moles = mass (g) ÷ molar mass (g/mol).
3. Identify the limiting reactant by calculating how much product each reactant could make. The smallest possible product amount sets the maximum.
4. Use the balanced-equation mole ratio to convert limiting-reactant moles into product moles, then multiply by the product molar mass to obtain grams.

For example, consider the balanced reaction 2H₂ + O₂ → 2H₂O. If 3.00 mol H₂ reacts with 2.00 mol O₂, the hydrogen could produce 3.00 mol H₂O, while the oxygen could produce 4.00 mol H₂O. Hydrogen is limiting. Using water’s molar mass of about 18.015 g/mol, the theoretical yield is 3.00 mol × 18.015 g/mol = 54.045 g, or about 54.0 g at three significant figures. An observed product mass can then be compared with that value.

Actual Yield, Percent Yield, and Interpretation

Actual yield is the quantity of product that was recovered or measured. It is ordinarily recorded after the product has been separated and weighed, with any necessary corrections specified by the experiment. A sample that contains solvent, unreacted material, or other impurities can have a measured mass that overstates the amount of the desired product.

Percent yield describes how actual yield compares with the theoretical maximum. A result of 85% means the measured product amount is 85% of the predicted maximum, provided both quantities refer to the same substance and basis. It does not mean that the product is 85% pure, nor does it directly measure reaction conversion or selectivity.

• A yield below 100% can reflect incomplete reaction, competing reactions, product lost during transfer or separation, or measurement and calculation errors.
• A yield near 100% means the isolated amount is close to the calculated maximum, but does not by itself establish purity.
• A calculated yield above 100% often indicates that the product is not dry or pure, the actual mass was recorded incorrectly, or the theoretical yield used an incorrect limiting reactant, equation, or unit.

A result over 100% is a warning to investigate, not proof that matter was created beyond the stoichiometric maximum. Keep unrounded values through intermediate calculations and round the final answer to a precision justified by the measurements.

Common Calculation Problems

The most consequential error is using the wrong limiting reactant. A balanced equation’s coefficients are mole ratios, not mass ratios; comparing reactant masses directly against coefficients does not identify the limiting reagent. Convert quantities to moles first and account for every reactant with a known amount.

Check that the actual and theoretical yields refer to the same product and units. If one value is in milligrams and the other in grams, convert before dividing. Also distinguish product mass from reactant mass: percent yield uses the mass of product obtained, not the mass of starting material consumed.

Percent yield is not the same as percent conversion. Conversion concerns how much of a reactant was consumed; yield concerns the product obtained relative to the theoretical amount. In reactions that can form multiple products, selectivity may also matter, because the desired product can be a small fraction of the converted material.

Frequently Asked Questions

What is the formula for actual yield?
Actual yield is the measured amount of product obtained from a reaction, usually reported as a mass or amount of substance. It is not calculated from the balanced equation alone; it comes from the experimental measurement.

How do you calculate theoretical yield?
Find the limiting reactant, use the balanced equation’s mole ratio to calculate product moles, and multiply by the product’s molar mass if the answer is wanted in grams.

What is the formula for percent yield?
Percent yield = (actual yield ÷ theoretical yield) × 100%. Use matching product quantities and units for both yields.

Can percent yield be greater than 100%?
A reported value can exceed 100%, but it is not a physically meaningful indication that the reaction surpassed its stoichiometric maximum. Wet or impure product, measurement errors, or an incorrect theoretical-yield calculation are common causes.

Is percent yield the same as purity?
No. Percent yield compares the amount obtained with the amount theoretically possible. Purity describes the proportion of a sample that is the desired substance; a high yield does not guarantee a pure product.

For bench work, follow your lab method, the safety data sheet (SDS), and your supervisor.

Related

• Empirical Formula Calculator and Calculation Table
• Theoretical Yield Formula and Worked Example
• Percent Yield Formula in Chemistry: Calculate Reaction Yield

in ar | Actual yield | g | 8.50 | 0
in tr | Theoretical yield | g | 10.00 | 0
out py | Percent yield | % | ar / tr * 100 | 2