Chemical Yield Calculator for Theoretical and Percent Yield
Solve actual yield, theoretical yield or percent yield. You can also enter balanced-equation coefficients, reactant amounts and molar masses to identify the limiting reactant and calculate the maximum product amount.
- Direct three-variable solver
- Limiting-reactant analysis
- Mass and mole conversions
- Exact stoichiometric arithmetic
Online Theoretical and Percent Yield Calculator
Use direct yield mode when the theoretical result is already known. Use reaction stoichiometry mode when you need to find it from available reactants and a balanced chemical equation.
Actual yield compared with the theoretical maximum.
Calculation Details
Yield Breakdown
| Quantity | Entered or available | Converted value | Result note |
|---|
Calculation Steps
How to Use This Chemical Yield Calculator
- Choose a calculation mode. Use the direct solver when two of actual yield, theoretical yield and percent yield are known, or use reaction stoichiometry to derive the theoretical yield.
- Select a compatible basis. Compare mass with mass or amount of substance with amount of substance. The stoichiometry mode uses molar mass when it must convert between them.
- Enter the known yield values. In direct mode, select the missing variable and enter the other two positive or nonnegative values as allowed.
- Use a balanced equation. In stoichiometry mode, enter the product and reactant coefficients from one correctly balanced chemical equation.
- Describe every reactant. Enter its available mass or amount, unit and molar mass when mass must be converted to moles.
- Add actual product if known. An optional actual product amount lets the reaction mode calculate percent yield after finding the theoretical maximum.
- Review the full result. Check the limiting reactant, theoretical product, remaining excess amounts, substitutions, units and any warning before using the value.
Actual, Theoretical and Percent Yield Formulas
Theoretical yield is the maximum amount of the specified product predicted by the stoichiometry of the balanced equation for the supplied reactants. Actual yield is the experimentally obtained amount of that product. Percent yield compares the two:
The inverse forms are equally useful:
Actual and theoretical yield must describe the same chemical product and the same quantity basis. Grams and kilograms are compatible mass units. Millimoles and moles are compatible amount-of-substance units. A mass cannot be divided directly by an amount in moles. A product molar mass is needed to bridge those bases.
How Theoretical Yield Is Found from Reactants
Start with a balanced reaction. Let ni be the available amount of reactant i in moles and νi its positive stoichiometric coefficient. Each reactant supplies a possible reaction extent:
The smallest value is the limiting one. If two or more values are exactly equal, those reactants are co-limiting for the entered data. If νP is the product coefficient, the theoretical amount of product is:
For a mass result, multiply the theoretical product amount by its molar mass MP:
The same reaction extent shows how much of each excess reactant remains. The consumed amount is extent × coefficient, and the remaining amount is available moles minus consumed moles. This is an ideal stoichiometric balance. It does not model equilibrium, kinetics, side reactions, purity, conversion or losses during isolation.
Worked Limiting-Reactant and Yield Example
Consider N2 + 3H2 → 2NH3. Suppose 28.014 g of N2 and 6.048 g of H2 are available. Using molar masses 28.014 g/mol and 2.016 g/mol gives 1 mol N2 and 3 mol H2.
Divide each amount by its coefficient:
Both reactants provide the same reaction extent, so they are co-limiting for these exact inputs. The balanced equation produces 2 mol NH3. With a product molar mass of 17.031 g/mol, the theoretical mass is 34.062 g. If 30 g is isolated, then:
Measured inputs usually have limited significant figures. The calculator retains exact entered decimals internally and rounds only the displayed result, but the reported laboratory value should still reflect the precision and uncertainty of the measurements.
Units, Moles and Molar Mass
Reaction coefficients relate amounts of substance, not raw gram values. A mass input therefore follows n = m/M. The tool converts the entered mass to grams and divides by the entered molar mass in grams per mole. An amount input is converted directly to moles.
| Basis | Supported units | Internal working unit | Important rule |
|---|---|---|---|
| Mass | ng, µg, mg, g, kg, avoirdupois oz and lb | Gram | Use active mass of the specified substance. Correct for assay, purity, solvent or inert material before entry. |
| Amount of substance | pmol, nmol, µmol, mmol, mol and kmol | Mole | Specify the chemical entity represented by the mole value. |
| Molar mass | g/mol | Gram per mole | Use the correct formula, hydration or solvation state, and isotopic-composition convention. |
Avoirdupois ounce and pound conversions follow the exact international pound definition. Molar masses entered from a periodic table are normally rounded measured values, so an exact calculator conversion does not make the underlying molar mass exact.
Direct mode intentionally compares mass or amount of substance, not volume. For gas-volume data, first convert volume to amount of substance using a relationship appropriate to the gas and conditions. Any direct comparison of actual and theoretical gas volumes must use the same temperature and pressure.
How to Interpret Percent Yield
A result below 100% does not by itself identify the cause. The reaction may be incomplete, a competing reaction may consume material, product may remain in solution, or transfers, filtration, washing, drying and purification may reduce the isolated amount.
A result above 100% is mathematically valid input, but it requires review. Common causes include residual solvent or water, impurities, weighing or transcription error, an incorrect product identity, an incorrect molar mass, an unbalanced equation, a wrong limiting reactant assumption or actual and theoretical values placed on different purity bases. The calculator shows the result and adds a warning rather than forcing it below 100%.
Percent yield is not the same as reactant conversion, selectivity or atom economy. Conversion describes how much reactant was consumed. Selectivity describes how product formation is distributed among possible products. Atom economy evaluates how the balanced equation directs reactant atoms into the desired product. One number must not be substituted for another.
Assumptions, Validation and Common Mistakes
- Balance the reaction before entering coefficients. Multiplying every coefficient by the same positive factor does not change the result, but an inconsistent coefficient changes the stoichiometric ratios.
- Include every reactant that can limit formation of the chosen product. Leaving out a scarce reactant can overstate theoretical yield. A one-reactant result assumes all unlisted required reactants are available in excess.
- Use the amount of reactive substance. Correct for assay, concentration, hydration, solvent or inert material before entry when the measured sample is not pure reactant.
- Use one defined product. If several products form, select the desired product and its coefficient from the balanced equation.
- Do not treat a catalyst or solvent as a stoichiometric reactant unless the balanced model actually consumes it.
- A theoretical yield assumes complete consumption of the limiting reactant according to the chosen reaction and allows excess reactants to remain. It does not predict reaction rate, equilibrium position, selectivity or isolated recovery.
- Zero actual yield is allowed when percent or actual yield is being calculated. Theoretical yield and divisors must remain positive in direct mode.
Related Calculators
Use these connected tools for molar mass, solution concentration and supporting unit calculations.
Chemical Yield Calculator FAQs
What is the formula for percent yield?
Percent yield equals actual yield divided by theoretical yield, multiplied by 100%. Both yields must refer to the same product and use compatible quantity units.
What is theoretical yield?
Theoretical yield is the amount of a specified product predicted from the supplied reactants and the stoichiometry of a balanced equation under the assumed complete-reaction model.
How does the calculator find the limiting reactant?
It converts each available reactant amount to moles, divides by that reactant’s coefficient and selects the smallest exact ratio. Equal smallest ratios are reported as co-limiting.
Can percent yield be more than 100%?
The arithmetic can exceed 100%, but the inputs or sample require review. Moisture, solvent, impurities, measurement error, wrong molar mass, wrong stoichiometry or mismatched purity bases can raise the apparent yield.
Can I compare grams with moles directly?
No. Convert mass to amount of substance with the product molar mass, or compare both yields on a mass basis. The calculator only crosses these bases when a molar mass is supplied.
Why must the chemical equation be balanced?
The coefficients define the mole ratios between reactants and products. An unbalanced or inconsistently scaled equation gives incorrect limiting-reactant and theoretical-yield results.
What does co-limiting mean?
Two or more reactants are co-limiting when their available mole amounts divided by their coefficients are exactly equal. Under the entered model, they are consumed together at the same reaction extent.
Does theoretical yield include purity or conversion losses?
No. Correct the entered reactive amount for purity when needed. The theoretical model assumes complete consumption of the limiting reactant according to the chosen reaction and allows excess reactants to remain.
Is percent yield the same as conversion or atom economy?
No. Percent yield compares obtained and theoretical product. Conversion tracks reactant consumption, while atom economy evaluates how the balanced equation incorporates reactant atoms into the desired product.
Should I use this result as a laboratory instruction?
No. Use it for education and preliminary checking. Verify the reaction, hazards, quantities, purity, equipment, significant figures and procedure with approved sources and qualified supervision.
Method and Review Basis
The calculator uses the standard actual-to-theoretical yield relationship and balanced-equation limiting-reactant method. Definitions, amount-of-substance units and mass conversions were reviewed against current official and educational references.
- OpenStax Chemistry 2e: Reaction Yields
- OpenStax Chemistry 2e: Limiting Reactant and Theoretical Yield Terms
- IUPAC Gold Book: Chemical Yield
- IUPAC Gold Book: Extent of Reaction
- BIPM SI Brochure: Mole and Amount of Substance
- NIST Guide to the SI: Mass Conversion Factors
- OSHA Occupational Exposure to Hazardous Chemicals in Laboratories
Chemistry notice: This tool supports learning and preliminary calculation. It does not identify reaction hazards or establish safe operating quantities. Verify the balanced procedure, current labels and Safety Data Sheets, risk assessment, engineering controls, PPE, storage and waste rules before laboratory work. Do not scale a reaction from this result alone.