Reaction Yield Calculator

Calculate percent yield, theoretical yield, and atom economy for chemical reactions.

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Percent Yield vs Atom Economy

These two measures answer different questions and are frequently confused. Percent yield asks how much of what was theoretically possible you actually obtained. Atom economy asks how much of the starting material mass ends up in the desired product at all, even in a perfect reaction.

% yield = (actual yield / theoretical yield) × 100
Atom economy = (Mr of desired product / Mr of all products) × 100

The crucial difference: percent yield is a practical measure that depends on your technique, losses on transfer, and how far the reaction went. Atom economy is a theoretical property of the balanced equation itself — it is fixed by the chemistry and cannot be improved by better lab work.

MeasureDepends onImproved byFixed by the equation?
Percent yieldTechnique, conditions, purificationBetter conditions, less lossNo
Atom economyReaction stoichiometry onlyChoosing a different reactionYes

A reaction can therefore have 95% yield and terrible atom economy, or perfect atom economy and 20% yield. Both matter, and a green chemistry assessment needs both.

Reaction Type and Atom Economy

Reaction typeTypical atom economyWhy
Addition100%All atoms of both reactants end up in the product
Rearrangement100%No atoms leave the molecule
SubstitutionModerateThe leaving group becomes waste
EliminationLowerA small molecule such as H2O or HCl is discarded
Wittig reactionPoorTriphenylphosphine oxide is a heavy by-product

This is why addition reactions such as Diels–Alder and catalytic hydrogenation are prized in industrial synthesis. Every atom of both reactants is incorporated, so atom economy is 100% by construction. The Wittig reaction, by contrast, is synthetically powerful but discards a triphenylphosphine oxide molecule heavier than the alkene it produces.

Worked Examples

Example 1: Synthesis: actual=8.5g, theoretical=10.0g
% yield = (8.5/10.0)×100
Result: 85% — good yield
15% lost to side reactions or workup
Example 2: Diels-Alder: MW product=160, all products=160
AE = 160/160×100
Result: 100% atom economy
No byproducts — ideal green chemistry
Example 3: Yield from the limiting reagent
10.0 g benzoic acid (Mr 122) esterified, 9.8 g ester (Mr 136) obtained
Result: Theoretical = 11.1 g; yield = 87.9%
The theoretical yield comes from moles of the limiting reagent multiplied by product molar mass — not from the mass of starting material directly.
Example 4: Poor atom economy despite high yield
Wittig: desired alkene Mr 132, by-product Ph3PO Mr 278
Result: Atom economy = 132/410 × 100 = 32%
Even at 95% yield, over two thirds of the product mass is waste. This is why atom economy is reported alongside yield in process chemistry.
Example 5: Overall yield across steps
Four-step synthesis, each step 80%
Result: Overall = 0.804 = 41%
Yields multiply across a sequence. Four apparently good steps deliver less than half the material, which is why step count matters as much as individual efficiency.

Common Mistakes

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Reporting yields above 100%

This always indicates a problem, not an exceptional result — usually residual solvent, water, or unreacted starting material in the product. Dry the sample thoroughly and check purity before reporting.

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Calculating theoretical yield from the wrong reactant

Theoretical yield must be based on the limiting reagent, not whichever reactant is most convenient. Using an excess reagent inflates the theoretical figure and makes the yield look artificially poor.

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Confusing atom economy with percent yield

Atom economy is determined by the balanced equation alone and cannot be improved by technique. A reaction with inherently poor atom economy is poor no matter how skilfully it is run.

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Ignoring solvent and reagent mass in green metrics

Atom economy counts only the reaction equation. Process mass intensity — total mass used per mass of product, including solvent — is often far more revealing for real environmental impact.

Frequently Asked Questions

Why is atom economy important?
High atom economy means less waste per unit product. The addition of Diels-Alder (100% AE) is more sustainable than substitution reactions that generate stoichiometric salt waste.
What causes low percent yield?
Side reactions, equilibrium limitations, incomplete reaction, losses during purification, or measurement errors. Multiple reaction steps compound yield losses multiplicatively.
What is the difference between percent yield and atom economy?
Percent yield measures how much product you obtained relative to the theoretical maximum. Atom economy measures what proportion of reactant mass could ever end up in the desired product, based on the balanced equation alone.
Why can percent yield never exceed 100%?
Because theoretical yield is the maximum permitted by stoichiometry. A result above 100% means the product contains impurities, residual solvent, or water — not that extra material was created.
Which reactions have 100% atom economy?
Addition and rearrangement reactions, since no atoms are discarded. Diels–Alder cycloadditions and catalytic hydrogenations are standard examples.
How do yields combine over multiple steps?
They multiply. Five steps at 90% each give an overall yield of 0.95 = 59%, which is why shorter routes are strongly preferred even when individual steps are less efficient.
How do I find the theoretical yield?
Identify the limiting reagent, convert its mass to moles, apply the stoichiometric ratio to get moles of product, then multiply by the product’s molar mass.

Formula Explorer connections

Interpretation: This relationship converts chemical amount, mass, composition or balanced-equation ratios into a reaction quantity. Assumption: Use a balanced reaction, consistent units and the correct molar mass. Purity, side reactions and limiting reagents can change experimental results.

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