Percent Yield Calculator

Calculate theoretical yield, percent yield, and overall multistep synthesis yield.

Mode

Actual mass obtained (g) (g)

Moles or mass of limiting reagent (g or mol)

Molar mass of limiting reagent (g/mol) (g/mol)

Molar mass of product (g/mol) (g/mol)

Step yields (%, comma-separated for multistep) (%)

e.g. 85,90,75 for 3 steps

Please check your inputs and try again.

Why Yields Multiply

In a linear synthesis, each step operates on whatever the previous step delivered. Losses therefore compound rather than add, and the effect is far more severe than intuition suggests.

Overall yield = y₁ × y₂ × ... × y_n

Steps	At 90% each	At 80% each	At 70% each
3	72.9%	51.2%	34.3%
5	59.0%	32.8%	16.8%
10	34.9%	10.7%	2.8%
15	20.6%	3.5%	0.5%

Ten steps at 90% — individually excellent yields — deliver only 35% overall. This is why total synthesis of complex natural products can require kilograms of starting material for milligrams of product, and why step count is the dominant consideration in route design.

Convergent Versus Linear Synthesis

The strategic response is convergent synthesis: build two fragments separately and join them late, rather than adding to one chain sequentially. A linear eight-step route at 80% gives 16.8%. Two four-step branches at 80% each give 41% per fragment, and coupling them at 80% yields 32.8% overall — nearly double the linear route, because the longest path any material travels is five steps rather than eight.

The key insight is that losses late in a linear sequence are most costly, because they discard material that has already absorbed many steps of work. Convergent routes keep the expensive steps short.

Worked Examples

Example 1: 3 steps: 85%, 90%, 75%

Overall = 0.85×0.90×0.75×100

Result: 57.4% overall yield

Each low-yield step kills overall synthesis

Example 2: 10g reactant MW=100, product MW=180, got 3.5g

Theory=0.1mol×180=18g

Result: Yield=3.5/18×100=19.4% — poor

Needs optimization

Example 3: The cost of one extra step

Eight steps at 85% versus nine steps at 85%

Result: 27.2% falls to 23.2%

Adding a single step costs about 15% of the remaining material. Route design therefore prioritises brevity over individual step optimisation.

Example 4: Convergent advantage

Linear 8 steps at 80% versus two 4-step branches coupled at 80%

Result: 16.8% versus 32.8% overall

The convergent route nearly doubles the yield because no material passes through all eight steps — the longest path is four steps plus the coupling.

Common Mistakes

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Averaging step yields instead of multiplying

Yields compound multiplicatively. Three steps at 90%, 80% and 70% give 50.4%, not the 80% an average would suggest.

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Adding a step for a marginal improvement

Each additional step multiplies the overall yield down. A step that improves purity slightly but costs 20% yield is rarely worth it.

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Comparing linear and convergent routes on overall yield alone

Convergent routes may show similar overall percentages but consume far less starting material, because losses occur on smaller fragments.

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Ignoring where in the sequence a loss occurs

A 50% loss in the final step discards material that has absorbed the entire synthesis. The same loss in step one costs very little.

Frequently Asked Questions

Why does multistep hurt yield?

Multiplied not added. Three 90% steps: 72.9% overall. Ten 90% steps: 34.9%. This drives synthesis design — minimize steps, maximize each yield. Natural product synthesis may have 20-30 steps, so 90%+ per step is critical.

Improving yield strategies?

Optimize reaction conditions (T, concentration, solvent). Use better catalysts. Extend reaction time. Purify intermediates. Improve workup/isolation. Sometimes redesign to change route entirely.

Why do multistep yields fall so fast?

Because each step operates on the output of the previous one, so yields multiply. Ten steps at 90% give 35%, not 90%.

What is convergent synthesis?

Building two fragments in parallel and joining them near the end, rather than extending one chain sequentially. It substantially improves material efficiency.

Where in a synthesis do losses hurt most?

In the later steps, because that material has already absorbed the cost and effort of everything before it.

Is it worth adding a step to improve purity?

Rarely, unless the yield cost is small. Each step multiplies the overall yield downward, so brevity usually wins.

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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