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Rolled first-pass yield calculator

Multiply sequential first-pass stage yields to estimate the fraction passing without rework.

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Your result

Rolled first-pass yield92.17%
Expected units passing all stages921.69units

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How to calculate

Rolled first-pass yieldA 95%, 98% and 99% process gives 92.169% rolled yield, not the arithmetic average of those three percentages. Concept diagram; not to scale.Rolled first-pass yield1Stage 1 first-pass yield (%)952Stage 2 first-pass yield (%)983Rolled first-pass yield92.169 %MyCalCute.com
A 95%, 98% and 99% process gives 92.169% rolled yield, not the arithmetic average of those three percentages. Concept diagram; not to scale.

Multiply sequential first-pass stage yields to estimate the fraction passing without rework.

Rolled first-pass yield = a*b*c/10000 %
Expected units passing all stages = n*a*b*c/1e6 units

Worked example

  • Stage 1 first-pass yield (%): 95
  • Stage 2 first-pass yield (%): 98
  • Stage 3 first-pass yield (%): 99
  • Starting units: 1000
  • Rolled first-pass yield: 92.17 %
  • Expected units passing all stages: 921.69 units

Assumptions and limits

Use conditional yields for units entering each successive stage of the same process. Reworked units and final shipped yield are different measures.

Results are rounded for display; calculations use unrounded values. Read our calculation methodology.

Understanding the result

Multiply sequential first-pass stage yields to estimate the fraction passing without rework. A 95%, 98% and 99% process gives 92.169% rolled yield, not the arithmetic average of those three percentages.

When this tool is useful

A 95%, 98% and 99% process gives 92.169% rolled yield, not the arithmetic average of those three percentages.

Understanding your inputs

InputExample
Stage 1 first-pass yield (%) a95
Stage 2 first-pass yield (%) b98
Stage 3 first-pass yield (%) c99
Starting units n1000

Frequently asked questions

What does this model leave out?

Use conditional yields for units entering each successive stage of the same process. Reworked units and final shipped yield are different measures.

How do I reproduce the example?

Enter the displayed example values in their labelled units. Apply the formula before rounding; change one input at a time to compare scenarios.

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