Yield Analysis Calculator
Calculate First Pass Yield (FPY) and Rolled Throughput Yield (RTY) across up to 4 process stages. Track cumulative defects and identify the weakest process stage.
About this calculator
A single overall yield number can hide where a process is actually bleeding units. This calculator takes the good-unit percentage at up to four sequential stages and multiplies them together — Rolled Throughput Yield (RTY) = Stage1% × Stage2% × Stage3% × Stage4% — which is mathematically the same figure it reports as First Pass Yield here, since each stage is treated as an independent one-pass step with no rework loop. Starting from your Total Input Units, it walks that population through each stage in sequence, rounding the surviving count at every step, so you get concrete unit counts (input, output, defects) per stage alongside the percentages — not just an abstract yield figure.
The "Weakest Stage" call-out simply flags whichever stage has the lowest individual yield percentage, which is usually your highest-leverage place to invest improvement effort, since low yields compound multiplicatively rather than averaging out. One nuance worth knowing: the Hidden Factory % here is computed as the gap between a naive traditional yield (final good units ÷ total input) and RTY — but because this calculator's stages are independent and RTY is derived the same way, that gap is essentially zero (rounding noise only). The classic "hidden factory" concept — the unbudgeted labor and time consumed by inspection, rework, and scrap loops — isn't separately modeled here, since this tool assumes defective units simply exit the process rather than cycling back through rework.
Inputs
Results
First Pass Yield (FPY)
89.4%
Rolled Throughput Yield (RTY)
89.4%
How to Use This Calculator
- Enter Stage 1 Yield (%), Stage 2 Yield (%), and Stage 3 Yield (%).
- Set Stage 4 Yield (%) and Total Input Units.
- Review First Pass Yield (FPY) (%) and Rolled Throughput Yield (RTY) (%).
- Use Final Good Units and Total Defective Units to inform your decision.
- Use the chart to visualize the results and explore different scenarios by adjusting inputs.
How the result changes with Stage 3 Yield (%)
| Stage 3 Yield (%) | First Pass Yield (FPY) | Rolled Throughput Yield (RTY) |
|---|---|---|
| 48 | 45.17% | 45.17% |
| 71 | 66.82% | 66.82% |
| 100 | 94.11% | 94.11% |
What each input means
- Stage 1 Yield (%)
- Percentage of units passing Stage 1 without defects.
- Stage 2 Yield (%)
- Percentage of units passing Stage 2 without defects.
- Stage 3 Yield (%)
- Percentage of units passing Stage 3 without defects.
- Stage 4 Yield (%)
- Percentage of units passing Stage 4 without defects.
- Total Input Units
- Number of units entering the first stage of the process.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersStage 1 Yield (%) = 98, Stage 2 Yield (%) = 97, Stage 3 Yield (%) = 95, Stage 4 Yield (%) = 99 = 5 input(s) provided
- Calculate First Pass YieldFirst Pass Yield89.4039 = 89.4039
- Calculate Rolled Throughput YieldRolled Throughput Yield89.4039 = 89.4039
- Calculate Final Good UnitsFinal Good Units8941 = 8941
- Calculate Total Defective UnitsTotal Defective Units1059 = 1059
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why are First Pass Yield and Rolled Throughput Yield the exact same number here?
FPY and RTY are mathematically identical when every stage is treated as an independent one-pass step, which is what this calculator assumes: it multiplies Stage1% × Stage2% × Stage3% × Stage4% for both figures. They diverge in real factories when a stage has internal rework loops that let a unit be inspected and reworked multiple times before moving on — a scenario this tool doesn't model, since it just walks units forward through four sequential stages.
Why is the Hidden Factory % almost always showing close to zero?
Hidden Factory % is defined here as the gap between a naive traditional yield (final good units divided by total input) and RTY. Because this calculator's stages are independent with no rework, and both figures are derived the same way from the same stage percentages, that gap collapses to essentially zero — only rounding noise remains. The classic hidden-factory concept, the extra labor and time consumed by inspection and rework loops, would only show up as a real gap if the model tracked units cycling back through a stage instead of exiting the process on failure.
How does the calculator decide which stage is the 'Weakest Stage'?
It simply compares the four stage yield percentages you entered and flags whichever one is lowest — it doesn't weight by unit volume or defect count, just the percentage itself. Because yields compound multiplicatively across stages, the weakest single stage is usually the highest-leverage place to focus improvement, since even a small yield loss there pulls down every unit that has already survived the earlier stages.
Why do the Output Units numbers get rounded at every stage instead of carrying decimals through?
The calculator rounds the surviving unit count after each stage so the per-stage table reports whole, physically meaningful units rather than fractional ones. This means the reported stage-by-stage defect counts can differ very slightly from what you'd get by applying the overall yield percentage to the total in one step, though the difference is only ever a rounding artifact of a unit or two per stage.
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