First Pass Yield Calculator
Enter units in, good first time, rework and scrap to get first pass yield, or list your process steps for rolled throughput yield.
How to use the First Pass Yield Calculator
- Under Calculate, choose “First pass yield of one step or process” for a single step, or “Rolled throughput yield of several steps” for a chain of steps.
- In single-step mode, type Units entering (must be above zero) and Units good the first time. The good count cannot be higher than units entering.
- Open More options if you also know the scrapped or reworked counts. Enter Units scrapped and/or Units reworked-then-passed. If you give only one of them, the other is worked out for you.
- In multi-step mode, type one line per step in the text box, using either
step name, units in, units good first timeorstep name, yield %. A header line is skipped. You need at least 2 and at most 60 steps. - Read the result. It updates as you type. Open How it was calculated under the result to see the formula, the values substituted and the answer with units.
- To start from a typical case, click a preset button above the form: “1000 in, 912 good”, “250 in, 238 good”, “4-step electronics” or “Four yields in %”. Click Reset to return to the starting example.
Copy link keeps every input in the page address, and Print / save as PDF gives a dated record.
What is the first pass yield formula?
First pass yield is units good the first time divided by units entering, shown as a percentage: FPY = units good first time ÷ units entering. It counts only units that passed without rework, repair or retest. For example, if 912 of 1,000 units pass a step first time, FPY = 912 ÷ 1,000 = 91.2 %.
How do you calculate rolled throughput yield?
Rolled throughput yield (RTY) is the probability that a unit passes every step first time. It is found by multiplying the step yields: RTY = FPY₁ × FPY₂ × … × FPYₙ. For four steps with yields of 98 %, 95 %, 97 % and 99 %, RTY = 0.98 × 0.95 × 0.97 × 0.99 = 89.40 %.
Because each step multiplies the result, RTY is never higher than the lowest single step yield, and usually well below it. The calculator also shows the normalized yield, RTY^(1/n), which is the geometric-mean yield per step. The weakest step is the one with the lowest FPY. When the first step has unit counts, the page also shows how many of the units entering that step are expected to pass every step first time: units in × RTY.
How are final yield and the hidden factory calculated?
Final yield counts units that pass in the end, including those reworked. It is (good first time + reworked) ÷ units entering. The hidden factory is final yield minus FPY, which equals the share of units that needed rework to pass.
Using the default example of 1,000 units in, 912 good first time, 18 scrapped and 70 reworked: final yield = (912 + 70) ÷ 1,000 = 98.2 %, and the hidden factory = 98.2 % − 91.2 % = 7 %. The rework rate is 7 % and the scrap rate is 1.8 %. A total of 88 units (18 scrapped plus 70 reworked) were not good the first time.
The calculator shows a warning when more than 10 % of units go through rework.
Worked examples
| Input | Result |
|---|---|
| 912 of 1000 units good the first time | FPY = 91.2 %, final yield 98.2 % |
| 238 of 250 units good the first time | FPY = 95.2 % |
| 4 process steps | RTY = 89.8 % |
| 4 process steps | RTY = 89.4 % |
| 4392 of 4800 units good the first time | FPY = 91.5 %, final yield 97.75 % |
Calculated by the tool above with these values.
Frequently asked questions
Can I use the results in commercial projects or client reports?
Yes. Results may be used in commercial work, including reports, audits, client projects and training material, without attribution. Check the figures against your own process data before acting on them, as the page advises.
Is the calculator free, and is anything I type uploaded?
The calculator is free, and there is no account or sign-up. Everything is calculated in your browser, and nothing you type is uploaded.
Can I print or share a calculation?
Yes. Copy result copies the result lines with a link. Copy link copies the page address, which stores your inputs, so the calculation reopens exactly as you left it. Print / save as PDF produces a one-page record with inputs, results, calculation steps and the date.
What happens if my scrap and rework counts do not add up?
If you enter both scrapped and reworked units and they add up to less than units entering, a warning says the missing units are counted as not passed. If the total is higher than units entering, the calculator shows an error.
Is first pass yield the same as FPY calculation in quality reports?
Yes. FPY is first pass yield; the calculation is the same: good units first time divided by units entering.
Where do the formulas come from?
- Pyzdek & Keller, The Six Sigma Handbook, and the ASQ Six Sigma glossary: first pass yield, rolled throughput yield and normalized yield.
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