Cpk to PPM calculator
Enter a capability index, get the expected parts per million outside specification. Free, no signup, nothing leaves your browser.
Cpk to PPM reference table
These are the rungs you meet in practice: the customer minimums, the six sigma target, and the failing end a process is trying to climb off. Every row is computed by the same arithmetic as the converter above, assuming a normal, centered process and counting both tails.
| Cpk | Expected PPM | Percent outside | What it means |
|---|---|---|---|
| 0.50 | 133,614 | 13.4% | Well outside the limits, more than one part in ten |
| 0.67 | 44,431 | 4.4% | The two sigma process, still failing |
| 1.00 | 2,700 | 0.270% | Nearest limit exactly three sigma away |
| 1.10 | 967.0 | 0.097% | |
| 1.20 | 318.3 | 0.032% | |
| 1.33 | 66.1 | 0.007% | The common customer minimum |
| 1.50 | 6.8 | 6.8e-4% | |
| 1.67 | 0.545 | 5.5e-5% | Often required for safety or special characteristics |
| 2.00 | 0.002 | 2.0e-7% | The six sigma target, before any long term shift |
How the conversion works
Cpk measures how many process spreads fit between the mean and the nearest specification limit, in units of three standard deviations. Multiply the index by three and you have that distance in sigmas. The normal distribution then gives the probability of a part falling beyond it. Double that probability to count both tails, scale by one million, and you have PPM.
Φ is the standard normal cumulative distribution. A Cpk of 1.0 puts the nearest limit three sigma from the mean, and Φ(−3) is about 0.00135, so both tails together predict about 2,700 PPM. A Cpk of 1.33 pushes the limit out to four sigma and the prediction drops to roughly 66.1 PPM. By 1.67, five sigma, it is about 0.545 PPM, well under one defective part per million.
What the prediction assumes
Three things, and each can bend the number in practice. The process is normal: a skewed or bimodal distribution will not honour the prediction, and the tails are exactly where non-normality bites hardest. The process is centered: an off-center process loads its defects into the nearer tail, so the true rate at the same Cpk approaches half the two-tailed figure. And the process is stable: the index is a snapshot, and a process that drifts between studies will beat the prediction on paper and miss it in the field.
That last point is where the famous six sigma figure comes from. Quoting 3.4 defects per million for a six sigma process builds in an assumed 1.5 sigma long-term drift of the mean. Without the drift, a centered Cpk of 2.0 predicts about 0.002 PPM. Neither figure is wrong; one describes the short-term snapshot and the other a pessimistic long-term view.
Reading PPM in the other direction
The conversion also answers the question customers actually ask, which arrives in PPM. A supplier agreement capped at 100 PPM implies a Cpk of at least about 1.30 on a centered, normal process. A 50 PPM cap implies just over 1.35, and single-digit PPM commitments imply 1.5 and up. If a required PPM lands between the rows of the table, run the converter above until the output crosses it.
Where the Cpk itself comes from
This page converts an index you already have. If you are starting from raw measurements, the full capability calculator takes a pasted column of values and specification limits and reports Cp, Cpk, Pp and Ppk with a histogram and a plain-English verdict, then this same conversion is applied to the result.