Process capability calculator: Cp, Cpk, Pp, Ppk and PPM
Enter your spec limits, the process mean and your two standard deviations. Every number updates as you type, and the curve shows where the process sits against the limits. Leave a limit blank for a one-sided spec. Leave a σ blank to skip those indices. Nothing you type leaves your browser.
σ within is usually R̄/d₂, s̄/c₄ or MR̄/1.128. σ overall is the ordinary sample standard deviation of all readings. Only have raw data? Estimate both from your data, then send the results here.
What each number means
| Index | Formula | What it tells you |
|---|---|---|
| Cp | (USL − LSL) / 6σwithin | How well the spread fits the tolerance if the process were perfectly centered. Ignores the mean. |
| CPU, CPL | (USL − x̄) / 3σwithin, (x̄ − LSL) / 3σwithin | Capability toward each limit separately. |
| Cpk | min(CPU, CPL) | Short-term capability toward the nearer limit. This is the one that counts for a one-sided spec. |
| Pp, PPU, PPL, Ppk | Same formulas with σoverall | What the process actually delivered over the whole data set, shifts and drift included. |
| k | |m − x̄| / ((USL − LSL) / 2), where m is the midpoint | How far off-center the mean is, as a fraction of half the tolerance. Cpk = Cp(1 − k). |
| Expected PPM | 10⁶ × [Φ((LSL − x̄)/σ) + 1 − Φ((USL − x̄)/σ)] | Parts per million out of spec if the process is normal and stays as it is. No 1.5σ shift is added. |
Cpk and expected PPM at a glance
For a normal process, Cpk fixes how many standard deviations sit between the mean and the nearer limit (3 × Cpk). That sets the fallout on that side. If the process is centered, the other side contributes the same amount again.
| Cpk | σ to nearer limit | PPM, nearer side | PPM, both sides if centered (Cp = Cpk) |
|---|---|---|---|
| 0.67 | 2σ | 22,750 | 45,500 |
| 1.00 | 3σ | 1,350 | 2,700 |
| 1.33 | 4σ | 31.7 | 63.3 |
| 1.67 | 5σ | 0.287 | 0.573 |
| 2.00 | 6σ | 0.000987 | 0.00197 |
"1.33" in this table means exactly 4σ to the limit (Cpk = 4/3). A mean at 1.33 × 3 = 3.99σ gives about 33 PPM rather than 31.7. A common mix-up: a Cpk of 1.33 means about 32 PPM on one side. The 63 PPM figure applies only when both tails are counted for a centered process. The Six Sigma "3.4 PPM" figure assumes a 1.5σ long-term shift (a 6σ limit treated as 4.5σ), which this calculator does not apply.
Reading Cpk against Ppk
- Cp much higher than Cpk: the spread is fine but the mean is off-center. Re-centering is usually cheaper than reducing variation. The k value tells you how far to move.
- Cpk much higher than Ppk: each subgroup is tight, but the process moves between subgroups (setups, lots, shifts, tool wear). Look at the control chart before you report anything.
- Cpk and Ppk close together: consistent with a stable process. That is the only situation where either number predicts future output well.
- Common targets: many customers ask for Cpk ≥ 1.33 on ongoing production. New processes and safety-critical characteristics often need 1.67 or more. Your customer's requirements override any rule of thumb.
The Cpk vs Ppk guide works through these same numbers by hand, step by step.
Before you trust the result
- Stability first. Capability only predicts the future for an in-control process. Check an I-MR or X̄-R chart and the run rules first.
- Normality. The PPM figures assume a normal distribution. Skewed characteristics (flatness, runout, impurity levels) need a transformation or a non-normal capability method, or the tail estimates can be off by orders of magnitude.
- Measurement system. Gage variation inflates both σ's. If %GRR is high, part of your "process" variation is really the gage. See Gage R&R explained.
- Sample size. A Cpk from a small sample is uncertain. With 30 parts, a measured Cpk of 1.40 has an approximate 95% confidence interval of 1.02 to 1.78 (Bissell's approximation), so it does not prove 1.33. More data narrows the interval.
- Correct σ in each box. Putting the overall σ in the within box makes Cpk equal Ppk and hides any between-subgroup shifts.
Capability questions show up in Section VI of the CQE Body of Knowledge. The free 5-question CQE diagnostic includes calculation problems with fresh numbers and explains every wrong answer. No account needed.
Take the free CQE diagnosticMore free tools: Cpk from raw data · Control chart constants · Control chart picker · Sample size calculator · Printable CQE formula sheet · Sigma level and DPMO
Results are estimates from the numbers you enter and assume a stable, normal process. Not affiliated with ASQ.