Cpk Calculator
Work out Cp, Cpk, Pp and Ppk from your spec limits and the process mean and standard deviation, or from raw measurements, with the expected defects per million. Two-sided or one-sided limits; paste measurements to get the within sigma from the moving range and a histogram.
Your numbers
The standard deviation of all the measurements. It gives Pp and Ppk.
Short-term sigma from a control chart (R̄ ÷ d2 or MR̄ ÷ 1.128). It gives Cp and Cpk; leave empty to use the overall s for both.
Cpk
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- Cp
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- Cpu (upper)
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- Cpl (lower)
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- Pp
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- Ppk
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- Sigma level (3 × Cpk)
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- Expected out of spec, within sigma
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- Expected out of spec, overall s
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The indices and the ppm assume the measurements are normally distributed and the process is stable (in statistical control). Formulas from the NIST/SEMATECH e-Handbook of Statistical Methods, section 6.1.6.
1.33 and 1.67 are figures customers commonly ask for, not a law; the number that counts is the one in your customer's drawing or supplier quality manual.
The calculation runs in your browser and ParrotNotes does not store your numbers. They sit in the page address so you can bookmark or share the result.
How the Cpk calculator works
Pick two-sided or one-sided limits and type them. If you already have the mean and the standard deviation, type those; add the within sigma from your control chart if you have it, and the page gives Cp and Cpk from it and Pp and Ppk from the overall s. If you have the measurements, paste them in production order: the page works out the mean, the sample standard deviation and the within sigma from the moving range, and draws a histogram with your limits.
You get Cpk with a plain verdict against the figures customers commonly ask for, Cp, Cpu, Cpl, Pp, Ppk, the sigma level and the expected parts per million out of spec. The working shows every number, so you can check it or paste it into a report.
Cpk from raw measurements
With individual measurements there are no subgroups, so the within sigma comes from the moving range: the difference between each value and the one before it. The average moving range divided by 1.128 (the d2 constant for ranges of two, from the NIST/SEMATECH e-Handbook's individuals control chart) estimates the short-term sigma. The overall s is the ordinary sample standard deviation, with n − 1 in the denominator.
Order matters for the moving range, so paste the values in the order they were made. For example 10, 12, 11, 13, 12 has a mean of 11.6, s = 1.140, moving ranges 2, 1, 2, 1 (MR̄ = 1.5) and a within sigma of 1.5 ÷ 1.128 = 1.330. With limits 8 and 16 that is Cpk 0.90 and Ppk 1.05. Five values are only an example: NIST asks for about 50 and 100 or more for a capability study.
Cpk and expected ppm
The expected parts per million out of spec for common Cpk values, from the normal distribution. A centred two-sided process has a tail beyond each limit; a one-sided specification has one.
| Cpk | Sigma level | Centred, two-sided | One limit |
|---|---|---|---|
| 0.67 | 2.01 | 44,431 ppm (4.44%) | 22,216 ppm (2.22%) |
| 1 | 3 | 2,700 ppm (0.27%) | 1,350 ppm (0.13%) |
| 1.33 | 3.99 | 66.1 ppm | 33 ppm |
| 1.5 | 4.5 | 6.8 ppm | 3.4 ppm |
| 1.67 | 5.01 | 0.544 ppm | 0.272 ppm |
| 2 | 6 | 0.002 ppm | < 0.001 ppm |
Expected parts per million out of spec
If the measurements are normal, the share beyond each limit is the normal tail area at 3 × Cpl below the mean and 3 × Cpu above it. The page adds the two and multiplies by a million, once with the within sigma and once with the overall s. The sigma level shown is 3 × Cpk, the distance from the mean to the nearer limit in sigmas; some Six Sigma tables add a 1.5 sigma shift on top, and this page does not.
Real data are often not normal (a dimension that cannot go below zero, a flatness, a burr height). Then the ppm here is only a rough guide: look at the histogram, and use a transformation or percentile-based indices, as the NIST handbook suggests, for the number you report.
For quality engineers, sales engineers and manufacturers' reps
The capability question usually comes up in a meeting: a buyer asks for the Cpk on a critical dimension before a PPAP, a supplier review shows a Ppk below target, or a quality manager wants to know when the corrective action will bring it up. Have the limits, the sample size and the dates of the run ready, and write down what was agreed and who owns each action.
Sources, each read on 2026-10-31. The verdict uses figures customers commonly ask for; your customer's own requirement decides:
- NIST/SEMATECH e-Handbook of Statistical Methods, 6.1.6: What is process capability? (Cp, Cpk, Cpu, Cpl, sample size, the ppm table)
- NIST/SEMATECH e-Handbook, 6.3.2.2: Individuals control charts (moving range and d2 = 1.128)
- SPC for Excel, Cpk vs Ppk: within-subgroup sigma for Cpk, overall standard deviation for Ppk
Related: the takt time calculator for the line rate and OEE (this page measures how well a dimension holds its tolerance, not how fast the line runs), and the meeting minutes generator to write up the supplier review.
More for manufacturing sales: Manufacturing sales process, OEM sales, Sales engineer.
Capability numbers come up in the supplier review
The Cpk on the critical dimension, the target the customer wants and the date the fix is due are all said out loud in the review meeting. Record it in ParrotNotes and you get a transcript and a summary that lists the corrective actions and who owns them.
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