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Process Capability (Cpk) Calculator

Calculate Cp and Cpk to assess how well a process fits within its specification limits.

Result

Cpk
1.2
Cp
1.333
Rating
Marginally capable

Cpk of 1.33 or higher is a common industry benchmark for a capable process - Cpk below Cp indicates the process is off-center relative to the specification limits.

About the Process Capability Cpk

Process capability analysis compares how much a manufacturing or production process varies against how much variation its specification allows. This calculator computes both Cp, which checks whether the process spread could fit within specification limits under ideal centering, and Cpk, which accounts for how far off-center the process actually runs. Together they're standard metrics in Six Sigma and statistical process control for judging whether a process reliably produces output within tolerance.

How It Works

Enter the upper and lower specification limits (USL and LSL), the process mean, and the process standard deviation. The calculator computes Cp from the full specification width relative to six standard deviations, then computes two one-sided indices, Cpu and Cpl, measuring the distance from the mean to each specification limit relative to three standard deviations. Cpk is reported as the smaller of those two one-sided indices, since that's the side where the process is closer to failing, along with a plain-language capability rating.

Cp = (USL - LSL) / (6 x sigma). Cpu = (USL - Mean) / (3 x sigma). Cpl = (Mean - LSL) / (3 x sigma). Cpk = the smaller of Cpu and Cpl.

Formula & Methodology

The rating label follows common industry benchmarks: a Cpk of 1.67 or higher is labeled Excellent, 1.33 or higher is Capable, 1.0 or higher is Marginally capable, and anything below 1.0 is Not capable. Cpk can never exceed Cp - the two are equal only when the process mean sits exactly at the midpoint between USL and LSL, and the gap between them grows as the mean drifts toward one limit.

Examples

An Off-Center Process

With USL of 110, LSL of 90, a process mean of 101, and a standard deviation of 2.5, Cp comes to 1.333, but Cpu is only 1.2 versus Cpl of 1.467. Cpk takes the smaller value, 1.2, earning a rating of Marginally capable even though Cp alone looked stronger.

A Perfectly Centered Process

With USL of 52, LSL of 48, a process mean of exactly 50, and a standard deviation of 0.5, Cpu and Cpl both come out to 1.333, so Cpk equals Cp at 1.333. That matching value reflects a process sitting exactly at the midpoint of its specification range, earning a Capable rating.

Advantages

  • Reports Cp and Cpk side by side, making it easy to see at a glance whether a capability problem comes from excess variation or from poor centering.
  • Applies the same industry-standard rating thresholds (1.67, 1.33, 1.0) used across Six Sigma and quality engineering, so results translate directly into familiar capability language.
  • Calculates both one-sided indices (Cpu and Cpl) internally, so you don't need to work out which specification limit the process is closer to failing by hand.

Common Mistakes

  • Reporting Cp alone as evidence the process is capable - Cp only checks whether the spread could theoretically fit within limits assuming perfect centering, and says nothing about where the process mean actually sits.
  • Feeding in a standard deviation estimated from a small or unstable sample - Cpk is only as trustworthy as the sigma estimate behind it, and a shaky variation estimate produces a misleadingly precise-looking Cpk.
  • Assuming Cpk and Cp will always sit close together - a wide gap between them is itself the diagnostic signal that the process mean has drifted toward one specification limit.

Edge Cases to Watch For

  • USL must be greater than LSL and the standard deviation must be greater than zero, or the calculator returns an error rather than a nonsensical result.
  • If the process mean sits outside the specification limits entirely, Cpu or Cpl comes out negative, and Cpk will report that negative value, signaling the process is centered on the wrong side of a limit rather than merely off-center within it.
  • This calculation assumes the standard deviation entered accurately reflects the process's actual variation - it does not distinguish short-term from long-term variation, so the reliability of Cpk depends entirely on the quality of the sigma estimate you provide.

Common Use Cases

  • Manufacturing and quality engineers checking whether a process meets Six Sigma or ISO capability requirements before releasing product.
  • Process improvement teams diagnosing whether a capability shortfall stems from too much variation, too little centering, or both.
  • Suppliers preparing process capability documentation for customer quality audits.
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

What's the difference between Cp and Cpk?

Cp measures whether the process spread (variation) could theoretically fit within the specification limits, assuming perfect centering. Cpk accounts for how well the process is actually centered between those limits - a process can have a good Cp but a poor Cpk if its mean has drifted off-center, even without any change in variation.

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Conclusion

Cpk's dependence on both spread and centering is exactly why it's used alongside, not instead of, Cp. Reading the two together shows not just whether a process could be capable, but whether it actually is right now.