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Process Capability Index (Cp, Cpk) Calculator

Enter the spec limits, process mean and sigma to get Cp and Cpk.

How it is calculated

The tool takes the upper spec limit USL, lower spec limit LSL, the process mean μ and the process standard deviation σ, all in the same unit. It returns Cp = (USL − LSL) ÷ (6σ) and Cpk = min(USL − μ, μ − LSL) ÷ (3σ), each rounded to two decimals. Sigma must be above zero and USL must be greater than LSL, otherwise there is no result. Cp ignores where the mean sits, while Cpk uses the nearer limit. If the mean is outside the limits, Cpk turns negative (the tool does not warn you). The formulas assume a roughly normal, stable process, and the sigma you enter should be the process's own (within-subgroup) estimate.

Worked example

A shaft diameter has limits 9.5 to 10.5 mm. Measurements show a mean of 10.1 mm and a standard deviation of 0.12 mm. Cp: (10.5 − 9.5) ÷ (6 × 0.12) = 1 ÷ 0.72 = 1.39. Distances to the limits: 10.5 − 10.1 = 0.4 and 10.1 − 9.5 = 0.6; the smaller is 0.4. Cpk: 0.4 ÷ (3 × 0.12) = 0.4 ÷ 0.36 = 1.11. The gap between 1.39 and 1.11 shows the process is off-centre; centring it at 10.0 would lift Cpk to the Cp value.

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Common mistakes

  • Entering the sample range or variance instead of the standard deviation; sigma must be the standard deviation in the same unit as the limits.
  • Using the spec limits in one unit (mm) and sigma in another (microns); the two must match.
  • Quoting Cp alone as proof of capability: a process with a good Cp but an off-centre mean can still make out-of-spec parts, which only Cpk reveals.
  • Using the overall (long-term) standard deviation for one run and a short-term sigma for another and then comparing the indices; they answer different questions.
  • Ignoring a negative Cpk: it means the mean lies outside a spec limit, so most output is already out of tolerance.

About this calculator

This calculator computes the two core Six Sigma process capability indices from a process's spec limits, mean and standard deviation. Cp = (USL − LSL) ⁄ 6σ compares the width of the tolerance band to the natural spread of the process (six standard deviations), assuming the process is perfectly centred — it answers “could this process fit the spec if it were centred?”

Cpk = min[(USL − μ) ⁄ 3σ, (μ − LSL) ⁄ 3σ] is the more realistic sibling: it accounts for where the process mean μ actually sits relative to the limits, taking the tighter of the two one-sided distances. Cpk is always ≤ Cp, and the gap between them tells a quality engineer whether a process needs to be re-centred, tightened, or both — a Cpk of 1.33 or higher is a common industry threshold for a “capable” process.

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