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Process Capability (Cp, Cpk) Calculator

Compute Cp, Cpk, Cpu, Cpl and the expected defect rate from specification limits, process mean and standard deviation.

Upper specification limit (USL)
Lower specification limit (LSL)
Process mean
Process standard deviation
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How it works

Cp = (USL − LSL) ÷ 6σ · Cpk = min[(USL − μ), (μ − LSL)] ÷ 3σ

Cp compares the width of the tolerance band to the ±3σ spread of the process, ignoring where the process sits. Cpk penalises off-centre processes by using only the distance to the nearer limit. A Cpk of 1.33 (4σ to the nearest limit) is a common minimum for new processes.

Worked example

USL 10.5, LSL 9.5, mean 10.1, σ 0.12 → Cp = 1.39 but Cpk = 1.11 because the mean sits closer to the upper limit; about 430 ppm out of spec.

Frequently asked questions

Cp vs Pp?

Cp/Cpk use within-subgroup (short-term) σ; Pp/Ppk use overall long-term σ. The formulas are the same.

Only one specification limit?

Use Cpu (upper only) or Cpl (lower only) — shown above — as your capability index.

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Standard Deviation Calculator
Paste a list of numbers and get the sample or population standard deviation, variance, mean, standard error, confidence interval, quartiles, z-scores, a frequency table and a histogram, with every step worked out.

For education — check assumptions (sample size, distribution) before using statistics in real decisions.