Engineering Tools

Process Capability (Cpk) Calculator

Enter your spec limits and either summary statistics or raw measurement data, and get Cp, Cpk, and the estimated parts-per-million out of spec — with the distribution drawn against your limits.

Process inputs

Leave LSL or USL blank for a one-sided specification. Any consistent units work.

Data entry

Lower spec limit (LSL)

Upper spec limit (USL)

Process mean x̄

Std deviation s

Reference

How the numbers are derived

Capability indices compare the spread and centering of your process against the specification window.

Equations

Cp	(USL − LSL) / 6s — potential capability if the process were perfectly centered. Needs both limits.
Cpu	(USL − x̄) / 3s — capability against the upper limit.
Cpl	(x̄ − LSL) / 3s — capability against the lower limit.
Cpk	min(Cpu, Cpl) — actual capability including centering. Cpk < Cp means the process is off-center.
PPM	Expected fraction outside each limit from the normal distribution: PPM = 10⁶·[Φ(−zᵤ) + Φ(−zᵥ)] with z = distance to the limit in standard deviations.

Watch-outs

Capability indices only mean something if the process is stable — check a control chart first. An out-of-control process has no Cpk.
These are short-term indices from sample s. Long-term performance (Ppk) uses overall variation and is usually worse.
Non-normal data (flatness, runout, position — bounded at zero) needs transformation or different methods; blindly computing Cpk overstates capability.
Sample size matters: below ~30 points the confidence interval on Cpk is wide. 100+ points is a much stronger statement.
A great Cpk on the wrong characteristic proves nothing — measure what actually matters to function.

Numbers say the process isn’t capable?

A low Cpk is a symptom. The cause lives in the tolerance, the process, the fixture, or the measurement system — and fixing the right one is the difference between a tweak and a re-tool. If a capability problem is holding up your launch, bring the data to a consultation.

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