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Cp / Cpk calculator

Paste measurements — or type a mean and a sigma — with your tolerance, and get Cp, Cpk, Pp, Ppk, the sigma level and the expected parts per million out of spec.

Nothing you paste leaves this calculation. It is not stored, not logged and not sent anywhere else — the numbers are computed and returned, and that is all.

One reading per line, or a row per subgroup. Commas, tabs and semicolons all work; a header row is ignored.

How this is calculated

Capability compares the width of your tolerance to the width of your process. Cp is the ratio of the two; Cpk penalises the process for sitting off centre, so it can never be larger than Cp and is the number worth quoting. 

Cp  = (USL − LSL) / 6σ
CPU = (USL − x̄) / 3σ
CPL = (x̄ − LSL) / 3σ
Cpk = min(CPU, CPL)

The part most people get wrong

Which sigma. Cp and Cpk use within-subgroup variation — estimated from R̄/d₂ across subgroups, or from the mean moving range for individual readings. Pp and Ppk use the plain sample standard deviation of everything. If your process shifts between subgroups, the two disagree, and that gap is the interesting result: the process is capable of better than it is currently delivering. A capability number with no stated sigma is not a result, it is a rumour.

Two assumptions worth stating

  • The process is stable. Capability on an out-of-control process describes something that will not happen again. Chart it first — that is what the chart generator is for.
  • The data is roughly normal. The expected PPM figure comes from the normal distribution. For a skewed characteristic (flatness, roundness, anything bounded at zero) treat it as indicative only.

Want this to keep itself up to date?

A calculator answers for the data you pasted. A control chart answers for the data your line produced this morning — limits frozen at a baseline you locked, rules evaluated on every new reading, an alert when one trips.

Start a free trial See it on live data

Other free tools

  • Control limit calculator — Give it subgroups or individual readings and it returns the control limits for the chart, the range or sigma chart beneath it, and every constant it used to get there.
  • Control chart generator — Paste a column of numbers, or rows of subgroups, and get a real control chart: limits from the data, Nelson rules 1–4 evaluated, out-of-control points marked.
  • Control chart constants — The whole table, n = 2 to 25, with the formula each constant belongs to. The same values the charts on this site are computed from.