Process Capability Calculator

This process capability calculator works out the process capability ratio Cp and the index Cpk, which show whether a stable process fits inside its specification limits. Enter the lower and upper spec limits, the process mean and the standard deviation.

Lower spec limitLSLUpper spec limitUSL

Process meanAverage of your measurementsStandard deviationFrom a stable process, ideally 100+ readings

1.39

Spread only

Cpk

1.11

Spread and centering

Cpu: 1.11
Cpl: 1.67
Outside spec: 429 ppm

The mean sits nearer the upper limit. Centering it would raise Cpk toward 1.39.

Your process between the spec limitsNormal curve from your mean and standard deviation. Orange is the share outside the limits.

Example values are filled in. Replace them with your own; nothing you type leaves your browser.

Worked example

The example values, step by step

Step 1 · Spec width
10.05 − 9.95 mm
= 0.10 mm
Step 2 · Cp
0.10 ÷ (6 × 0.012)
= 1.39
Step 3 · Cpu
(10.05 − 10.01) ÷ (3 × 0.012)
= 1.11
Step 4 · Cpl
(10.01 − 9.95) ÷ (3 × 0.012)
= 1.67
Step 5 · Cpk
Smaller of 1.11 and 1.67
= 1.11

Reading the result

In the example, the spread fits the specification with room to spare (Cp 1.39), but the mean sits 0.01 mm above the center. That pulls Cpk down to 1.11 and puts about 430 parts per million above the upper limit.

Moving the mean back to 10.00 mm would raise Cpk to match Cp, without reducing the spread at all. Centering is often the cheaper fix.

Cp and expected parts per million outside spec (centered process)

Cp = Cpk	Parts per million outside
1.00	2,700
1.33	63
1.67	0.57
2.00	0.002

Computed from the normal distribution for a process centered between its limits, the same way as the calculator.

Common data mistakes

Calculating capability from an unstable process, so the figures do not predict what comes next.
Using a short-term standard deviation from a few consecutive parts and reporting it as long-term performance.
Assuming the data is normal without checking. Skewed data gives a misleading parts-per-million figure.

The methods behind the number

The formula

How it's calculated

Cp: (USL − LSL) ÷ (6 × σ)
Cpu: (USL − mean) ÷ (3 × σ)
Cpl: (mean − LSL) ÷ (3 × σ)
Cpk: The smaller of Cpu and Cpl

Check stability first

Capability only predicts future output when the process is stable. Plot the data on a control chart before you calculate Cp or Cpk.

Cp shows spread, Cpk shows centering too

Cp compares the width of the specification with the spread of the process. Cpk also accounts for where the mean sits, so an off-center process has a Cpk lower than its Cp.

Use enough data

Estimates from a handful of readings move a lot. Many practitioners use at least 100 readings taken over normal running conditions.

Frequently asked questions

What is the process capability ratio?

Cp, the width of the specification divided by six standard deviations of the process. It shows how well the spread fits, ignoring centering.

What is the difference between Cp and Cpk?

Cp only looks at spread. Cpk also looks at centering, using the distance from the mean to the nearer limit, so Cpk is never higher than Cp.

What Cpk value is acceptable?

Many customers ask for 1.33 or higher, and some ask for 1.67 on critical features. The requirement is set by the customer or industry standard.

How do you calculate Cpk?

Work out (USL − mean) ÷ 3σ and (mean − LSL) ÷ 3σ, then take the smaller of the two.

What is the difference between Cpk and Ppk?

Cpk usually uses the within-subgroup, short-term standard deviation. Ppk uses the overall standard deviation of all the data, so it reflects long-term performance.

Sources and further reading

NIST/SEMATECH e-Handbook: process capability ↗
Douglas C. Montgomery, Introduction to Statistical Quality Control (book)

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