Process Capability (Cp/Cpk) Calculator

Find Cp, Cpu, Cpl and Cpk from specification limits and process stats.

How process capability (Cp/Cpk) works

Process capability indices measure how well a process's natural variation fits within its specification limits. Cp compares the spec width to process spread assuming perfect centering; Cpk additionally accounts for how far off-center the process actually is — the pair is reported together because Cp alone can overstate a poorly centered process's real capability.

Enter your upper and lower specification limits, the process mean, and the process standard deviation. The calculator returns Cp, Cpu (capability toward the upper limit), Cpl (capability toward the lower limit), and Cpk (the more conservative of the two).

A commonly cited rule of thumb treats Cpk ≥ 1.33 as capable and Cpk ≥ 1.67 as highly capable, though the right target depends on your industry and the cost of a defect.

The formula

Cp = (USL−LSL) ÷ 6σ. Cpu = (USL−mean) ÷ 3σ. Cpl = (mean−LSL) ÷ 3σ. Cpk = min(Cpu, Cpl).

Cp uses the full specification width divided by six standard deviations (the process's natural variation). Cpu and Cpl measure capability toward each individual limit; Cpk takes the more restrictive of the two.

Worked example

USL 110, LSL 90, mean 100 (centered), standard deviation 2

Cp = (110−90) ÷ (6×2) = 1.67. Since the process is exactly centered, Cpk equals Cp: 1.67.

Frequently asked questions

Why is Cpk usually lower than Cp?

Cp assumes the process is perfectly centered between the specification limits. Any real off-centering reduces capability toward whichever limit the process mean is closer to — Cpk captures that; Cp does not.

What Cpk value is considered good?

1.33 is a commonly cited minimum for a capable process, and 1.67 or higher is often considered highly capable — but the right target depends on your industry, the cost of a defect, and any customer or regulatory requirement.

Does this assume a normal distribution?

Yes — Cp/Cpk are defined assuming the process output is approximately normally distributed. For strongly non-normal processes, other capability methods are more appropriate.

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