Process Capability Index Calculator — Cp and Cpk
Enter your specification limits (LSL and USL), the process mean and the process standard deviation to calculate Cp, Cpk, the sigma level and the estimated percentage of output outside specification.
Marginally capable (Cpk ≥ 1.0)
- 1
Specification width (USL − LSL)
105 − 95 = 10 - 2
Cp — potential capability
10 ÷ (6 × 1.5) = 1.1111Cp assumes the process is perfectly centred; it measures only the spread relative to the specification width. - 3
CPU — upper capability
(105 − 100) ÷ (3 × 1.5) = 1.1111 - 4
CPL — lower capability
(100 − 95) ÷ (3 × 1.5) = 1.1111 - 5
Cpk = min(CPU, CPL)
min(1.1111, 1.1111) = 1.111
How does this calculator work?
Cp = (USL−LSL)/(6σ) measures potential capability assuming a centred process. Cpk = min((USL−μ)/(3σ),(μ−LSL)/(3σ)) corrects for centering. Cpk ≥ 1.33 is typically required; Cpk < 1.0 means the process produces defects. Sigma level ≈ Cpk × 3.
Formula
How this is calculated
Cp (the potential capability ratio) measures how many specification widths fit inside six sigma, assuming the process is perfectly centred. A Cp of 1.0 means the process spread exactly fills the spec; higher is better. But Cp ignores centering: a process drifted toward one limit may still have a high Cp yet produce many defects.
Cpk corrects for centering. It takes the smaller of two one-sided ratios — (USL − μ)/(3σ) and (μ − LSL)/(3σ) — so a perfectly centred process gives Cpk = Cp, and any shift reduces Cpk below Cp. The industry threshold for capability is Cpk ≥ 1.33 (4σ margin on each side). Automotive and aerospace standards often require Cpk ≥ 1.67. Below 1.0 the process is not capable and defects are expected.
This calculator uses a normal-distribution approximation to estimate the fraction of output outside the specification limits, expressed as a percentage. It assumes the characteristic is normally distributed and uses the short-term, within-subgroup standard deviation σ (as used in SPC control charts). Long-term variation, measurement system error, and non-normality are not modelled here.
Frequently asked questions
Cp measures only the width of the process spread relative to the specification width — it ignores where the distribution is centred. Cpk also accounts for centering by using the distance from the mean to the nearer limit. Cpk ≤ Cp always; they are equal only when the mean is exactly at the midpoint of the specification.
The common minimum is Cpk ≥ 1.33 (equating to roughly 63 ppm out-of-spec assuming a centred normal process). Many automotive and aerospace contracts require Cpk ≥ 1.67. Six Sigma targets a Cpk of 2.0 (accounting for a ±1.5σ shift the longer-term Ppk metric would show).
Yes. Cp and Cpk are derived from normal-distribution theory. For highly skewed or non-normal processes the indices can give misleading estimates of defect rates. In those cases use non-parametric capability measures or transform the data first.
Also known as
TG we-Calculate Editorial Team. (2026). Process Capability Index Calculator — Cp and Cpk [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/process-capability-index-calculator
TG we-Calculate Editorial Team. "Process Capability Index Calculator — Cp and Cpk." TG we-Calculate. 2026. https://we-calculate.com/calculator/process-capability-index-calculator.
TG we-Calculate Editorial Team, "Process Capability Index Calculator — Cp and Cpk," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/process-capability-index-calculator
@misc{wecalculate_process_capability_index_calculator, title = {Process Capability Index Calculator — Cp and Cpk}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/process-capability-index-calculator}}, year = {2026}, note = {TG we-Calculate} }
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