Cp/Cpk Calculator: Formula, Example & Instant Result
Cp and Cpk are process capability indices. Cp compares the width of the tolerance with the natural spread of the process (6σ); Cpk also accounts for how well the process is centred, so it is never higher than Cp. A Cpk of 1.33 or more is a widely used target for a capable process.
↳ Values are pre-filled with an example — replace them with your own data.
Your data
mm
mm
mm
mm
Use the within-subgroup σ, for example R̄/d2 from your control chart.
Result
CpkBorderline1.20
Borderline: the limits are met, but with little margin to the nearest one.
Cp1.333
The tolerance is 1.33 times as wide as the process spread (6σ).
Cpu1.200
Room between the mean and the upper limit, in units of 3σ.
Cpl1.467
Room between the mean and the lower limit, in units of 3σ.
Sigma level3.60
The nearest limit is about 3.6 standard deviations from the mean.
Expected out-of-spec (PPM)165
Expected parts per million outside the limits if the process is stable and normal: 159 above USL, 5 below LSL.
Cp is higher than Cpk because the process is off-centre. Centring it at 10.000 mm would raise Cpk to 1.33.
Normal distribution of the process with mean 10.020 mm, LSL 9.800 and USL 10.200; the red tails show the expected out-of-spec share (165 PPM).
6PPM ≈ Φ(−3.6) + Φ(−4.4) ≈ 159 + 5 ≈ 165 parts per million outside the limits
What it means
The spread itself would be good enough (Cp 1.33), but the mean sits 0.02 mm high, so the shafts are closer to the upper limit and Cpk drops to 1.20. Re-centring the process at 10.00 mm would lift Cpk to 1.33 without any reduction in variation — the cheapest improvement available.
Tips & common mistakes
▲Use the within-subgroup (short-term) σ for Cpk and the overall σ for Ppk. Mixing the two is the most common reporting error.
▲Capability only has meaning for a stable process. Check the control chart first: a Cpk from an unstable process predicts nothing.
▲The PPM estimate assumes a normal distribution. Characteristics that are naturally skewed, such as flatness or runout, need a different model.
▲A Cpk from very few parts is very uncertain. Collect enough measurements (many teams aim for 100 or more) before you report it.
▲AI assistants frequently mis-parse decimal separators (10,02 vs 10.02) or silently use the overall σ — always re-check their result with this calculator.
AI prompt for this calculation
Paste it into your AI assistant to be walked through the calculation with your own data.
Act as a quality engineer and help me calculate process capability (Cp and Cpk) for my data.
Use exactly these formulas:
Cp = (USL − LSL) / (6σ)
Cpu = (USL − μ) / (3σ)
Cpl = (μ − LSL) / (3σ)
Cpk = min(Cpu, Cpl)
Expected out-of-spec PPM = [Φ((μ − USL)/σ) + Φ((LSL − μ)/σ)] × 1,000,000, where Φ is the standard normal CDF.
σ must be the within-subgroup (short-term) standard deviation.
Rules:
1. Work step by step and state the unit at every step.
2. Before calculating, repeat my numbers back and check the decimal separators (for example 10,02 means 10.02).
3. If any input (USL, LSL, mean, σ) is missing or unclear, ask me for it — never invent or assume a value.
4. Tell me whether the process is centred and what Cpk would be if it were centred.
5. End with a one-sentence verdict: below 1.00 insufficient, 1.00–1.33 borderline, 1.33–1.67 good, 1.67 or more excellent.
My data:
USL =
LSL =
Mean =
σ (within) =
Unit =
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Next step · DOCAMIN
Turn this result into a controlled process capability report in DOCAMIN.
For a centred, normally distributed process, Cpk 1.33 puts the nearest limit four standard deviations from the mean, which corresponds to roughly 32 parts per million outside the limits on that side (about 63 PPM if both sides are equally close). Cpk 1.00 corresponds to about 1,350 PPM per side.
What is the difference between Cp and Cpk when the process is off-centre?
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Cp only compares the tolerance width with the spread, so it ignores where the process sits. Cpk measures the distance from the mean to the nearest limit. When the process drifts off-centre, Cp stays the same but Cpk falls; the gap between them shows how much you would gain just by re-centring.
Can Cpk be negative?
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Yes. A negative Cpk means the process mean lies outside one of the specification limits, so more than half of the output on that side is out of tolerance. It is a signal to stop and correct the setting, not to fine-tune the statistics.
How many measurements do I need for a meaningful Cpk?
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As many as practical from a stable process: the confidence interval of Cpk is wide for small samples. Many teams collect at least 25 subgroups (around 100 measurements) before reporting a capability figure, and state the sample size alongside it.
Should I report Cpk or Ppk?
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Cpk uses short-term, within-subgroup variation and shows what the process can do; Ppk uses the overall variation and shows what it actually delivered over time. Customers often ask for both. Use the Pp/Ppk calculator to compare them.
Last tested: October 2026 · Tested with: automated math tests (3+ cases) · Reviewed by: Quality for Everyone editorial team
