Pp/Ppk Calculator: Formula, Example & Instant Result

Pp and Ppk are process performance indices. They use the overall (long-term) standard deviation of all your data, so they show what the process actually delivered over time, including shifts and drift between subgroups. Ppk is usually lower than Cpk; the gap tells you how much instability costs you.

↳ Values are pre-filled with an example — replace them with your own data.

Your data

Upper specification limit (USL)

Lower specification limit (LSL)

Process mean (μ)

Standard deviation σ (overall, long-term)

Standard deviation of all individual values over the period (n − 1).

Within σ for comparison (optional)

Enter the short-term σ (for example R̄/d2) to see Cpk next to Ppk.

Unit

Result

PpkInsufficient1.00

The process delivered a noticeable share of out-of-tolerance parts over the period.

Pp1.111

Over the long term, the tolerance is 1.11 times as wide as the overall spread (6σ).

Ppu1.000

Long-term room between the mean and the upper limit, in units of 3σ.

Ppl1.222

Long-term room between the mean and the lower limit, in units of 3σ.

Sigma level3.00

Over the long term, the nearest limit is about 3.0 standard deviations from the mean.

Expected out-of-spec (PPM)1,473

Parts per million outside the limits implied by the long-term spread: 1,350 above USL, 123 below LSL.

Pp is higher than Ppk because the process ran off-centre. Centring it at 10.000 mm would raise Ppk to 1.11.

Short-term vs long-term

Cpk (within σ)	1.20
Ppk (overall σ)	1.00

Ppk is 0.20 lower than Cpk: variation between subgroups over time (shifts, setups, tool wear) is costing that much capability.

Long-term distribution with mean 10.020 mm, LSL 9.800 and USL 10.200; the red tails show the expected out-of-spec share (1,473 PPM).

Formula

Pp  = (USL − LSL) / (6σ_overall)
Ppu = (USL − μ) / (3σ_overall)
Ppl = (μ − LSL) / (3σ_overall)
Ppk = min(Ppu, Ppl)
σ_overall = standard deviation of all individual values (long-term)
Compare: Cpk uses the within-subgroup σ; Ppk ≤ Cpk when the process shifts over time

Worked example

The same shaft line, measured over three weeks of production. What did customers actually receive?

Data

• LSL = 9.80 mm, USL = 10.20 mm, mean μ = 10.02 mm
• Overall standard deviation of all 375 shafts σ_overall = 0.06 mm
• Within-subgroup σ from the control chart = 0.05 mm (Cpk 1.20)

Step by step

1Pp = (10.20 − 9.80) / (6 × 0.06) = 0.40 / 0.36 = 1.111
2Ppu = (10.20 − 10.02) / (3 × 0.06) = 0.18 / 0.18 = 1.000
3Ppl = (10.02 − 9.80) / (3 × 0.06) = 0.22 / 0.18 = 1.222
4Ppk = min(1.000, 1.222) = 1.00 → borderline
5Cpk 1.20 − Ppk 1.00 = 0.20: variation between subgroups (shifts, tool wear, setups) adds about 20 % to the spread

What it means

In the short term the line could reach Cpk 1.20, but over three weeks it delivered only Ppk 1.00 — about 1,470 parts per million outside the limits instead of 165. The difference comes from drift between subgroups, so the first actions are on stability (tool-wear compensation, setup standard), not on the machine's inherent precision.

Tips & common mistakes

Ppk uses every individual value; do not average subgroups first or you hide exactly the variation Ppk is meant to show.
If Ppk is much lower than Cpk, look for shifts between shifts, batches, tools or operators before trying to reduce the short-term spread.
Ppk can be computed for an unstable process, but then it only describes the past: it does not predict the next lot.
Report the period and the number of values with Ppk — 'Ppk 1.00 over 3 weeks, 375 parts' is meaningful, 'Ppk 1.00' alone is not.
AI assistants often swap the two sigmas or compute σ with n instead of n − 1; check which σ they used against 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 long-term process performance (Pp and Ppk) and compare it with Cpk.

Use exactly these formulas:
Pp = (USL − LSL) / (6σ_overall)
Ppu = (USL − μ) / (3σ_overall)
Ppl = (μ − LSL) / (3σ_overall)
Ppk = min(Ppu, Ppl)
σ_overall is the sample standard deviation (n − 1) of all individual values.
If I also give the within-subgroup σ, compute Cpk with the same formulas and explain the gap.

Rules:
1. Work step by step and state the unit at every step.
2. Repeat my numbers first and check the decimal separators (10,02 means 10.02).
3. If any input is missing or unclear, ask me — never invent a value or a σ.
4. If σ_overall is smaller than the within σ, warn me that this usually indicates a data or calculation error.
5. End with a one-sentence verdict using: below 1.00 insufficient, 1.00–1.33 borderline, 1.33–1.67 good, 1.67+ excellent.

My data:
USL = 
LSL = 
Mean = 
σ overall = 
σ within (optional) = 
Period / number of values =

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Frequently asked questions

Why is Ppk usually lower than Cpk?

Cpk only sees the variation inside each subgroup, while Ppk sees all of it, including shifts between subgroups over time. Because total variation is at least as large as within-subgroup variation, Ppk is normally equal to or lower than Cpk. A big gap points to instability.

Which index does a customer report usually expect?

It depends on the customer's requirements: many ask for Ppk during approval of a new process (a short study of real output) and for Cpk once the process is in series production and under statistical control. When in doubt, report both with the sample size and the period.

Should I use Pp/Ppk or Cp/Cpk for a new process?

For a brand-new process you rarely have enough subgroups to estimate the within σ reliably, so a preliminary Ppk from an initial run is common. Once the process is stable and you have control-chart data, Cpk becomes meaningful and the two can be compared.

Can I estimate long-term capability from control-chart data?

Yes: take all individual values recorded on the chart over the period and compute their overall standard deviation for Ppk, and use R̄/d2 from the same chart for the within σ and Cpk. Use the Cp/Cpk calculator for the short-term side.

Last tested: October 2026 · Tested with: automated math tests (3+ cases) · Reviewed by: Quality for Everyone editorial team