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    Statistics / capability

    Process capability calculator

    Cp tells you what a process could do if it were perfectly centred; Cpk tells you what it actually does. This calculator computes both from the mean, the standard deviation and the specification limits, and converts the result into an estimated defect rate.

    Mean10.020σ0.0300VerdictCapable
    Cpk
    2.00
    Minimum 1.33 required
    Cp
    2.22
    Capability if perfectly centred
    Sigma to limit
    6.00
    Distance to the nearer specification
    Estimated defects
    <1 ppm
    Normal approximation
    Capability against common targets
    Cpk 1.33 is the usual minimum for an existing process; 1.67 for a new one.
    Cpk 2.00
    Capability against common targets
    TargetCpkYour process
    Minimum acceptable1.00Meets
    Minimum acceptable1.33Meets
    New process1.67Meets
    Six sigma2.00Below

    Cpk falls as the process drifts off-centre even when Cp stays constant.

    Inspect the model
    Choose a quick result view, a scaled comparison, or the complete diagnostic set.
    Cpk against process drift
    Cp stays flat while Cpk collapses as the mean moves toward a limit.
    Cpk against process drift0.0000.4980.9961.491.992.49+0.00+0.00+0.02+0.02+0.04+0.04+0.06+0.06+0.08+0.08+0.10+0.10+0.12+0.12+0.14+0.14+0.16+0.16+0.18+0.18+0.20+0.20Cpk
    Cp against Cpk
    The gap is the cost of being off-centre.
    Cp against Cpk0.0000.5241.051.572.102.622.22CpCp2.00CpkCpkIndex
    Canonical equations
    The exact relationships implemented by this engine.

    (USL − LSL) / 6σ · Potential capability, ignoring centring.

    min(USL − μ, μ − LSL) / 3σ · Actual capability, including drift.

    2·(1 − Φ(z)) · z = distance to the nearer limit in sigma.

    engineering methodology

    A clear path from inputs to results.

    Cp tells you what a process could do if it were perfectly centred; Cpk tells you what it actually does. This calculator computes both from the mean, the standard deviation and the specification limits, and converts the result into an estimated defect rate.

    Step-by-step methodWorked exampleAssumptions explained

    How to use

    1. Enter the measured process mean and standard deviation.
    2. Enter the lower and upper specification limits.
    3. Set the Cpk your quality system requires.
    4. Read Cp, Cpk and the estimated defect rate.

    The formula

    Cp=USL−LSL6σ,Cpk=min⁡(USL−μ,  μ−LSL)3σC_p = \frac{USL - LSL}{6\sigma}, \qquad C_{pk} = \frac{\min(USL - \mu,\; \mu - LSL)}{3\sigma}

    Reference: Standard capability indices; Cpk 1.33 minimum for existing processes, 1.67 for new ones.

    Worked example

    Mean 10.02, σ 0.03, limits 9.8–10.2

    Inputs
    • Mean 10.02.
    • σ 0.03.
    • LSL 9.8, USL 10.2.
    Calculation path
    1. 1

      Cp: (10.2 − 9.8)/(6 × 0.03) = 2.22.

    2. 2

      Cpk: (10.2 − 10.02)/(3 × 0.03) = 2.00.

    3. 3

      Distance to the nearer limit: 6σ.

    4. 4

      Estimated defects: under 0.01 ppm.

    Result

    Cp 2.22 · Cpk 2.00 · under 1 ppm · capable.

    Interpreting the result

    Cp and Cpk diverge when the process drifts. Here the 0.22 gap is the cost of running 0.02 above centre. A process with Cp 2.0 and Cpk 1.0 has plenty of potential but is using half of it on offset — usually a setup or tool-wear issue, not a variance problem.

    Assumptions & limitations

    • The process is stable and normally distributed.
    • Specification limits are the true requirements, not arbitrary round numbers.
    • No measurement-system error; gauge R&R should be a fraction of the tolerance.

    Frequently asked questions

    What Cpk should I aim for?

    1.33 for an existing process, 1.67 for a new one, and higher for safety-critical characteristics.

    Does a high Cpk mean good quality?

    Only if the specification is right and the measurement system is capable. A tight process around the wrong target is still wrong.

    Can Cpk be negative?

    Yes, when the mean sits outside the specification limits.

    Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.