Process Capability Index (Cpk) Calculator
Judge whether a process fits inside its specification limits and whether it is centred.
Cpk
1.667
- Cp (potential capability)
- 1.667
- CPU (upper side)
- 1.667
- CPL (lower side)
- 1.667
- Distance of the mean from centre
- 0
Calculated from the values you entered. Formula version 1; last reviewed 2026-09-15.
What this calculator does
Capability compares specification width with process spread; Cpk also accounts for how far the mean sits from centre. Direct calculation from the four entered values. No capability target is assumed.
Inputs and what they mean
- Upper specification limit
- — number value.
- Lower specification limit
- — number value.
- Process mean
- — number value.
- Process standard deviation
- — number value.
How to use it
- Enter your own figures — the calculator never fills in a rate, price or benchmark for you.
- Press Calculate to see the result.
- Read the formula, variables, assumptions and source below the result before you rely on it.
Formula
Cp = (USL − LSL) ÷ (6σ); Cpk = min[(USL − μ) ÷ (3σ), (μ − LSL) ÷ (3σ)]
Worked example
Specification 9.5 to 10.5, mean 10, sigma 0.1
A centred process with capability well inside its limits.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
Results depend entirely on the figures you enter and are rounded for display. They are for general information and education, not professional advice.
Reference: NIST — NIST/SEMATECH e-Handbook of Statistical Methods
Last reviewed:
Common questions
Formula, source and verification
Capability compares specification width with process spread; Cpk also accounts for how far the mean sits from centre.
The question it answers: Is this process capable of staying inside the tolerance, and is it centred?
The formula
Cp = (USL − LSL) ÷ (6σ); Cpk = min[(USL − μ) ÷ (3σ), (μ − LSL) ÷ (3σ)]
- USL — Upper specification limit
- (measurement). Highest acceptable value.
- LSL — Lower specification limit
- (measurement). Lowest acceptable value.
- μ — Process mean
- (measurement). Average of the measured output.
- σ — Process standard deviation
- (measurement). Within-subgroup standard deviation.
Units: All four inputs share one unit of measurement; the indices are dimensionless.
What kind of calculation this is
Deterministic formula. The same inputs always give the same answer. The maths is fixed and does not depend on judgement.
Method
Direct calculation from the four entered values. No capability target is assumed.
Published alternatives
More than one published form of this calculation exists. Each one assumes something different, so the right one depends on your situation.
Capability against the nearer limit (Cpk) (used by default)
Cpk = min(USL − μ, μ − LSL) ÷ 3σ
Use it when: Use when the process may not be centred between the limits.
It assumes: The measurements are approximately normal and the process is stable.
Potential capability (Cp)
Cp = (USL − LSL) ÷ 6σ
Use it when: Use alongside Cpk to see how much is lost to being off centre.
It assumes: The measurements are approximately normal and the process is stable.
Assumptions built into the result
- Statistical: The process is in statistical control and the output is approximately normal.
Figures this calculator will never guess for you
- No minimum acceptable Cpk (such as 1.33) is treated as a rule.
Limitations
- Meaningless for a process that is not in control, or for strongly non-normal data.
Source and version
- Standard or reference
- Process capability indices — NIST (NIST/SEMATECH e-Handbook of Statistical Methods, process capability indices.)
- Published source
- NIST — e-Handbook
- Formula version
- Version 1
- Verification
- Reviewed against the cited source on
- How much weight the source carries
- Standards or government
- Applies to
- Currency
- The result is a ratio or index, so it does not depend on currency.
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