Process Capability Index (Cpk) Calculator
Judge whether a process fits inside its specification limits and whether it is centred.
In short
Judge whether a process fits inside its specification limits and whether it is centred.
Formula: Cp = (USL − LSL) ÷ (6σ); Cpk = min[(USL − μ) ÷ (3σ), (μ − LSL) ÷ (3σ)]
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.
Use it to turn Upper specification limit, Lower specification limit, Process mean, Process standard deviation into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this professional & industry calculation.
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)].
Inputs used: Upper specification limit, Lower specification limit, Process mean, Process standard deviation.
Edge handling: Upper specification limit is required.; Upper specification limit must be no more than 1000000000000.; Lower specification limit is required.; Lower specification limit must be no more than 1000000000000.; Process mean is required..
Worked example
Specification 9.5 to 10.5, mean 10, sigma 0.1
- Start with Upper specification limit: 10.5, Lower specification limit: 9.5, Process mean: 10, Process standard deviation: 0.1.
- Apply the method: Cp = (USL − LSL) ÷ (6σ); Cpk = min[(USL − μ) ÷ (3σ), (μ − LSL) ÷ (3σ)].
- 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
- Inputs outside the supported range are rejected rather than forced into a result.
- The result depends on the values you enter for this process capability index (cpk) calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Reference: NIST — NIST/SEMATECH e-Handbook of Statistical Methods
Last reviewed:
Common questions
Where does this formula come from?
NIST/SEMATECH e-Handbook of Statistical Methods, process capability indices. See the source link on this page.
What kind of calculation is this?
Capability compares specification width with process spread; Cpk also accounts for how far the mean sits from centre. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.
What are its limits?
Meaningless for a process that is not in control, or for strongly non-normal data. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.
How do I use the Process Capability Index (Cpk) Calculator?
Enter the required values for Upper specification limit, Lower specification limit, Process mean, Process standard deviation. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Process Capability Index (Cpk) Calculator use?
Cp = (USL − LSL) ÷ (6σ); Cpk = min[(USL − μ) ÷ (3σ), (μ − LSL) ÷ (3σ)] The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.
Can the Process Capability Index (Cpk) Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
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.
Cite this page
Free Calculator. (2026, September 15). Process Capability Index (Cpk) Calculator. https://freecalculator.tech/tools/cpk-calculator
"Process Capability Index (Cpk) Calculator." Free Calculator, 15 Sept. 2026, https://freecalculator.tech/tools/cpk-calculator.
Process Capability Index (Cpk) Calculator — Free Calculator, https://freecalculator.tech/tools/cpk-calculator
Related tools
Work out the hourly rate to charge a client so that target margin is met after overhead and non-billable time.
Find the true hourly cost of an employee once benefits, payroll cost and overhead are included.
Size a software application from its data and transaction functions before estimating effort or cost.
Estimate development effort, schedule and average team size for a software project of a known size.
Express cloud spend as a cost per customer, per transaction or per other business unit.
Set the rate used to apply manufacturing overhead to jobs for the coming period.