Free tool
Process capability (Cp, Cpk) calculator
Process capability measures how well a stable process fits inside its specification limits. Cp compares the width of the tolerance with the spread of the process, and Cpk also accounts for how well the process is centered, so it is the index most people quote. Pp and Ppk are the same indices worked out from the overall spread of the data.
CpequalsUSL − LSL divided by 6σ
Cpkequalssmaller of USL − mean divided by 3σ and mean − LSL divided by 3σ
Pp, Ppkequalsthe same formulas with the overall sample standard deviation
Leave blank if there is no lower limit
Leave blank if there is no upper limit
Same unit as the limits
Pre-filled with the worked example. If your standard deviation is the overall sample one, the same formulas give Pp and Ppk.
Cpk
1.33
At or above 1.33, a commonly used minimum. That is a rule of thumb, not a universal standard.
Cp
1.67
Spread against tolerance
Expected out of spec
31.7 ppm
If the process is normal and stable
Cpu (upper side)
1.33
(USL − mean) ÷ 3σ
Cpl (lower side)
2.00
(mean − LSL) ÷ 3σ
Next step
Want to track this every week?
Bring this result to a 45-minute demo and we will show where it fits in LeanSuite's Quality Improvement.
How to calculate it
Limits, a mean and a spread
Specification limits come from the drawing or the customer: the values a part must stay between. Many characteristics have only one, such as a maximum burr height or a minimum weld strength; leave the other blank.
Mean and standard deviation describe where the process runs and how much it varies. If you have them from a study or your SPC software, type them in. Otherwise paste the measurements in the order they were made and the calculator works out both.
Pasted measurements give two spreads. The short-term spread, from the average difference between consecutive values divided by 1.128, gives Cp and Cpk. The overall sample standard deviation gives Pp and Ppk. A large gap between Cpk and Ppk means the process drifts or shifts over time.
Check the gauge before trusting the result: a gauge R&R study shows how much of the spread comes from the measurement itself.
Worked example
Illustrative numbers, not a benchmarkA filling line with a fill weight specification of 500 g ± 5 g (LSL 495 g, USL 505 g). The process runs at a mean of 501 g with a standard deviation of 1 g.
Step 1
Cp = (505 − 495) ÷ (6 × 1) = 10 ÷ 6 = 1.67.Step 2
Upper side: (505 − 501) ÷ (3 × 1) = 4 ÷ 3 = 1.33.Step 3
Lower side: (501 − 495) ÷ (3 × 1) = 6 ÷ 3 = 2.00.Step 4
Cpk = the smaller side = 1.33.
Embed this calculator
Teaching this, or writing about it? Paste this code into your site, course page or intranet and the calculator works right there. It is free, with no sign-up.
<iframe src="https://www.theleansuite.com/tools/process-capability-calculator/embed" title="Process capability (Cp, Cpk) calculator by LeanSuite" width="100%" height="1460" style="border:0;max-width:1000px" loading="lazy" allow="clipboard-write"></iframe>
<p style="font:13px/1.4 sans-serif"><a href="https://www.theleansuite.com/tools/process-capability-calculator">Process capability (Cp, Cpk) calculator</a> by LeanSuite</p>How LeanSuite helps
LeanSuite's Quality Improvement tools log quality issues from the floor, trace each one to its root cause and follow the corrective action through to closure, with custom KPIs that show where defects happen.
See Quality ImprovementRead more
- Free template: I-MR chart template (individuals and moving range)
- Free template: Measurement uncertainty budget template
- Process capability (Cp, Cpk) in the lean glossary
- Right First Time Manufacturing: Principles and Implementation
- Statistical process control (SPC) in the lean glossary
- Measurement system analysis in the lean glossary
- Measurement System Analysis: Validating Gauge Reliability in Manufacturing
- The Most Popular Lean Six Sigma Tools and Techniques
- Histogram guide: check the shape before trusting Cp and Cpk
- Control chart guide: capability only means something for a stable process
- Box plot maker: compare the spread of batches or machines
FAQ
Process capability (Cp, Cpk) calculator: common questions
Cp is the tolerance width divided by six standard deviations: (USL − LSL) ÷ 6σ. Cpk is the distance from the mean to the nearer limit divided by three standard deviations: the smaller of (USL − mean) ÷ 3σ and (mean − LSL) ÷ 3σ. For limits of 495 and 505, a mean of 501 and σ of 1, Cp = 10 ÷ 6 = 1.67 and Cpk = 4 ÷ 3 = 1.33.
Cp only compares the spread of the process with the width of the tolerance, as if the process were perfectly centered. Cpk also accounts for where the mean sits, so it drops as the process drifts toward a limit. Cp equals Cpk only when the mean is exactly in the middle of the limits; otherwise Cpk is lower.
A Cpk of 1.33 is a commonly used minimum. It is a rule of thumb rather than a universal standard, and some customers and industries set their own requirement. A Cpk of 1.00 means the process spread of plus or minus three standard deviations just reaches the nearer limit, and below 1.00 some output is expected out of spec.
Both use the same formula but a different standard deviation. Cpk uses the short-term, within-subgroup spread, and Ppk uses the overall spread of all the data, including drift and shifts over time. With pasted measurements, this calculator estimates the short-term spread from the average moving range divided by 1.128 and uses the sample standard deviation for Pp and Ppk.
Yes. With only an upper limit, Cpk is (USL − mean) ÷ 3σ; with only a lower limit, it is (mean − LSL) ÷ 3σ. Cp cannot be calculated, because it needs the full width between two limits. Leave the missing limit blank in the calculator.
The process should be stable, meaning in statistical control on a control chart, because capability predicts future output only for a stable process. The data should be roughly normal, since the expected parts per million out of spec assume a normal distribution. The measurement system should also be reliable, which a gauge R&R study checks.
More free lean tools
All tools- OEE calculatorOverall equipment effectiveness from shift time, downtime, ideal cycle time and part counts.
- Downtime cost calculatorWhat an hour, an event and a year of unplanned downtime cost, from lost output, idle labour, scrap and overtime.
- SMED changeover calculatorTime saved by moving changeover steps from internal to external, capacity freed per week and the smaller batch it allows.
- Takt time calculatorThe pace a line must hit to meet customer demand, from shift time, breaks and daily demand.
- Cycle time calculatorCycle time against takt, units per hour, capacity per shift and the gap to daily demand.
- Line balancing calculatorLine efficiency, balance delay and the minimum number of stations from station times and takt.
- Bottleneck calculatorThe step that limits your line, from each step's cycle time, machines and uptime, with daily capacity and the gap to demand.
- First pass yield (FPY) calculatorFirst pass yield at each step and rolled throughput yield (RTY) across the whole process.
- Cost of poor quality (COPQ) calculatorTotal COPQ and cost of quality, and each as a share of revenue, from the four quality cost categories.
- DPMO and sigma level calculatorDPMO, defects per unit, yield and sigma level from the defects found, units checked and opportunities per unit.
- MTBF and MTTR calculatorMean time between failures, mean time to repair and availability from operating time, failures and repair time.
- Lead time calculatorManufacturing lead time from WIP and throughput (Little's Law), and the share of it that adds value.
- Throughput time calculatorThroughput time from process, inspection, move and wait time, the share of it that adds value, and units per hour.
- Kaizen savings calculatorYearly savings, payback in months and first-year ROI of an improvement, from time saved, scrap avoided and its costs.
- TEEP calculatorTotal effective equipment performance: OEE multiplied by how much of all calendar time you plan to run.
- Overall labor effectiveness (OLE) calculatorHow well paid labor hours turn into good output: availability, performance and quality of the crew.
- Inventory turnover and days on hand calculatorHow many times stock turns over in a period and how many days of it you hold, from COGS and average inventory.
- Safety stock calculatorSafety stock and reorder point from the service level you want, average demand and lead time, and how much each varies.
- Scrap rate calculatorScrap rate, the cost of scrap per period and per year, and what reaching a target rate would save.
- TRIR and DART rate calculatorOSHA recordable and DART incident rates from your 300A case counts and hours, and what one more case does to them.
- NIOSH lifting equation calculatorRecommended weight limit and lifting index for a two-handed lift, with every multiplier shown so you can see what to redesign.
- Time study sample size calculatorHow many cycles of an element to time, from your first readings, with the t formula, the ILO formula and the range method.
- Maintenance strategy selectorAnswer the RCM questions for one failure mode and get the maintenance strategy, the reasoning and the check or test interval.
- Noise dose and TWA calculatorDose and 8-hour TWA for a shift of noise levels under OSHA and NIOSH, which limits are reached and how much loud time to cut.
- Risk matrix calculatorSeverity times likelihood on a 3 x 3, 4 x 4 or 5 x 5 risk matrix, the band and its action, editable banding, and the score after further controls.
- Repair or replace calculatorEquivalent annual cost of keeping and repairing an old machine against buying a new one, with each one's economic life and the break-even figures.
- Compressed air leak cost calculatorAir lost, kW and cost a year for each tagged leak from its size and the pressure, ranked so the biggest gets fixed first.
- Machine hour rate calculatorWhat one productive hour of a machine costs, with and without the operator, the cost per part and how utilisation moves the rate.
- Total manufacturing cost calculatorTotal manufacturing cost, cost of goods manufactured, cost per unit and the overhead rate from materials, labor and overhead.
- Acceptance sampling calculatorRead the OC curve and the real risks of a sampling plan, find the plan for your AQL and LTPD, or size a zero-defect test.
- Shift schedule plannerTen shift patterns on real dates: calendar for each crew, hours a week, weekends off, coverage and the weeks over 40 hours.
- Pareto chart makerPaste categories and counts: sorted bars, cumulative percentage line and the vital few at the 80% line, as a PNG or SVG.
- Histogram makerPaste measurements: the histogram with automatic or chosen bins, plus mean, median and standard deviation, as a PNG or SVG.
- Box plot makerPaste one or more groups of numbers: box plots with quartiles, IQR, whiskers and outliers by the 1.5 IQR rule, as a PNG or SVG.
- Fishbone diagram makerName the problem, list causes under the 6M bones, and download the Ishikawa diagram as a PNG or SVG.
- 5 Whys canvasWrite the problem, answer up to five whys, state the root cause and countermeasure, then print the one-page canvas.
- Lean maturity self-assessmentScore 27 statements across nine dimensions and get a band for each, an overall band, where to start and the guides to read.
- Lean method navigatorSix questions about one problem, then the lean method to start with, the two that follow, why each fits, five steps for Monday and what it will not solve.
- Manufacturing ROI calculatorAnswer a few questions about your shop floor, shifts and downtime to estimate your potential ROI with LeanSuite.