Introduction
This Cpk calculator shows how well your process fits inside your spec limits. Cpk is a process capability index. It compares your process spread and center to the Upper Spec Limit (USL) and Lower Spec Limit (LSL). A higher Cpk means fewer bad parts.
You can use it three ways:
- Raw Data: Paste your measurements from Excel or a CSV. The tool finds the mean and standard deviation for you.
- Mean & Std. Dev.: Already have your stats? Just type them in.
- Target Planner: Pick a Cpk goal, like 1.33, and see the standard deviation your process needs to hit it.
You get Cp, Cpk, CPU, CPL, Ppk, sigma level, DPMO, and the percent of parts outside spec. Charts show a run chart, a histogram with a fitted normal curve, and a bell curve against your limits. A step-by-step section shows every formula, so you can check the math or use it in a report.
It works with two-sided, upper-only, or lower-only specs, and with units like mm, inches, mils, or no units at all. Use it for machining, molding, assembly, or any job where parts must stay in tolerance. For related shop-floor metrics, see the OEE calculator, the true position calculator, and the TRIR calculator.
How to use our Cpk Calculator
Enter your process data or your mean and standard deviation, plus your spec limits. The Cpk calculator returns your Cpk, Cp, CPU, CPL, sigma level, DPMO, scrap rate, step-by-step math, and charts of your process capability.
Input Unit: Pick the unit you typed your numbers in. All values you enter — data, mean, sigma, USL and LSL — must use this one unit. If your prints mix systems, the mm to inches calculator and the unit converter calculator can convert them first.
Result Display Unit: Pick the unit you want results and charts shown in. The tool converts for you. Cpk and Cp have no units, so they never change.
Tab choice: Use Raw Data if you have measurements. Use Mean & Std. Dev. if you already know your stats. Use Target Planner to find the spread you need to hit a Cpk goal.
Enter Data Values (Raw Data tab): Paste or type your measured parts. Split values with commas, spaces, tabs, or new lines. You can paste straight from Excel. You need at least 2 numbers. Click Load Sample Data to try it out. To review the same data set other ways, try the statistics calculator, the mean median mode calculator, or the outlier calculator.
Specification Type: Choose Two-Sided when the part has both a high and low limit. Choose Upper-Only or Lower-Only when just one side matters, like flatness or strength.
Upper Specification Limit (USL): Type the largest value a part can have and still pass.
Lower Specification Limit (LSL): Type the smallest value a part can have and still pass. It must be less than the USL.
Histogram Bin Count: Set how many bars the histogram uses, from 3 to 50. Use the plus and minus buttons. More bars show more detail; fewer bars show the shape better with small samples.
Process Mean (μ): Type the average of your process. This tells the tool where your parts sit between the limits. You can find it fast with the average calculator.
Process Standard Deviation (σ): Type your process spread. It must be greater than zero. The variance calculator is handy if you only have variance on hand.
Target Cpk (Target Planner tab): Type the Cpk you want to reach, such as 1.33 or 1.67. The tool shows the largest sigma that still meets it.
Two-Sided Input Basis (Target Planner tab): Choose Tolerance half-width to enter a plus/minus value from the mean, or Specification limits to enter the USL and LSL yourself.
Tolerance Half-Width (±): Type how far a part can drift each way from the mean and still pass.
Calculate and Reset: Results update as you type, but you can click Calculate anytime. Click Reset to load the default example again.
What Is Cpk?
Cpk is a process capability index. It tells you how well a process makes parts that fit inside your spec limits. It compares the spread of your process to the room you have between the Lower Spec Limit (LSL) and the Upper Spec Limit (USL). It also looks at where your average sits between those limits.
A high Cpk means most parts land safely inside spec. A low Cpk means parts are drifting out and scrap or rework is coming.
The Cpk Formula
Cpk uses two half-checks and keeps the worse one:
- CPU = (USL − mean) ÷ (3 × σ) — room on the top side
- CPL = (mean − LSL) ÷ (3 × σ) — room on the bottom side
- Cpk = the smaller of CPU and CPL
Here σ (sigma) is the standard deviation, which measures how much your parts vary.
Cpk vs. Cp
Cp only asks: is my process spread narrow enough for the tolerance? It ignores where the average sits. Cpk asks the harder question: is my spread narrow enough and is it aimed at the middle?
If Cp is high but Cpk is low, your spread is fine but your process is off-center. Shifting the mean back toward the middle can fix that fast. If both are low, you need to cut variation.
What Cpk Values Mean
| Cpk | Meaning | Roughly |
|---|---|---|
| Below 1.00 | Not capable | Lots of defects |
| 1.00 – 1.32 | Marginal | Tight, risky |
| 1.33 – 1.66 | Capable | Common goal in industry |
| 1.67 and up | Highly capable | Very few defects |
Many auto and aerospace customers ask for Cpk ≥ 1.33. Some safety-critical parts ask for 1.67 or 2.00.
Sigma Level and DPMO
Sigma level is just Z = 3 × Cpk. A Cpk of 1.33 equals a 4-sigma process. DPMO means "defects per million opportunities." It turns your capability number into an easy count: how many bad parts you would expect out of a million. The tail math behind DPMO is the same idea used by the Z score calculator and the normal distribution calculator.
Cpk vs. Ppk
Cpk uses within-subgroup sigma, which shows short-term spread. Ppk uses overall sample sigma, which shows long-term spread across shifts, lots, and tool changes. When you only have one column of data and no subgroups, the number you get is really Ppk. Ppk is usually a bit lower than Cpk, since it includes drift over time.
Before You Trust the Number
Cpk only works if a few things are true:
- The process is stable. Check a run chart first. If there are trends, jumps, or wild swings, fix those before judging capability.
- The data is close to normal. A histogram with a fitted bell curve shows this. Skewed data (like flatness or roundness) needs a different method.
- You have enough parts. Aim for 30 or more measurements. Fewer than that gives a shaky answer — the sample size calculator and the confidence interval calculator help you judge how firm your estimate is.
- Your gauge is good. If the measuring tool has too much error, it inflates sigma and drags Cpk down for no real reason. A percent error calculator is a quick way to size up gauge bias against a master part.
One-Sided Specs
Some features only have one limit. Surface roughness has a max. Weld strength has a min. In those cases there is no Cp, and you report only CPU (upper-only) or CPL (lower-only). Use the matching setting so the math does not invent a second limit.
How to Raise a Low Cpk
- Center the process. Adjust the tool offset or setpoint so the mean sits near the middle of the tolerance. This is often the quickest win.
- Cut variation. Control temperature, material lots, fixtures, and operator method. Lower sigma raises both Cp and Cpk. On cutting jobs, steady feeds and speeds and consistent surface footage go a long way.
- Fix the gauge. Run a Gage R&R study and remove measurement noise.
- Open the tolerance. Only if engineering confirms the wider spec still works for the part.
Quick Example
Say a shaft spec is 49.6 mm to 50.4 mm. Your mean is 50.05 mm and sigma is 0.105 mm. CPU = (50.4 − 50.05) ÷ (3 × 0.105) = 1.11. CPL = (50.05 − 49.6) ÷ (3 × 0.105) = 1.43. Cpk = 1.11, the smaller one. Cp would be 1.27. The gap between 1.27 and 1.11 is caused by the process running high. Aim it 0.05 mm lower and Cpk jumps to about 1.27 with no other change.