Cp vs Cpk comes down to one distinction: Cp measures a process’s potential capability, while Cpk measures its actual capability. Cp compares the specification width to the natural six-sigma spread of the process and assumes the mean is perfectly centered. Cpk drops that assumption and measures the distance from the process mean to the nearest specification limit. Because of this, Cp is always greater than or equal to Cpk, and the two are equal only when the process is perfectly centered. Read together, they reveal whether a capability shortfall comes from excess variation or from poor centering.
These two indices are among the most commonly reported numbers in quality engineering. They are calculated from the same measurement data, yet confusing them leads to the wrong conclusion about whether a process is actually capable.
This article focuses specifically on the difference between Cp and Cpk. If you need a fuller introduction to capability indices, sampling requirements, and interpretation, start with the complete guide on process capability analysis. Here, the goal is to make the distinction between these two indices unambiguous.
What Cp Measures
Cp measures how wide your specification range is compared to how much your process actually varies.
The logic comes directly from the normal distribution. For a stable process, six standard deviations — that is, ±3σ around the mean — contain approximately 99.7% of all output. Cp compares the width of your specification limits against that six-sigma spread.
Cp = (USL − LSL) / 6σ
The numerator, upper specification limit minus lower specification limit, is how wide your tolerance is. The denominator, six sigma, is how wide your process actually spreads. Reading the result is straightforward:
- Cp < 1: the process spread is wider than the specification. Some defects are unavoidable, regardless of where the process is centered.
- Cp = 1: the six sigma spread exactly fills the tolerance, leaving no margin for any shift in the mean.
- Cp > 1: the process variation fits inside the specification, with room to spare.
That is useful, but Cp has a built-in blind spot: it assumes the process is perfectly centered. It cannot tell whether the mean sits in the middle of the tolerance or is drifting toward a limit. A process could already be producing defects while Cp still reports a healthy number, because Cp only ever describes the best-case scenario.
What Cpk Measures
Cpk closes the gap that Cp leaves open. Instead of assuming the process is centered, it accounts for where the mean actually sits relative to the specification limits.
Cpk = min [ (USL − μ) / 3σ, (μ − LSL) / 3σ ]
The concept is simpler than the formula looks. Cpk checks two distances — how far the mean is from the upper specification limit, and how far it is from the lower limit — then takes the smaller of the two. The side closest to a limit is the side most likely to produce defects, so that side defines the process’s real, current capability.
Two consequences follow directly from this:
- In the best case, a perfectly centered process, Cpk equals Cp.
- As the process drifts off-center, Cpk drops below Cp.
Mathematically, Cp ≥ Cpk always holds, and the reason is clear once you see what each index represents: Cp describes the best case, and Cpk describes reality. One practical note: both indices are only meaningful for a process in statistical control, which is why capability analysis always begins with a control chart.
Cp vs Cpk: Why Track Both Instead of Just Cpk?
A natural question follows: if Cpk already accounts for centering, why bother with Cp at all?
The cleanest way to hold the distinction in your head is this: Cp measures potential capability, and Cpk measures actual capability. This is the same potential-versus-actual framing used by the American Society for Quality in its process capability resource and formalized in the ISO 22514 capability-and-performance standards.
With Cpk alone, you cannot tell whether the process even has the potential to be capable. The relationship between the two numbers is what carries the diagnostic value:
| Cp | Cpk | |
|---|---|---|
| Question it answers | Potential capability | Actual capability |
| Formula | (USL − LSL) / 6σ | min[(USL − μ)/3σ, (μ − LSL)/3σ] |
| Centering | Assumes centered | Accounts for the mean |
| Relationship | Always ≥ Cpk | ≤ Cp; equal only when centered |
| One-sided spec | Not defined | Can be calculated |
Good Cp, bad Cpk
The variation itself is fine, but the process is off-center. This is generally the better problem to have, because re-centering the mean is often a faster, lower-cost fix than reducing variation. It may be as simple as a machine offset, a setpoint correction, or a calibration adjustment.
Bad Cp
The variation itself is too large. Even with perfect centering, the process cannot consistently fit inside the specification. This points to a deeper improvement effort, since reducing variation is typically harder and slower than recentering a process that is already tight.
Cp and Cpk work as a pair, not as substitutes. Cpk tells you whether the process is meeting requirements today. Cp, read alongside it, tells you whether a shortfall is a centering problem or a variation problem — exactly the information you need before deciding where to direct improvement effort. Both indices use the short-term, within-subgroup estimate of sigma; long-term performance is measured by their counterparts, covered in Cp/Cpk vs. Pp/Ppk. You can compute all four from your own data with the free process capability calculator on SigmaDesk.
Frequently Asked Questions
What is the difference between Cp and Cpk?
Cp measures potential capability, while Cpk measures actual capability. Cp compares the specification width to the six-sigma process spread and assumes the process is perfectly centered, whereas Cpk uses the distance from the mean to the nearest specification limit. A gap between the two indicates the process is running off-center.
Can Cpk be higher than Cp?
No, Cpk can never exceed Cp; mathematically, Cp ≥ Cpk always holds. The two are equal only when the process mean sits exactly at the midpoint of the specification limits. Cpk can even fall to zero or below when the mean lies on or outside a limit.
What is a good Cp and Cpk value?
A common minimum is 1.33 for both indices, which corresponds to a 4-sigma margin between the mean and the nearest limit. Many industries, especially automotive, require 1.67 for new processes or critical characteristics. For a full breakdown of what each value implies in defect rates, see Cpk values and sigma levels.
Can Cpk be negative?
Yes. A negative Cpk means the process mean has shifted entirely outside the specification limits, so the nearest limit is on the wrong side of the average — a serious condition that needs immediate attention. Cp, by contrast, can never be negative, because it only measures spread relative to the tolerance width and ignores where the process is centered.