Enter the upper specification limit, process mean, process standard deviation, and lower specification limit into the calculator to determine the Cpk index.

Cpk Index Formula

The following formula is used to calculate the Cpk index.

Cpk = min[(USL - μ) / 3σ, (μ - LSL) / 3σ]


  • Cpk is the process capability index
  • USL is the upper specification limit
  • μ is the process mean
  • σ is the process standard deviation
  • LSL is the lower specification limit

To calculate the Cpk index, subtract the process mean from the upper specification limit and divide the result by three times the process standard deviation. Then, subtract the lower specification limit from the process mean and divide the result by three times the process standard deviation. The Cpk index is the minimum of these two values.

What is a Cpk Index?

The Cpk index, also known as Process Capability Index, is a statistical tool used in quality control to measure a process’s ability to produce output within specified limits. It indicates how closely a process is running to its specification limits, relative to the natural variability of the process. The higher the Cpk value, the better the process is considered to be. A Cpk value of 1.0 is considered acceptable, indicating the process is capable of producing a product within its specification limits.

How to Calculate Cpk Index?

The following steps outline how to calculate the Cpk Index.

  1. First, determine the upper specification limit (USL).
  2. Next, determine the process mean (μ).
  3. Next, determine the process standard deviation (σ).
  4. Next, determine the lower specification limit (LSL).
  5. Next, calculate the numerator of the formula: (USL – μ).
  6. Next, calculate the denominator of the formula: 3σ.
  7. Next, calculate the numerator of the alternative formula: (μ – LSL).
  8. Finally, calculate the Cpk Index using the formula: Cpk = min[(USL – μ) / 3σ, (μ – LSL) / 3σ].
  9. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

USL: 10

μ: 8

σ: 1.5

LSL: 6