Process Capability Index (Cp & Cpk) Upper/Lower Specification Limits Calculator

Evaluate manufacturing tolerance capability via Cp, Cpk, Cpu, Cpl, and 1.33 benchmark.

Centered Process Capability (Cpk)
1.19 Cpk (Marginal (1.00–1.32))
Unshifted Process Potential (Cp) 1.48 Cp
Upper Capability Index (Cpu) 1.19 Cpu
Lower Capability Index (Cpl) 1.78 Cpl
Inputs
⚡ Scenarios:
Amounts are treated in the selected currency; no foreign-exchange conversion is applied.
LSL
Lower Specification Limit (LSL).
USL
Upper Specification Limit (USL).
μ
Observed process mean (μ).
σ
Within-subgroup process standard deviation (σ).
Results & Graph
Centered Process Capability (Cpk)
1.19 Cpk (Marginal (1.00–1.32))
Unshifted Process Potential (Cp)
1.48 Cp
Upper Capability Index (Cpu)
1.19 Cpu
Lower Capability Index (Cpl)
1.78 Cpl

Centered Process Capability (Cpk)

Graph 1 • Process Capability (Cp & Cpk) • Domain Architecture & Live Telemetry Maps Lower Spec Limit Lsl, Upper Spec Limit Usl, Process Mean Mu through Process Capability (Cp & Cpk) Formula.
Process Capability (Cp & Cpk) • Operations & Process Control Telemetry Threshold / ROP (1.19 Cpk (Marg) Safety Buffer (1.48 Cp) Centered Process Capability (Cpk 1.19 Cpk (Marginal (1. Unshifted Process 1.48 Cp Upper Capability I 1.19 Cpu
Graph 2 • Centered Process Capability (Cpk) Across Lower Spec Limit Lsl Sweep (40% → 160%) Evaluates Cp = (USL − USD) / (6σ); Cpu = (USL − μ) / (3σ); Cpl = (μ − USD) / ( across 7 operating points (current input highlighted).
-41.78 Cpk (M -20.24 Cpk (M 1.31 Cpk (M 1.19 3.92LSL 1.19 5.88LSL 1.19 7.84LSL 1.19 9.80LSL -12.74 11.76LSL -27.26 13.72LSL -41.78 15.68LSL
Graph 3 • Joint Sensitivity: Lower Spec Limit Lsl × Upper Spec Limit Usl Compares Centered Process Capability (Cpk) when Upper Spec Limit Usl is shifted +25% (solid) vs. −25% (dashed).
-20 Cpk (M 1.04 Cpk (M 22.08 Cpk (M --- Upper Spec Limit Usl @ 75% 20.07 -30% 12.67 -15% 1.78 +0% -9.11 +15% -20 +30%
Summary: Process Potential Cp = 1.481 (Cpu = 1.185, Cpl = 1.778), yielding Cpk = 1.185 (Marginal (1.00–1.32)).
Summary: Process Potential Cp = 1.481 (Cpu = 1.185, Cpl = 1.778), yielding Cpk = 1.185 (Marginal (1.00–1.32)).
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Formula & Mathematical Methodology: Process Capability (Cp & Cpk) Formula

Cp = USL − LSL6σ
Cpu = USL − μ3σ
Cpl = μ − LSL3σ
Cpk = min(Cpu, Cpl)
Cp = (USL − LSL) / (6σ); Cpu = (USL − μ) / (3σ); Cpl = (μ − LSL) / (3σ); Cpk = min(Cpu, Cpl)
  • lowerSpecLimitLsl: Lower Specification Limit (LSL).
  • upperSpecLimitUsl: Upper Specification Limit (USL).
  • processMeanMu: Observed process mean (μ).
  • processStdDevSigma: Within-subgroup process standard deviation (σ).

Rounding: Internal floating-point calculations preserve full precision; currency and percentage outputs round to 2 decimal places.

Worked Example: Process Capability (Cp & Cpk) Worked Example

Evaluate manufacturing tolerance capability via Cp, Cpk, Cpu, Cpl, and 1.33 benchmark.

  1. Enter your operational, financial, or physical measurement inputs.
  2. Apply the standard domain equation: Cp = (USL − LSL) / (6σ); Cpu = (USL − μ) / (3σ); Cpl = (μ − LSL) / (3σ); Cpk = min(Cpu, Cpl).
  3. Review the primary result, sensitivity metrics, and 3 interactive SVG graphs.
Result: Calculates Process Capability (Cp & Cpk) via Cp = (USL − LSL) / (6σ); Cpu = (USL − μ) / (3σ); Cpl = (μ − LSL) / (3σ); Cpk = min(Cpu, Cpl).

Frequently Asked Questions

How does the Process Capability Index (Cp & Cpk) Upper/Lower Specification Limits Calculator calculate results?

It computes Cp = (USL − LSL) / (6σ); Cpu = (USL − μ) / (3σ); Cpl = (μ − LSL) / (3σ); Cpk = min(Cpu, Cpl) directly in your browser and updates three custom SVG visualizations in real time.

Can I use Goal Seek to solve backwards for any input variable?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any input parameter.

Are my business and personal numbers kept private?

Yes. All calculations execute 100% locally in your browser with zero server transmission.

Business & Marketing · Lean Manufacturing & Six Sigma

Process Capability Index (Cp & Cpk) Upper/Lower Specification Limits Calculator: inputs, method, and how to read the result

Evaluate manufacturing tolerance capability via Cp, Cpk, Cpu, Cpl, and 1.33 benchmark.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Display Currency: Amounts are treated in the selected currency; no foreign-exchange conversion is applied.
  • Lower Spec Limit Lsl: Lower Specification Limit (LSL).
  • Upper Spec Limit Usl: Upper Specification Limit (USL).
  • Process Mean Mu: Observed process mean (μ).

What the calculation includes

With the default values shown, Centered Process Capability (Cpk) is 1.19 Cpk (Marginal (1.00–1.32)). The calculation follows Process Capability (Cp & Cpk) Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Lower Spec Limit Lsl from 9.8 LSL to 10.78 LSL changes Centered Process Capability (Cpk) from 1.19 Cpk (Marginal (1.00–1.32)) to -5.48 Cpk (Not Capable (<1.00)). This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses industry-standard APICS/ASCM supply chain, lean manufacturing, and consumer physics formulas.
  • Actual commercial freight tariffs, marketplace commissions, and utility rates vary by carrier and contract.

Scope: Global Supply Chain, Business & Consumer Standard Check the assumptions and limitations against your situation before relying on the estimate.

More in Business & Marketing: ROI Calculator (Return on Investment), Percentage Calculator.