Skip to content
ENExplore Calculators

Control Chart Limits Calculator

Work out control chart limits instantly with clear inputs, formula shown and shareable results.

About Control Chart Limits Calculator

Shewhart X-bar and R limits are built from the average subgroup range rather than a computed standard deviation. The A2, D3 and D4 constants depend only on subgroup size and convert R-bar into three-sigma limits, which is why the method survives on a shop floor with no statistics software.

Formulas

X-bar limits

UCL = X-double-bar + A2 x R-bar; LCL = X-double-bar - A2 x R-bar

R chart limits

UCL_R = D4 x R-bar; LCL_R = D3 x R-bar

Worked example

With the default values below, Control Chart Limits Calculator returns Upper control limit (X-bar) of 26.4386. Change any input above and every figure here is recalculated in your browser.

Inputs used

Grand mean (X double bar)
25.4
Average subgroup range (R bar)
1.8
Subgroup sizeaccepts 2–10
5

Results

Upper control limit (X-bar)
26.4386
Lower control limit (X-bar)
24.3614
Upper control limit (R chart)
3.8052
Lower control limit (R chart)
0.0000

Step by step

  1. 1Values used
  2. 2X-bar limits
  3. 3R chart limits
  4. 4Upper control limit (X-bar)= 26.4386
  5. 5Lower control limit (X-bar)= 24.3614
  6. 6Upper control limit (R chart)= 3.8052
  7. 7Lower control limit (R chart)= 0.0000

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
  • This is an estimate for general information and not professional financial, tax or legal advice. See the full disclaimer for the limits that apply to this kind of calculator.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why not use specification limits on a control chart?

Control limits describe what the process does; specification limits describe what the customer wants. Mixing them hides the difference between an unstable process and an incapable one.

Why is the R-chart lower limit often zero?

Because D3 is zero for subgroups of six or fewer — with so few readings a range of zero is not statistically surprising.

Related Calculators

Control Chart Limits Calculator | Calcrivo