Free SPC Calculator · X̄-R · Cp · Cpk

X̄-R chart and Cpk, from your readings.

Paste your measurements, set the tolerance and the subgroup size, and get X̄ and R control charts, Cp, Cpk, Pp and Ppk, a capability histogram and out-of-control signals flagged. Free, no sign-up, runs in your browser.

Open the calculator →See the formulas

No sign-upNothing storedSubgroups 2–10Rules: limits, run of 7, trend of 6

X̄-R CONTROL CHART CONSTANTSn = 2 – 10

n	A₂	D₃	D₄	d₂
2	1.880	0	3.267	1.128
3	1.023	0	2.574	1.693
4	0.729	0	2.282	2.059
5	0.577	0	2.114	2.326
6	0.483	0	2.004	2.534
7	0.419	0.076	1.924	2.704
8	0.373	0.136	1.864	2.847
9	0.337	0.184	1.816	2.970
10	0.308	0.223	1.777	3.078

STANDARD SPC CONSTANTSUSED BY THE CALCULATOR BELOW

The calculator

Paste readings. Read the charts.

Enter measurements in production order, separated by spaces, commas or new lines. Consecutive readings are grouped into subgroups of the size you choose.

Paste your readings, in production order

LSL USL Subgroup n

—

Cpk

—

Ppk

—

X̿ (grand mean)

—

R̄ (mean range)

—

σ within

—

Signals

—

X̄ chart · subgroup means- - spec

R chart · subgroup ranges

Capability histogramnormal fit

RUNS IN YOUR BROWSER · NOTHING YOU PASTE IS STORED OR SENT · AIAG SPC CONSTANTS · RULES: BEYOND LIMITS, RUN OF 7, TREND OF 6

How to read it

Stable first. Capable second.

Step 1

Check the R chart

If ranges are out of control, the spread is not stable and every other number is unreliable. Fix that first.

Step 2

Check the X̄ chart

Points beyond the limits, runs on one side or steady trends mean something changed: a tool, an offset, a batch of material.

Step 3

Then read Cpk

Only for a stable process does Cpk predict the future. Compare it with Cp: a big gap means re-centre, not rebuild.

Formulas

The maths behind every number.

X̄ CHART

CL = X̿
UCL = X̿ + A₂·R̄
LCL = X̿ − A₂·R̄

X̿ is the mean of the subgroup means; R̄ is the mean of the subgroup ranges.

R CHART

CL = R̄
UCL = D₄·R̄
LCL = D₃·R̄

For subgroups of 6 or fewer, D₃ is 0 and the range chart has no lower limit.

CAPABILITY

σ = R̄ / d₂
Cp = (USL − LSL) / 6σ
Cpk = min(USL − X̿, X̿ − LSL) / 3σ

Pp and Ppk use the same formulas with the overall standard deviation of all readings.

Benchmarks

What your Cpk is telling you.

Cpk	What it means	Typical use
Below 1.00	Spread wider than tolerance, or off-centre: out-of-spec parts expected	Contain and sort; fix before running
1.00 – 1.33	Inside tolerance with little margin for drift	Tighten control; monitor closely
1.33 and above	Capable	Common minimum for ongoing production
1.67 and above	Capable with margin	Often asked for new or safety-critical characteristics

Beyond the spreadsheet

Run this live on every characteristic.

MachineWise Quality & SPC builds these charts automatically from Bluetooth gauge readings at the machine, alerts when a rule breaks, and schedules QC patrol inspections.

Gauges

Readings without retyping

Bluetooth calipers, micrometers, bore gauges and indicators from multiple brands. Gauge integration →

Live

Charts per characteristic

Every characteristic on the inspection plan gets its own X̄-R chart and Cpk, always current. Quality & SPC →

Plan

From the drawing

AI balloons the drawing and builds the inspection plan in minutes. MachineWise AI →

Questions

Straight answers.

What is an X-bar R chart?

An X̄-R chart is a pair of control charts for measurements taken in small subgroups, typically 2 to 10 consecutive parts. The X̄ chart plots each subgroup's average to show whether the process centre is stable; the R chart plots each subgroup's range to show whether the spread is stable.

How are X-bar R control limits calculated?

Centre lines are the grand mean X̿ and the mean range R̄. Limits are X̿ ± A₂·R̄ for the X̄ chart and D₃·R̄ to D₄·R̄ for the R chart, with A₂, D₃ and D₄ taken from the constants table for your subgroup size.

What is the difference between Cp and Cpk?

Cp compares the tolerance width with the process spread and ignores where the process is centred. Cpk also accounts for centring, using the distance from the mean to the nearer specification limit. If Cp is good but Cpk is low, the process is capable but off-centre.

What is a good Cpk value?

1.33 is the common minimum for ongoing production, and 1.67 is often required for new processes or critical characteristics. Below 1.00, out-of-tolerance parts should be expected.

What is the difference between Cpk and Ppk?

Cpk uses the within-subgroup standard deviation estimated from R̄/d₂, so it shows what the process can do when stable. Ppk uses the overall standard deviation of all readings, so it includes drift between subgroups and shows what the customer actually received.

Is my data stored or sent anywhere?

No. The calculator runs entirely in your browser. Nothing you paste is stored or sent. To run SPC live on every characteristic, fed by Bluetooth gauges, see MachineWise Quality & SPC.

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