QC Calculator: Mean, SD, CV% and Westgard Rules
Paste your control results in time order. The tool calculates mean, SD and CV%, plots a Levey-Jennings chart with ±1, 2 and 3 SD lines, and checks each point against the Westgard multirules.
Runs in your browser. Nothing you type is sent or saved.
For learning and checking your own calculations. Always follow your laboratory's SOPs and verified procedures.
Westgard rules used
| Rule | Action | When |
|---|---|---|
1-2s | Warning | One value beyond ±2 SD. Check the other rules; do not reject on this alone. |
1-3s | Reject: random error | One value beyond ±3 SD. |
2-2s | Reject: systematic error | Two consecutive values beyond the same 2 SD limit. |
R-4s | Reject: random error | One value beyond +2 SD and the next beyond −2 SD (range over 4 SD). |
4-1s | Reject: systematic error | Four consecutive values beyond the same 1 SD limit. |
10x | Reject: systematic error | Ten consecutive values on the same side of the mean. |
Good to know
SD uses n − 1 (sample SD). Calculating limits from only a few values is unreliable; at least 20 values are usually recommended to establish a new mean and SD. Westgard defines R-4s within one run across two control levels; for a single control level this tool applies it to consecutive runs. When a run is rejected, do not report patient results: find and correct the cause, then rerun controls and affected samples.
Formula
Mean = Σx ÷ n
SD = √(Σ(x − mean)² ÷ (n − 1))
CV% = SD ÷ mean × 100
z = (x − mean) ÷ SD
Common questions
How is CV% calculated?
CV% = SD ÷ mean × 100. It expresses precision as a percentage.
Which Westgard rules detect systematic error?
2-2s, 4-1s and 10x. 1-3s and R-4s mainly detect random error.
Is a 1-2s violation a rejection?
No. It is a warning that triggers checking the other rules.