Calculator inputs
Plotly graph
The chart compares the reported mean interval with the estimated standard deviation interval from your entered settings.
Formula used
E = (Upper CI − Lower CI) ÷ 2
SE = E ÷ Critical Value
s = SE × √n
Lower SD = √(((n − 1) × s²) ÷ χ²upper)
Upper SD = √(((n − 1) × s²) ÷ χ²lower)
For 95% intervals, the critical value is usually t0.975, n−1 for sample-based work, or 1.96 when using the large-sample z approximation.
How to use this calculator
- Enter the sample mean from your study or report.
- Add the lower and upper limits of the reported confidence interval for that mean.
- Enter the sample size used to create the interval.
- Keep the mean confidence level at 95 if the published interval is 95%.
- Choose the SD interval level you want to report, such as 95% or 99%.
- Select the t method for most sample-based analyses.
- Press calculate to show the result directly below the header and above the form.
- Use the CSV or PDF buttons to save your output.
Example data table
| Scenario | Mean | Lower CI | Upper CI | n | Method | Estimated SD |
|---|---|---|---|---|---|---|
| Coating thickness batch A | 50.00 | 47.20 | 52.80 | 30 | t | 7.50 |
| Response time sample | 120.00 | 118.60 | 121.40 | 64 | z | 5.71 |
| Sensor voltage set | 3.30 | 3.24 | 3.36 | 25 | t | 0.15 |
FAQs
1. What does this calculator estimate?
It estimates a sample standard deviation from a reported mean confidence interval and sample size. It also produces a confidence interval for the standard deviation, plus variance, standard error, and exportable result summaries.
2. Can I recover standard deviation from a 95% CI for the mean?
Yes. First convert the interval half-width into a margin of error. Then divide by the chosen critical value to get standard error, and multiply that result by the square root of the sample size.
3. Should I use the t method or the z method?
Use the t method for most sample-based confidence intervals, especially with modest sample sizes. Use the z method when the interval was clearly built with a normal critical value or when large-sample reporting rules require it.
4. Why does sample size affect the derived standard deviation?
A fixed interval width becomes more informative when n changes. Since standard error equals standard deviation divided by square root of n, the same margin paired with a larger sample implies a larger underlying standard deviation.
5. How do I calculate a 99% CI for the standard deviation of coating layer thickness?
Estimate the sample standard deviation from the mean interval first. Then apply the chi-square confidence formula with n−1 degrees of freedom and choose 99% as the SD interval level. This calculator performs both steps from the same inputs.
6. What if the entered mean is not the midpoint of the interval?
The tool still estimates standard deviation from the interval width and sample size, because those values determine the margin of error. It also shows a note so you can quickly spot a possible reporting or rounding mismatch.
7. Can I export the results for reports or audits?
Yes. Use the CSV button for spreadsheet-friendly output and the PDF button for a clean summary document. Both exports capture the latest calculated values shown in the result section above the form.
8. Does this estimate population or sample standard deviation?
It estimates a sample standard deviation implied by the reported interval and sample size. The separate chi-square interval then gives plausible bounds for the underlying process standard deviation, assuming the sample came from a roughly normal distribution.