What this calculator does
Standard error of the mean works out how much a sample mean is expected to vary from the true population mean. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaSE = s/√n; with a known finite population, SE = s/√n × √((N−n)/(N−1))
The inputs explained
| Field | What to enter |
|---|---|
| Sample standard deviation | A number. Starts at 12. |
| Sample size | A number. Starts at 36. |
| Population size (0 = treat as infinite) | A number. Starts at 0. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with sample standard deviation
Every other input is held at the calculator’s starting values while sample standard deviation varies. Select any row to load that scenario into the calculator.
How the answer changes with sample standard deviation
| Sample standard deviation | Standard error | Without finite-population correction | Finite population correction factor |
|---|---|---|---|
| 6 | 1.000 | 1.000 | not applied: population size not given |
| 9 | 1.500 | 1.500 | not applied: population size not given |
| 12 | 2.000 | 2.000 | not applied: population size not given |
| 18 | 3.000 | 3.000 | not applied: population size not given |
| 24 | 4.000 | 4.000 | not applied: population size not given |
| 36 | 6.000 | 6.000 | not applied: population size not given |