# Standard Error Calculator

URL: https://speedycalculator.com/calculators/statistics/standard-error/
Last updated: 2026-10-25

> The standard error calculator finds the standard error of the mean from a list of data, or from a standard deviation and sample size. It shows how precisely the sample mean estimates the population mean.

## Inputs

- Data

## Results

- Standard error of the mean
- Standard deviation
- Sample size
- Mean

## Formula

```
SE = s ÷ √n
```

## Explanation

Larger samples give smaller standard errors: quadrupling the sample size halves the SE.

### How to use the Standard Error Calculator

- **Data**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Divide the sample standard deviation by the square root of the sample size.

### What each result means

- **Standard error of the mean** = stdev([Data])÷sqrt(count([Data]))
- **Standard deviation** = stdev([Data])
- **Sample size** = count([Data])
- **Mean** = mean([Data])

## Worked example

Inputs — Data: 12.1, 11.8, 12.4, 12.0, 11.9, 12.3, 12.2.

Results — **Standard error of the mean = 0.08165**; Standard deviation = 0.21602; Sample size = 7; Mean = 12.1.

## FAQ

**Is standard error the same as standard deviation?**
No; SD describes spread of data, SE describes uncertainty in the mean.

**How is SE used?**
To build confidence intervals and test statistics.

**What formula does the Standard Error Calculator use?**
SE = s ÷ √n.


## Sources

- [NIST/SEMATECH e-Handbook of Statistical Methods](https://www.itl.nist.gov/div898/handbook/)