Standard Error Calculator

What Standard Error Means

Standard error measures uncertainty in a sample estimate. For a mean, SEM shows how much the sample mean would vary across repeated samples. Related tools: Standard Deviation Calculator, Relative Standard Error Calculator, and P Hat Calculator.

Standard Error of the Mean

$$SEM = \frac{s}{\sqrt{n}}$$

where $s$ is the sample standard deviation and $n$ is the sample size.

Standard Error of a Proportion

$$SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Use this when estimating a population proportion from successes and sample size.

Example

Twelve height measurements with mean 179.5 cm and sample SD 6.52 cm give SEM ≈ 1.88 cm. That means repeated samples would produce sample means typically within about 1.88 cm of the true average.