Standard Error Calculator

Quick answer

This calculator computes the standard error of the mean with relative SE and a 95% confidence half-width in one pass.

Just SD and sample size.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

How the Standard Error Calculator Works

SE = SD / sqrt(n); relative SE = SE / SD x 100; 95% half-width = 1.96 x SE

The standard error measures how much sample means wobble around the true mean. It shrinks with the square root of the sample size.

1
Enter standard deviation
Give your SD, for example 15.
2
Enter sample size
Type n, like 100 observations.
3
Read the outputs
See SE, relative SE, and the CI half-width.

FAQs

What is the SE for SD 15 and n = 100?

SE = 15 / 10 = 1.5, giving a 95% CI half-width of 1.96 x 1.5 = 2.94.

How do I cut the standard error in half?

Quadruple n: SE scales as 1 / sqrt(n), so n = 400 with the same SD gives SE = 0.75.

What is relative standard error?

SE as a percent of SD: at n = 100 it is exactly 10 percent, a common quality threshold.

What is the 95% half-width good for?

It approximates your margin of error: mean plus or minus 2.94 when SE is 1.5.

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