Standard Error Calculator
Compute the standard error of a sample mean or a sample proportion from the standard deviation and sample size.
Standard error
1.50
Breakdown
- Half-width of 95% CI (± 1.96 SE)
- 2.94
- Formula used
- SE = s / √n
Last updated:
FAQ
Standard deviation vs standard error — which is which?
Standard deviation describes spread among individuals in one sample; standard error describes how much the sample mean itself wobbles from sample to sample. Dividing by √n turns one into the other.
Why does the SE shrink with sample size?
Averaging cancels out random ups and downs, and the cancellation scales with √n. Four times the data yields a mean only half as uncertain — diminishing returns built into the square root.
Can the standard error be larger than the SD?
No — since n ≥ 2, dividing by √n always makes the SE smaller than the SD. If you see the opposite, the SD and SE columns are probably swapped in the source.
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