Margin of Error Calculator
Enter the sample SD, size, and confidence level.
Result
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Enter numbers to see the result.
Standard error
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z multiplier
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Formula: E = z x (s / sqrt(n)). Quadrupling n halves the margin of error.
Compute the margin of error of a survey or sample from the SD, sample size, and confidence level.
Enter the sample SD, size, and confidence level.
Enter numbers to see the result.
The margin of error is z times the standard error s/sqrt(n). Because of the square root, halving the error takes four times the sample: going from n = 100 to n = 400 cuts E in half, as the default example shows (+/- 1.176 at n = 400).
A poll reporting 52% with a 3-point margin of error at 95% confidence means the true value plausibly lies between 49% and 55%. If two candidates sit inside each other's margins, the race is a statistical tie.