Margin of Error Calculator

Your details

Switch to reverse-solve to find the sample size that achieves a target margin of error.
The result you observed, e.g. 52% said yes. Use 50% for the most conservative (largest) margin.
%
How many people or items were in your sample (n).
respondents
Enable when your sample is 5% or more of the total known population. FPC shrinks the margin because you have sampled a large fraction.
Margin of error
3.1%
Lower bound46.9%
Upper bound53.1%
Standard error1.581%
z critical value1.96
50 %
  • Lower bound
  • Upper bound

The margin of error is ±3.1 percentage points at 95% confidence.

  • We are 95% confident the true value lies between 46.9% and 53.1%, centered on the observed 50%.
  • The margin shrinks with the square root of the sample size: to halve it you need roughly four times as many respondents.
  • A result near 50% produces the widest margin; results near 0% or 100% are estimated more precisely.

Next stepSwitch to Reverse-solve mode to find the sample size needed for a tighter margin.

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