Sampling Error Calculator

Your details

Proportion mode is for survey-style questions (e.g. % who prefer X). Mean mode is for continuous measurements (e.g. average height).
Number of observations in your sample.
Observed proportion in your sample, expressed as a decimal (e.g. 0.45 for 45%). Use 0.5 when unknown - this maximises the margin of error.
(0 to 1)
How confident you want to be that the true value falls within your interval. 95% is the most commonly reported level in research.
Turn on to apply the finite population correction (FPC), which reduces the margin of error when your sample is a large fraction of the population.
Sampling errorAcceptable error
0.049

Margin of error (half-width of the confidence interval)

CI lower bound0.451
CI upper bound0.549
Critical value (z or t)1.96
Standard error0.025
FPC factor1
0.049
Very low<0.01Low0.01-0.03Acceptable0.03-0.05High0.05-0.1Very high0.1+

Sampling error: 4.90% at 95% confidence (n = 400).

  • At 95% confidence, the true proportion lies between 45.10% and 54.90%.
  • To halve this margin of error, you would need to approximately quadruple your sample size to around 1,600 observations.

Next stepYour margin of error is within an acceptable range. Report it alongside the confidence level and sample size so readers can judge precision.

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