Math
Margin of Error Calculator
Compute the margin of error for a survey or poll from sample size, proportion, and confidence level (90, 95, 99 percent). Optional finite population correction.
Margin of error
Number of respondents in the sample.
Use 0.5 for the worst-case margin when the true split is unknown.
Leave blank for large populations. Used for the finite population correction.
Margin of error
± 3%
With 95% confidence, the true value lies between 47% and 53% when the sample proportion is 50%.
Critical z*
1.96
Standard error
0.0153
Lower bound
47%
Upper bound
53%
Frequently Asked Questions about the Margin of Error Calculator
What does margin of error actually mean?
Margin of error is the +/- range around a survey result that accounts for random sampling noise. A poll that says 52% plus or minus 3% means the true value is likely to fall between 49% and 55%. It captures only sampling variability, not bias from a bad question, a skewed frame, or low response rates, so a tight margin on a flawed survey is still a flawed survey.
Why is 0.5 the most conservative proportion to use?
The standard error formula contains p * (1 - p), which is maximized when p = 0.5 (giving 0.25). Any other value of p produces a smaller product and therefore a smaller margin. Plugging in 0.5 gives you the widest possible margin for your sample size, which is the safe choice before you have data or when you want to report a worst-case headline number.
Which confidence level should I pick: 90, 95, or 99?
95% is the default in polling, marketing research, and academic work; it gives a critical z of 1.96. Use 90% (z = 1.645) when a narrower interval matters more than rigor, for example fast-turn product experiments. Use 99% (z = 2.576) when the cost of missing the true value is high, such as clinical or safety contexts. Higher confidence always means a wider interval for the same sample.
When does the finite population correction matter?
The standard formula assumes you are sampling from an effectively infinite population. Once your sample is more than about 5% of the actual population, that assumption breaks and the real margin is smaller than the formula suggests. The correction factor sqrt((N - n) / (N - 1)) shrinks the margin to reflect that. It matters for small populations like one company's employees or one school's students, and is negligible for national polls.
Why are political polls almost always around 1,000 respondents with a 3% margin?
Plugging n = 1,067, p = 0.5, and 95% confidence into the formula gives a margin of error of almost exactly 3%. To halve it to 1.5% you would need roughly four times the sample (about 4,268 respondents), because margin shrinks with sqrt(n). Doubling the sample to 2,134 only drops the margin to about 2.1%, so 1,000 to 1,100 respondents at +/-3% is the industry sweet spot between precision and cost.