Margin of Error Calculator
Find the margin of error for a survey or poll from its sample size, expected proportion and confidence level.
How it works
E = z × √(p(1 − p) ÷ n)
The margin of error is the half-width of a confidence interval for a proportion. It grows with the z-value for your confidence level and with the spread p(1 − p), and shrinks with the square root of the sample size. Using p = 0.5 gives the widest, most conservative margin, which is why reported poll margins usually assume it.
Worked example
For a poll of 1,000 people at 95% confidence with p = 0.5: E = 1.96 × √(0.25 ÷ 1000) = 1.96 × 0.0158 ≈ 0.031, or about ±3.1%. So a candidate polling at 50% is really somewhere between roughly 46.9% and 53.1%.
Frequently asked questions
Why do so many national polls report about ±3%?
Because a sample of around 1,000 at 95% confidence produces a margin near 3.1%. It is a sweet spot: large enough for a tight margin, small enough to stay affordable, so it became the industry standard.
Does the size of the population change the margin?
Barely, once the population is large. The formula depends on sample size, not population size — sampling 1,000 gives about the same margin whether the population is 100,000 or 100 million.
What does the margin of error leave out?
Only sampling error. It says nothing about biased questions, non-response, or bad sampling frames, which can distort a survey far more than the reported margin suggests.
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For education — check assumptions (sample size, distribution) before using statistics in real decisions.