Written by Dackohn; last reviewed November 2026.
The margin of error is half the width of a confidence interval: the “±” in “52% ± 3%”. For a percentage at 95% confidence it is 1.96 × √(p(1 − p) / n), so about ±3.1 points for 1,000 people. It covers random sampling error only, not biased samples or poor questions.
The calculation
A poll of 1,000 people finds 52% support. The margin of error at 95% confidence is:
1.96 × √(0.52 × 0.48 / 1000) = 0.031, or ±3.1 points
So the likely range for the true figure is 48.9% to 55.1%. If the poll were repeated many times, about 95% of such intervals would contain the true value.
Sample size
| Sample size | Margin of error (p = 50%, 95%) |
|---|---|
| 100 | ±9.8 |
| 400 | ±4.9 |
| 1,000 | ±3.1 |
| 1,600 | ±2.5 |
Halving the margin needs four times the sample. That is why so many polls stop at about 1,000: going further costs a lot and adds little. Population size barely matters unless the sample is a sizeable share of it.
The trap: comparing two figures
If candidate A has 52% and B has 48% in a two-way race, the lead is 4 points, but its margin of error is about double, ±6.2 points, because a gain for one is a loss for the other. So “52 vs 48, ±3” is not a clear lead. For two separate groups of 1,000, a difference has a margin of about ±4.4 at p = 50%. Subgroups have larger margins too: a figure based on 200 of the 1,000 respondents has about ±7.
What it does not cover
- Selection bias: an online poll of volunteers can be far off however many answer.
- Non-response: if those who answer differ from those who do not.
- Question wording: leading questions shift answers.
- Change over time: a poll describes the moment it was taken.
Real polling errors are often larger than the published margin for these reasons.
For a mean
The margin of error for a mean is t × s / √n. With mean 100, SD 15 and n = 40, it is 2.023 × 15 / 6.32 = ±4.80. See how to calculate a confidence interval.
Try it yourself
Margin of Error Calculator →For percentages and means, with an optional population size. Survey Sample Size Calculator →Plan how many responses you need.Frequently asked questions
What does a margin of error of 3% mean?
The true value is likely within 3 points of the reported figure, usually at 95% confidence, considering only random sampling error.
Why do polls survey about 1,000 people?
It gives a margin of about plus or minus 3%, and further precision gets expensive, because halving the margin takes four times the sample.
Is margin of error the same as confidence interval?
The margin is half the width of the interval. The interval is the estimate plus and minus the margin.
Related reading: How to calculate sample size · Confidence intervals explained · Confidence interval for a proportion
Sources & further reading: NIST/SEMATECH e-Handbook of Statistical Methods · OpenStax Introductory Statistics. How we compute & validate: methodology. Written & reviewed by Dackohn; last reviewed August 2026.