The calculation, without hidden assumptions
Margin of error is half the width of a confidence interval under a stated sampling model. For a proportion it depends on p(1−p); for a mean it depends on a standard deviation. This calculator keeps those two cases separate, supports an optional finite-population correction, and reports the proportion result in percentage points so “±3” is not confused with “3% of the estimate.”
How to use this calculator
Choose proportion or mean, enter sample size and select the confidence level.
For a proportion, enter an expected proportion; for a mean, enter the standard deviation used by the model.
Optionally enter a finite population size and read both the margin and the assumptions shown in the working.
Where people use it
- •Checking a survey margin
- •Reproducing a reported confidence calculation
- •Exploring how sample size changes precision
Example: n = 1,067, p = 50%, 95% confidence
With z = 1.96 and p = 0.5, the standard error is √(0.25/1067). Multiplying by 1.96 gives a margin a little above three percentage points before any finite-population correction.
What the result does not assume
- •This implementation is z-based. For a mean with an unknown population standard deviation—especially with a small sample—a t-based interval can be more appropriate.
- •A margin of error describes sampling uncertainty under the model; it does not include nonresponse bias, coverage error, question wording effects or other non-sampling errors.
Frequently asked questions
Why is 50% called conservative for a proportion?+
Because p(1−p) reaches its maximum at p = 0.5, producing the widest basic z-based margin for a fixed sample size.
When does population size matter?+
Finite-population correction matters when sampling without replacement from a known population and the sample is a meaningful share of that population.
Does ±3 points mean the estimate is guaranteed to be within three points?+
No. It is a confidence-interval quantity tied to a sampling procedure and stated confidence level, not a guarantee about one estimate.
Semantic next steps
Continue the calculation
These links move to a different input, formula or project stage rather than a keyword variation of this page.
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