You get the margin in percentage points and the assumptions used in the calculation.
Margin of error is the approximate half-width of a confidence interval for a proportion. This calculator always uses p=0.5, the conservative scenario, with a normal approximation. It combines sample size and confidence level; when population is provided, it also applies finite population correction. The result is expressed in percentage points, not as a relative percentage.
With 278 responses, a population of 1,000, and 95% confidence, the conservative margin is approximately ±5.0 percentage points. An observed result of 60% would be reported as roughly 55% to 65%, under the calculation assumptions.
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Complete the fields to see the result and interpretation here.
The margin shrinks as the number of responses grows.
A higher confidence level produces a wider interval.
This tool fixes p at 50%, the conservative estimate for a proportion.
We use p = 0.5. Without a population, margin = z × √(0.25 ÷ n); with N, we multiply by √[(N−n) ÷ (N−1)].
The margin covers sampling uncertainty; it does not measure bias, poor questions, or inaccurate responses.
Yes. The interface does not accept an observed proportion. A value of 50% maximizes variance and produces a conservative margin for the supplied sample size.
It is shown in percentage points. If the result is 60% with a ±5-point margin, the approximate interval runs from 55% to 65%.
Across repetitions of the same sampling procedure, about 95% of intervals built this way would contain the true proportion if the assumptions held.
No. Without it, the calculator uses a large population. Enter it when the total is known and the sample is a meaningful share of that population.
The references support the definitions and assumptions. The formula used is shown on this page and covered by automated tests.
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