How to use it
- Enter the number of completed interviews, n.
- Enter the observed percentage, or 50% for the most cautious estimate.
- Choose the confidence level: 90%, 95% or 99%.
- Add the population size only if the sample is a sizeable share of a small, known population.
Formula and logic
The calculator uses the standard formula for a proportion:
e = z · √(p(1 − p) / n) · √((N − n) / (N − 1))
Here p is the observed proportion as a decimal (0.40 for 40%) and n is the number of completed interviews. The multiplier z depends on the confidence you choose: 1.645 at 90%, 1.96 at 95% and 2.576 at 99%. The second square root is the finite population correction, with N as the population size. It is applied only when you enter N; otherwise the population is treated as very large.
The confidence interval is then p ± e. For 400 interviews and p = 0.5 at 95% confidence, e is ±4.9 points without the correction. If those 400 come from a population of only 2,000, the correction narrows the margin to ±4.4 points, because a fifth of the population has been interviewed.
How to read the result
At 95% confidence and p = 0.5, the margin of error falls as follows:
| Completed interviews | Margin of error |
|---|---|
| 100 | ±9.8 points |
| 200 | ±6.9 points |
| 400 | ±4.9 points |
| 1,000 | ±3.1 points |
| 1,500 | ±2.5 points |
The margin shrinks with the square root of the sample, so moving from 1,000 to 1,500 interviews buys much less precision than moving from 100 to 400. Results close to 0% or 100% have smaller margins than results near 50%.
Keep three limits in mind. The margin of error covers sampling error only; it says nothing about biased question wording, non-response bias or a sample source that misses part of the population. It applies to one percentage at a time, not to the difference between two groups. And for quota samples from online panels, it should be read as a guide rather than an exact confidence interval.
Frequently asked questions
What is a good margin of error?
It depends on the decision. For tracking a headline figure, such as brand awareness, ±3 to ±5 points is common. For an exploratory study whose aim is a rough ranking of options, ±7 to ±10 may be acceptable. Work backwards from the smallest difference that would change your decision, then use the sample size calculator to plan the interviews.
Why does the margin depend on the percentage itself?
Because the variance of a proportion, p(1 − p), is largest at 50% and falls towards zero at the extremes. A result of 50% from 400 interviews carries a margin of ±4.9 points, while a result of 10% from the same sample carries only ±2.9. Using 50% when you have no result yet gives the most cautious estimate.
Does the margin of error apply to online panel surveys?
Strictly, the formula assumes a random sample, which opt-in panels are not. In practice, researchers still report it as an indication of precision, ideally with a note that the sample is non-probability. What matters more for panel data is good quotas, sensible weighting and thorough cleaning, which our methodology describes.
How do I know whether two results differ significantly?
Overlapping margins of error are not a reliable test. To compare two percentages, such as this year's result with last year's or men with women, use a two-proportion test. Our A/B test significance calculator runs exactly that test and works for survey groups as well as website variants.
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