How precise is your survey result?
A result of 42 % is never exactly 42 %. The margin of error tells you how wide a band you have to put around your result.
42 % of respondents agree
Confidence interval at 95 %
Calculate margin of error
From sample size, result and confidence level.
Optional. Leave empty if it is very large or unknown.
Margin of error
± 4.4percentage points
Solide = z · √(p · (1 − p) / n), with an extra correction when the population is known.
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What is the margin of error?
The margin of error describes how much a survey result can swing purely because of who happened to end up in the sample. It is given in percentage points: “42 % ± 3.1 points” means an interval computed this way — here 38.9 % to 45.1 % — captures the true value at the chosen rate. It says nothing about other sources of error — badly worded questions or a skewed selection stay invisible.
How is the margin of error calculated?
e = z · √(p · (1 − p) / n). Here z is the value from the normal distribution for the confidence level, p the observed share and n the sample size. When the population is known and larger than the sample, the finite population correction √((N − n) / (N − 1)) is applied on top — it narrows the margin, because a larger slice of the group was actually surveyed.
Margin of error and sample size
The margin shrinks in inverse proportion to the square root of the sample size. Four times as many answers halve it — no more than that. This is why going from 100 to 400 answers buys you a lot and going from 2,000 to 4,000 buys you very little. Halving the margin means quadrupling the effort.
Margin of error by sample size at 95 % confidence
| Answers | Margin of error |
|---|---|
| 100 | ± 9.8 percentage points |
| 250 | ± 6.2 percentage points |
| 500 | ± 4.4 percentage points |
| 1,000 | ± 3.1 percentage points |
| 2,500 | ± 2.0 percentage points |
Common questions
Is the margin in percent or percentage points?
Percentage points. With a result of 42 % and a margin of 3.1, the interval runs from 38.9 % to 45.1 % — not from 40.7 % to 43.3 %.
Why is the margin largest at 50 %?
Because p · (1 − p) peaks there. The more lopsided a result is, the more precise it is at the same sample size.
When do I need the finite population correction?
When you surveyed a meaningful share of the population — say 60 out of 200 members. With a very large population the correction is negligible.
Does the margin of error cover every error in a survey?
No, only the random error from drawing a sample. Bias from who you selected, from how questions were worded, or from systematic non-response is not included.