Poll margin of error calculator
The margin of error quoted for an opinion poll comes from this one formula, and it is widest when the split is 50/50.
%
Leave at zero for an effectively infinite population.
Margin of error
3.0965%
- Lower bound
- 48.904 %
- Upper bound
- 55.096 %
- Margin at a 50/50 split
- 3.0990 %
- Finite population correction
- 1.000 000
Show the working
- Observed percentage = 52
- Sample size = 1000
- Confidence level = 1.959 96
- Population size = 0
- prop = 52 / 100 = 0.52
- raw = 1.959 96 * sqrt(0.52 * (1 - 0.52) / 1000) = 0.030 964 9
- Finite population correction = 0 > 1000 ? sqrt((0 - 1000)/(0 - 1)) : 1 = 1
- Margin of error = 0.030 964 9 * 1 * 100 = 3.096 49
- Lower bound = 52 - 3.096 49 = 48.9035
- Upper bound = 52 + 3.096 49 = 55.0965
- Margin at a 50/50 split = 1.959 96 * sqrt(0.25/1000) * 1 * 100 = 3.098 98
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- margin = z sqrt(p(1-p)/n)
- finite population correction = sqrt((N - n)/(N - 1))
Sampling error is only one source of error in a poll, and usually not the largest. Non-response and question wording are not in this formula.