Margin of Error Calculator for Survey Results
Find the margin of error for any survey result and sample size, including subgroups, small populations, weighting and the more accurate Wilson interval. Free.
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How to use the margin of error calculator
- Enter the number of completed interviews behind the result.
- Enter the result itself, for example 38% agree. Leave 50% to see the worst-case margin for the whole survey.
- Pick a confidence level. 95% is standard.
- Add a population size only for small, countable groups.
- If the data is weighted, enter the design effect. The weighting efficiency calculator works it out from your weights.
- List subgroup bases, such as each country or age band, to see how much wider their margins are.
What is the margin of error?
The margin of error is the half-width of a confidence interval. If 38% of 1,200 respondents agree and the margin is ±2.7 points at 95% confidence, the population figure is likely between 35.3% and 40.7%. It describes sampling error only: the chance difference between a random sample and the full population.
Two things surprise people. First, the margin depends on the sample size, not the population size, unless the population is small. Second, the margin is different for every result. It is largest at 50% and shrinks towards 0% and 100%. That is why the calculator shows a table by result.
Margin of error formula
MOE = z × √(p × (1 − p) ÷ n)
Here z is 1.96 for 95% confidence, p is the result as a decimal and n the sample size. Weighting reduces the effective sample to n ÷ deff. For small populations the margin is multiplied by √((N − n) ÷ (N − 1)).
The standard formula misbehaves when results are close to 0% or 100%, or samples are small. It can produce ranges below zero. The Wilson score interval fixes that and is the better default for small bases. Switch method in the advanced fields.
Worked example
A tracker of 1,200 adults finds 38% awareness. The data is weighted with a design effect of 1.4.
- Effective sample: 1,200 ÷ 1.4 = 857
- Margin: 1.96 × √(0.38 × 0.62 ÷ 857) = ±3.25 points
- Range: 34.8% to 41.3%
Without weighting, the margin would be ±2.75 points. Weighting cost about half a point of precision. A subgroup of 150 in the same survey has a margin of about ±9 points, which is why small cells need care. Press Example to load this case.
Margin of error in multi-country studies
Each country result carries its own margin based on its own base. A 6-country study with 500 per country has about ±4.4 points per country but about ±1.8 points for the pooled total if the countries are weighted equally. When country sizes are weighted to population, the design effect rises and the total margin widens. Report both levels so readers know which comparisons hold.
Frequently asked questions
What is an acceptable margin of error?
For decision-making surveys, ±3 to ±5 points at 95% confidence is typical. Political polls aim for ±3. Exploratory or hard-to-reach B2B work often accepts ±7 to ±10.
Does a bigger population need a bigger sample?
Not beyond a point. Once the population is more than about 20 times the sample, its size barely affects the margin of error.
How do I compare two results that each have a margin of error?
Overlapping ranges do not prove there is no difference. Use the statistical significance calculator to test the difference directly.
Does the margin of error apply to online panel surveys?
Strictly, it assumes a probability sample. For opt-in panels, AAPOR recommends describing precision with care, for example as a credibility interval. In practice it is still widely used as a guide to precision.
Why does my subgroup have a much bigger margin?
The margin grows with 1 ÷ √n. A subgroup a quarter the size of the total has double the margin of error.
Need the respondents, not just the numbers?
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<a href="https://globalvoxpopuli.com/tools/margin-of-error-calculator/">Margin of Error Calculator</a> by Global Vox Populi