Margin of error calculator
How reliable are your results?
Enter how many responses you've collected and your confidence level. We calculate the margin of error: how far your percentages can deviate from the population's true value.
Parameters
Leave empty if unknown or very large.
How margin of error is calculated
The margin of error is the interval around an observed percentage. If 60% pick an option with a ±4% margin, the population's true value is, at your confidence level, between 56% and 64%.
The more responses, the narrower the margin. We use a variability of 50%, the most conservative, and if you give the population we apply the finite-population correction: as you approach surveying the whole group, the margin tends to zero.
A methodological caveat: this formula assumes simple random sampling. If your sample is biased (say, only your happiest customers reply), the true margin is wider than what you see here. Non-response, later weighting and complex designs (cluster or quota sampling) also widen the error through what is called the design effect. Treat it as a reference for clean sampling, not a guarantee.
Frequently asked questions
- What is a good margin of error?
- It depends on the decision. ±5% is the standard for general studies; for critical decisions aim for ±3% or less. Above ±10% the results are only indicative.
- Does the margin apply to the whole survey?
- The margin is calculated per question and depends on how many people answered it. A question many skipped has a larger margin than the survey total.
- How many responses do I need for a specific margin?
- Use the sample size calculator: it does the inverse, starting from the margin you want to hit.
Where the formula comes from
- Cochran, W. G. (1977). Sampling Techniques, 3rd ed. WileyThe margin of error expression for a proportion, inverted from the sample size formula.
More calculators
Turn these numbers into a real survey
Camaleonic Survey collects the responses and shows you results live as they arrive.