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.
Margin of error
±4.99%A 50% reading would really sit between 45% and 55%.
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.
Related resources
Turn these numbers into a real survey
Camaleonic Survey collects the responses and shows you results live as they arrive.