Margin of error calculator
If 50% of 1,000 respondents said yes, this tool tells you how far that figure could reasonably be from the true value.
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Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter sample size (n), observed proportion (p), confidence level and population size (optional).
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Margin of error = z × √(p(1 - p) ÷ n). With a population of size N it is multiplied by √((N - n) ÷ (N - 1)).
Example
Inputs: Sample size (n) = 1,000, Observed proportion (p) = 50 %, Confidence level = 95%. Result: Margin of error (±): 3.1%; Likely range: 46.901% to 53.099%; Critical z: 1.96.
Limits and caveats
- Assumes a simple random sample and does not cover question wording or non-response bias.
- The normal approximation weakens when n × p or n × (1 - p) is below about 10.
Questions about this tool
Why is 50% the default proportion?
p(1 - p) peaks at 50%, so it gives the largest possible margin. That is the figure most polls publish.
When should I enter the population size?
When the sample is a noticeable part of the population, such as 200 staff out of 800. For very large populations leave it empty.
Does doubling the sample halve the margin?
No. The margin scales with 1 ÷ √n, so you need four times the sample to halve it.