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Every survey or poll based on a sample (not the entire population) carries some uncertainty — the margin of error quantifies how far the true population value could realistically differ from the sample result, at a chosen confidence level.
How it works
Choose a confidence level (90%, 95%, or 99%), enter the sample proportion (use 0.5 if unknown, since that produces the most conservative/largest margin of error), and the sample size. The calculator applies MOE = z√(p(1−p)/n), using the standard z-score for your chosen confidence level.
- Enter confidence level.
- Enter sample proportion (0-1, use 0.5 if unknown for the most conservative estimate).
- Enter sample size.
- Click Calculate to see your results.
Examples
A typical political poll
A poll of 1,000 people at 95% confidence (with an unknown true proportion, so p = 0.5) has a margin of error of about ±3.1% — the commonly cited "margin of error" figure in news coverage of polls this size.
Who should use it
- Interpreting or designing surveys and polls.
- Statistics coursework on confidence intervals and sampling.
Industry applications
- Market research and survey design
- Political polling and social science research
Advantages
- Standard, widely-used formula matching how most reported survey margins of error are calculated.
- Supports the three most commonly used confidence levels.
Limitations
- Only accounts for random sampling error — not sampling bias, question wording effects, or non-response bias.
Common mistakes to avoid
- Forgetting that margin of error only accounts for sampling error — it doesn't capture bias from a poorly designed survey, non-response, or a non-representative sample.
- Assuming a bigger sample always meaningfully shrinks the margin of error — due to the square root relationship, gains shrink quickly past a certain sample size.
Best practices
- Use p = 0.5 when you have no prior estimate of the true proportion, for the most conservative (largest) margin of error.
- Remember margin of error addresses sampling error only — a biased sampling method has separate, un-quantified error this calculation doesn't capture.
Tips
- If you need a specific margin of error for a planned survey, work backward from this formula to find the minimum sample size required.