Margin Of Error Calculator
Calculate the margin of error for a survey or experiment given sample size, population proportion, and confidence level.
Published by:
isCalculator Editorial Team
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How to Use the Margin of Error Calculator
This calculator computes the margin of error (MOE) for a survey or experiment using the formula: MOE = z × √(p̂(1-p̂)/n).
- Enter Sample Size (n) – The number of respondents or observations (must be ≥ 1).
- Enter Population Proportion (p̂) – The estimated proportion of the population (a decimal between 0 and 1). Default is 0.5 (50%), which gives the largest margin of error.
- Select Confidence Level – Choose 90%, 95% (default), or 99%. This sets the z-score automatically.
- Click "Calculate" – The margin of error appears as a percentage (e.g., ±3.45%). The formula with your inputs is shown below the result.
Tip: Use p̂ = 0.5 when you don’t have a prior estimate—it yields the most conservative (largest) margin of error.
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Frequently Asked Questions
Margin of error is a statistic expressing the amount of random sampling error in a survey's results. It represents the range within which the true population parameter is expected to fall.
The formula is MOE = z * sqrt( p̂(1-p̂) / n ), where z is the z-score corresponding to the confidence level, p̂ is the sample proportion, and n is the sample size.
This calculator supports 90% (z=1.645), 95% (z=1.96), and 99% (z=2.576) confidence levels.
