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Free margin of error calculator for polls, surveys, and proportion studies. Enter confidence level, sample size, expected proportion, and optional population size to estimate statistical precision quickly.
Last updated: April 20, 2026
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Margin of error
±4.90%
Finite-adjusted margin
±4.88%
Z-score
1.960
Standard error
0.02500
Interpretation
With finite population correction, estimated margin is ±4.88%.
Formula used:
MOE = Z × √(p(1-p)/n)
Use p = 50% for a conservative estimate when unsure.
Core formula
MOE = Z × √(p(1-p)/n)
Supported levels
80% to 99%
Adjustment effect
Typically lowers MOE
Confidence: 95%, Sample: 400, Proportion: 50%, Population: 50,000
Margin of error
±4.90%
Finite adjusted
±4.88%
This calculator estimates uncertainty around a sample proportion. It combines the selected confidence z-score with the sampling standard error and reports margin of error in percent terms.
SE = √(p(1-p)/n)MOE = Z × SEIf population size is provided, finite population correction is applied for a more practical estimate.
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