Margin of Error Calculator | CountingMethods.com

Statistical Inputs

Confidence Level (%)

Sample Size (n)

Population Proportion (%)

Population Size (Optional)

Calculated Margin of Error

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+/- Error range

Z-Score

Standard Error

Confidence Score

Low Precision High Precision

Reliability Spectrum

Precision vs. Sample Size

This curve shows how the Margin of Error decreases as your sample size increases. Diminishing returns occur as you move right.

Confidence Interval Comparison

Calculate results to see comparisons.

Statistical Formulas

The Margin of Error (MOE) represents the radius of the confidence interval for a proportion.

Standard MOE: MOE = z * √[ p(1-p) / n ]
Finite Population Correction (FPC): If population N is known, MOE is multiplied by √[ (N-n) / (N-1) ].

Note: 50% Proportion provides the "worst-case" (most conservative) Margin of Error.