Margin of Error Calculator

Find the margin of error for a survey from its sample size, proportion, and confidence level. Enter the sample size and pick the confidence.

Margin of Error
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Plus or minus.

Usage Tip

To halve the margin of error, you need about four times the sample size.

THE MATH
E = z × √(p(1 − p) ÷ n)
The plus-or-minus around a survey estimate
The margin of error is the plus-or-minus range around a survey result at a given confidence level.
It shrinks with larger samples and grows with higher confidence.
Enter the sample size and the proportion (50 percent is the most conservative).
Choose the confidence level.
The margin assumes simple random sampling.
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The calculators and tools on Formula Factory are provided for general guidance and informational purposes only. Results are estimates based on standard formulas and the values you enter — they do not constitute professional engineering, electrical, or architectural advice. Always verify calculations with a qualified professional before making decisions for any safety-critical, code-compliance, or commercial application. Formula Factory makes no representations or warranties as to the accuracy or completeness of any result, and accepts no liability for errors, omissions, or any outcomes arising from reliance on this information.