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Margin of Error Calculator: How Precise Are Your Results?
Calculate how precise your survey results are based on your sample size. The margin of error tells you the range within which the true population value likely falls.
How This Calculator Works
The margin of error calculator takes your sample size, confidence level, and response percentage to determine the precision of your results. Larger samples produce smaller margins of error.
The Formula
MOE = Z × √(p × (1-p) / n) where Z is the z-score for your confidence level (1.96 for 95%), p is the observed proportion, and n is sample size. For finite populations, multiply by √((N-n)/(N-1)).
How to Interpret Your Results
If your survey shows 60% agreement with a margin of error of plus or minus 4%, you can be confident the true population value is between 56% and 64%. The margin of error applies to each percentage independently.
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Try InqveyFrequently Asked Questions
Plus or minus 3-5% is good for most research. Political polls typically target plus or minus 3%. Exploratory research may accept plus or minus 8-10%.
Increase sample size. Doubling the sample roughly reduces margin of error by 30%. Quadrupling cuts it in half.
Yes, margin of error is highest at 50% and decreases toward 0% or 100%. Using 50% in calculations gives a conservative estimate.
Margin of error increases for subgroups based on their smaller sample sizes. Calculate separately for each subgroup you analyze.