Margin of Error Calculator

A margin of error is a statistical measure that expresses the amount of random sampling error in a survey's results. It tells you how much the survey result may differ from the true value of the whole population. For example, a margin of error of ±5% means the true answer is likely within 5 percentage points of your survey result.

The margin of error is calculated using the formula: MOE = Z × √(p(1−p)/n) × √((N−n)/(N−1)), where Z is the Z-score for your confidence level, p is the proportion (assumed 0.5 for maximum variability), n is the sample size, and N is the population size. The finite population correction factor √((N−n)/(N−1)) is applied when the sample is a significant portion of the population.

The accuracy of your survey data depends on your sample size, population size, and chosen confidence level. A larger sample size relative to your population generally produces a smaller margin of error, meaning more precise results. A 95% confidence level with a margin of error under ±5% is considered acceptable for most research purposes.

95% is the most commonly used confidence level in survey research and is the industry standard. It means that if you ran the same survey 100 times, 95 of those results would fall within the margin of error. Use 99% when higher certainty is critical (e.g. medical or policy research), or 90% when a slightly wider margin is acceptable to reduce cost or effort.

The most effective way to reduce your margin of error is to increase your sample size. Lowering your confidence level will also reduce the margin of error, but at the cost of less certainty. Targeting a more homogeneous population can also improve precision. Generally, diminishing returns set in as sample size grows, so doubling your sample does not halve your margin of error.

The confidence level is the probability that your margin of error actually captures the true population value — for example, 95% confident. The margin of error is the actual ± range of values around your result. Both work together: a higher confidence level requires a larger margin of error (or a larger sample) to maintain the same precision.

For large populations (above ~20,000), the population size has very little effect on the margin of error — sample size is the dominant factor. The finite population correction only becomes meaningful when your sample represents a substantial fraction of the total population. For small populations under 1,000, both population size and sample size have a significant impact.

A margin of error of ±5% or less at the 95% confidence level is generally considered acceptable for most surveys. For highly sensitive decisions — political polling, medical studies, or major business strategies — aim for ±3% or lower. The 'good' threshold depends on how close your expected results are and what decisions are riding on the outcome.