Survey Margin of Error Calculator

How it is calculated

The margin of error for a proportion is MOE = z × √(p × (1 − p) ÷ n). Here n is the number of respondents, p is the proportion as a decimal between 0 and 1 (0.5 means 50%), and z depends on the confidence level you pick: 1.645 for 90%, 1.96 for 95% and 2.576 for 99%. The result is shown as a percentage, so 3.10% means plus or minus 3.10 percentage points.

The tool assumes a simple random sample from a very large population; it does not apply a finite-population correction, and it does not account for weighting or clustering. The sample size must be above zero and the proportion must lie between 0 and 1, otherwise nothing is returned. Using p = 0.5 gives the largest possible margin for a given n, so it is the safe choice when you do not yet know the answer.

Common mistakes

• Entering the proportion as a percentage (50). The field expects a decimal such as 0.5; a value above 1 returns no result.
• Reading the margin as a percentage of the result rather than percentage points. A 3.10% margin on a 52% result means about 48.9% to 55.1%, not 50.4% to 53.6%.
• Expecting a larger sample to help much. The margin shrinks with the square root of n, so quadrupling the sample only halves it.
• Applying the figure to a non-random sample, such as an opt-in web poll. The formula covers sampling error only, not bias.
• Using the margin for a subgroup with the whole sample size. A subgroup of 100 people from a 1,000-person survey has a much wider margin; enter the subgroup's n instead.