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Survey Margin of Error Calculator

Find the margin of error for your survey based on sample size and confidence level.

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.

Worked example

A poll interviews 1,000 people, and you use p = 0.5 at 95% confidence (z = 1.96).

p × (1 − p) = 0.5 × 0.5 = 0.25. Dividing by n: 0.25 ÷ 1000 = 0.00025, and the square root is about 0.01581. Multiply by z: 1.96 × 0.01581 ≈ 0.0310, which is 3.10%. A reported 52% result is therefore best read as roughly 49% to 55%. With 4,000 respondents the margin falls to 1.55%, half as large.

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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.

About this calculator

The margin of error for a survey proportion is calculated as z times the square root of (p × (1 − p) divided by n), where z is the critical value from the standard normal distribution for the chosen confidence level (1.645 for 90%, 1.96 for 95%, and 2.576 for 99%), p is the expected or observed proportion, and n is the sample size — the formula behind the “plus or minus X points” figure reported alongside most polls.

Pollsters, market researchers, and survey statisticians use this calculation both to determine how large a sample they need before fielding a survey and to report the precision of results afterward, since the margin of error shrinks with the square root of sample size — quadrupling the sample only halves the margin of error — and is largest when the true proportion is near 50%.

Sample size, the proportion you expect and the confidence level determine how far your survey percentage could sit from the true value; that margin of error is what you get.

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  • Editorial team

    The margin belongs to the sample you enter, so a subgroup needs its own size. In a 1,000-person survey at 95% and a proportion of 0.5 the margin is 3.10%, but for 400 women inside that sample it is 4.90%. It also covers only sampling chance, not biased wording or non-response. Which subgroup in your survey worries you most about a wide margin?

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