Enter the Z-score, sample proportion, and sample size into the calculator to determine the 95 percent margin of error. This calculator can also evaluate any of the variables given the others are known.

95 Percent Margin Of Error Formula

The following formula is used to calculate the 95 percent margin of error.

E = Z * √((p * (1 - p)) / n)


  • E is the margin of error Z is the Z-score (for a 95% confidence level, Z = 1.96) p is the sample proportion (decimal) n is the sample size

To calculate the 95 percent margin of error, first determine the sample proportion and the sample size. Multiply the sample proportion by 1 minus the sample proportion. Divide the result by the sample size. Take the square root of the result. Finally, multiply the result by the Z-score.

What is a 95 Percent Margin Of Error?

A 95 percent margin of error is a statistical measure that indicates the range within which the true value of a population parameter is likely to fall 95 percent of the time. It is often used in polling or survey data to represent the uncertainty or variability that might be present in the data. The larger the margin of error, the less confidence one has that the poll’s reported percentages are close to the “true” percentages; that is, the percentages in the whole population.

How to Calculate 95 Percent Margin Of Error?

The following steps outline how to calculate the 95 Percent Margin Of Error.

  1. First, determine the Z-score. For a 95% confidence level, the Z-score is 1.96.
  2. Next, determine the sample proportion (p) as a decimal.
  3. Next, determine the sample size (n).
  4. Next, gather the formula from above = E = Z * √((p * (1 – p)) / n).
  5. Finally, calculate the 95 Percent Margin Of Error.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Z-score (Z) = 1.96

Sample proportion (p) = 0.5

Sample size (n) = 100