Margin of Error Calculator

This margin of error calculator tells you how far a survey or poll result might sit from the true population value, expressed as a plus or minus percentage. You enter the sample proportion, such as the share of people who answered yes, the sample size and the confidence level, and the tool returns the margin of error. The formula multiplies the z multiplier for your confidence level by the square root of the proportion times one minus the proportion, divided by the sample size. A 95 percent level uses a z value of about 1.96, a 90 percent level uses 1.645 and a 99 percent level uses 2.576. Pollsters, market researchers, students and anyone reading survey headlines use this figure to judge how reliable a result is. A result of 52 percent with a margin of error of 3 percent really means the true value is likely between 49 and 55 percent, which matters a lot when two options are close. Three tips help you use it well. First, the margin of error is largest when the proportion is near 50 percent, so using 0.5 gives the most cautious, conservative estimate when you are planning a sample size. Second, quadrupling the sample size only halves the margin of error, because the sample size sits under a square root, so chasing a tiny margin gets expensive fast. Third, this figure only captures sampling error, not bias from poor question wording, non response or an unrepresentative sample, so a small margin of error does not guarantee an accurate survey. Always report the margin of error and confidence level alongside any headline percentage.

MoE = z * sqrt(p(1-p)/n). Estimate only, not financial or tax advice.