Survey Margin of Error Calculator

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%.

This calculator takes your sample size, expected proportion, and confidence level and returns the resulting margin of error for your survey result.