Margin of Error Calculator for Surveys
For pollsters and research designers who need to state the precision of a survey result before fieldwork or in a topline, this tool turns sample size, expected proportion and confidence level into the ± percentage points they must quote — calculated from MOE = Z·√(p(1−p)/n) at the selected confidence level and sample size.
Results are estimates for educational and preliminary use.
How to Calculate Survey Margin of Error
- Enter the number of completed responses as the sample size n.
- Set the expected proportion p in percent — leave it at 50 if the outcome is unknown.
- Pick 90%, 95% or 99% from the confidence-level dropdown and note the Z multiplier it displays.
- Read the live margin of error in percentage points and the interval range around p.
FAQ
Q: What margin of error does a sample of 1,000 give at 95% confidence?
A: With p = 50%, MOE = 1.96 × √(0.25/1000) ≈ 3.1 percentage points, so the interval runs about 46.9% to 53.1%.
Q: Does a bigger sample always reduce the margin of error?
A: Yes — MOE scales with 1/√n, so quadrupling the sample halves the margin, while doubling it only cuts the margin by about 29%.
Q: What proportion should I enter when I don't know the expected survey result?
A: Enter 50 — p(1−p) is largest at 0.25 when p = 0.5, which produces the widest, most conservative margin of error for that sample size.
Q: Why won't the calculator accept a sample size of zero?
A: The formula divides by n, so n = 0 is mathematically undefined and the tool asks for a sample size of at least 1; all output is an estimate for educational and preliminary use.