How many people answered.
Everyone you could have asked. Leave empty if it's large or unknown.
The share that gave an answer. Keep 50% if you're not sure.
Margin of error
±4.9%
If 50% of your sample gave an answer, the true share is likely between 45.1% and 54.9%, at 95% confidence.
- z-score
- 1.960
- Standard error
- 2.50%
- Population correction
- None
The formula
When you know the population size N and your sample is a real part of it, multiply by the finite population correction:
Example: 400 answers, 95% confidence, p = 50%, large population. 1.960 × √(0.25 / 400) = 1.960 × 0.025 = 0.049, so the margin is ±4.9%.
Reading the result
A margin of ±4.9% at 95% confidence means: if you ran the same survey many times with new random samples, about 95 out of 100 of the ranges you'd get would contain the true value.
The margin shrinks with the square root of the sample. To halve it, you need four times as many answers: 400 gives about ±4.9%, 1,600 gives about ±2.5%.
Comparing two groups inside your survey (say, new and returning customers)? Each group has its own, wider margin, based on its own size. Working backward from a target margin? Use the sample size calculator.
Questions about margin of error
- What is a good margin of error?
- Most surveys aim for 5% or less at 95% confidence. For decisions that hinge on small differences, aim for 3% or less.
- Why use 50% as the proportion?
- p(1 − p) is largest at 50%, so 50% gives the widest, safest margin. If you already know a result is near 10% or 90%, enter that to get a tighter margin for it.
- Does the margin of error cover bad questions or a biased sample?
- No. It only covers random sampling error. Leading questions, low response rates from one group, or a sample that isn't random can make a result wrong by more than the margin.