Free interactive tool
Margin of Error Calculator
Certainty is priced in square roots — see what a bigger sample actually buys.
Buy certainty with sample size
Slide the number of people surveyed; the margin of error shrinks by the square-root rule.
Uncertainty is priced in square roots: quadrupling the sample only halves the margin, which is why small surveys are cheap and precise ones are not.
- Find the sample where the margin drops below ±3 points.
- Explain why 10 000 responses are not 10× better than 1 000.
For a proportion at 95% confidence, the margin of error is roughly 0.98/√n. A 100-person survey carries about ±10 points; reaching ±3 takes over a thousand people.
The square root is the story: precision gets expensive fast, which is why professional polls cluster around n = 1,000.
What does ±3% actually mean?
A reported 50% plausibly sits anywhere from 47% to 53% — differences inside the margin are noise.
Does population size matter?
Barely, once the population is large — sampling 1,000 people works for a city or a country.