Too few survey responses make results unreliable, while too many waste time and money. This calculator tells you how many responses you need to hit a target margin of error at a chosen confidence level.
How to use this calculator
Pick a confidence level (95% is the common choice), a margin of error (5% is typical) and the expected proportion. If you do not know it, keep 50%. Enter your total population if it is small and known, or leave 0 for a very large population.
The formula
For a large population: n = z^2 x p x (1 - p) / e^2, where z is 1.645, 1.96 or 2.576 for 90%, 95% or 99% confidence, p is the expected proportion and e is the margin of error. For a known population N the result is adjusted: n adjusted = n / (1 + (n - 1) / N). Results are rounded up.
Worked example
At 95% confidence, a 5% margin of error and p = 50%, you need 385 responses from a large population. If your population is only 1,000 people, the adjusted requirement drops to 279.
Frequently asked questions
Why use 50% when unsure? p x (1 - p) is largest at 50%, so it gives the safest, largest sample.
Does a bigger population need a much bigger sample? No. Beyond a few thousand people the required sample barely changes.