Sample Size Calculator
How many people must you survey for trustworthy results? Set your confidence level and acceptable margin of error — population size matters far less than intuition suggests, and this calculator shows exactly how little.
How to use this calculator
- Pick a confidence level — 95% is the research standard.
- Set the margin of error you can live with (±5% is common, ±3% for precision).
- Enter the population only if it's small (a company, a class); leave 0 otherwise.
Formula used
z is 1.96 at 95% confidence; p = 0.5 maximizes required size (the safe default when you don't know the answer's distribution). Halving the margin of error quadruples the sample — precision is expensive.
Example calculation
95% confidence, ±5% margin, unknown population: n = 1.96² × 0.25 ÷ 0.05² = 385 responses.
For a 2,000-person company, finite correction trims it to 323. At a 30% response rate, you'd invite ~1,077 people. Tightening to ±3% would demand 1,068 responses — precision quadruples with each halving.
The counterintuitive math of sampling
The surprise everyone meets: population size barely matters. Surveying a country of 50 million and a city of 100,000 both need ~385 responses for ±5% at 95% — the soup-tasting principle (one spoon suffices if the pot is stirred). Only small populations earn a discount via the finite correction.
The stirring is the real difficulty: sample size handles random error, but a biased sample (only enthusiasts respond, only one channel surveyed) stays biased at any n. A representative 385 beats a self-selected 10,000 — response-rate math and recruitment design deserve as much attention as the sample count.
Why use this calculator?
- Plan surveys with defensible statistics instead of round-number guesses.
- See the invite count implied by realistic response rates.
- Understand the cost curve — why ±3% costs nearly triple ±5%.
Frequently asked questions
Why doesn't a bigger population need a bigger sample?
Random sampling error depends on how many you ask, not how many exist — like tasting soup, one well-stirred spoonful judges any pot size. Population only matters when your sample becomes a large fraction of it (small populations).
What margin of error should I choose?
±5% suits most business decisions; ±3% for published research or close calls; ±10% for rough directional reads. Match it to the decision: if 45% vs 55% would change your action, you need a margin tighter than 5.
What is the expected proportion setting for?
Required sample peaks when the answer splits 50/50. If prior data says ~20% will answer yes, using p = 20% shrinks the required n. When unsure, 50% is the safe worst case.