Sample Size Formula
Finite correction: n = n₀ / (1 + (n₀−1)/N)
Where z = critical z-value for confidence level, p = estimated proportion (0.5 = most conservative), E = margin of error, N = population size (for finite correction).
Quick Reference Table
| Population | 95% CI, ±5% Error | 95% CI, ±3% Error | 99% CI, ±3% Error |
|---|---|---|---|
| 500 | 218 | 341 | 414 |
| 1,000 | 278 | 517 | 726 |
| 10,000 | 370 | 964 | 1,556 |
| 100,000 | 383 | 1,056 | 1,770 |
| Unlimited | 384 | 1,068 | 1,849 |
Frequently Asked Questions
Why use p = 0.5 if unsure of the proportion?
The expression p(1−p) is maximized when p = 0.5, giving the largest (most conservative) sample size estimate. Using p = 0.5 ensures your sample is large enough regardless of the actual proportion — it is the "safe" default when you have no prior estimate.
Does population size matter much?
Surprisingly, not much for large populations. The infinite-population formula already gives nearly the same answer for populations over 100,000. This is why national polls of 1,500–2,000 people can give ±3% margins of error for a country of 300 million.
What is the margin of error in practice?
The margin of error (±E) is the maximum likely difference between your sample result and the true population value. For example, a poll showing 52% with ±3% margin means the true value is likely between 49% and 55%. Smaller margins require larger samples and more cost.
How do I adjust for expected non-response?
Divide the calculated sample size by the expected response rate. If you need n = 385 completed responses but expect a 60% response rate, you need to contact 385 / 0.60 ≈ 642 people.