How it works
Every researcher asks the same question: how many people do I need? Too few and the results are unreliable; too many wastes time and money. This calculator uses Cochran’s formula, the standard for surveys, theses and market research, with the finite-population correction when you know how many people are in your population — the same logic behind the Krejcie & Morgan table.
n₀ = z² × p × (1 − p) ÷ e² finite population N: n = n₀ ÷ (1 + (n₀ − 1) ÷ N)Worked example. At 95% confidence (z = 1.96), a 5% margin of error and an expected proportion of 50%: n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.16, so 385 responses (always round up). If the whole population is only 1,000 employees: 384.16 ÷ (1 + 383.16 ÷ 1,000) = 278. At 99% confidence and a 3% margin the requirement jumps to 1,843.
The inputs explained
- Confidence level: how sure you want to be that the true value lies within your margin of error. 95% is standard; 99% for medical or high-stakes work.
- Margin of error: the ± range you can accept around the result. 5% is common; halving it roughly quadruples the sample.
- Expected proportion (p): if you have no prior estimate, leave it at 50% — it gives the largest, safest sample.
- Population size: enter it when the group is known and limited (a company, a school). Leave it blank for large or unknown populations.
Quick reference (95% confidence, ±5%)
| Population | Sample needed |
|---|---|
| 100 | 80 |
| 500 | 218 |
| 1,000 | 278 |
| 5,000 | 357 |
| 10,000 | 370 |
| 100,000+ | 383 – 385 |
Notice how little the sample grows beyond a few tens of thousands: a national poll needs roughly the same 385 responses as a large city. Published tables can differ by one or two because of rounding.
Allow for non-response
Not everyone you invite will answer. If you expect a 70% response rate, divide by 0.7: 385 becomes 550 invitations. The “to send” line shows the figure at 70% and 50% response.
Limits of the formula
Cochran’s formula assumes simple random sampling and a yes/no (proportion) outcome. Stratified or cluster samples need a design effect, and studies comparing two groups or estimating means need a power analysis instead. If your supervisor specifies another formula (such as Yamane’s n = N ÷ (1 + N e²)), cite it in your methods section — results are usually close.
Once data are in, measure spread with the standard deviation calculator, standardise values with the z-score calculator, and turn answer counts into shares with the percentage calculator.