Why sample size matters
Every survey of a sample carries uncertainty: ask 50 people and the results could easily be 10 points off from what the full population thinks; ask 500 and the noise shrinks dramatically. Sample size is the lever that controls how much you can trust what your survey tells you.
Too few responses and you risk acting on noise — launching a feature because 12 of 20 respondents liked it, or reorganizing a team over a survey that a different random group would have answered differently. Too many and you're spending time and goodwill on precision you don't need. The right sample size is a deliberate trade-off, and this calculator makes the trade-off explicit: pick your confidence level and margin of error, and it tells you the number of completed responses that gets you there.
This tool is the mirror image of our margin of error calculator: there you start with responses you already have and see how precise they are; here you start with the precision you want and see how many responses it takes.
The formula behind the calculator
For a proportion (the most common case for surveys), the baseline sample size is:
n₀ = z² × p(1−p) / e²
- z is the z-score for your confidence level: 1.645 for 90%, 1.96 for 95%, 2.576 for 99%.
- p is the expected response distribution. Using 50% maximizes p(1−p) and gives the most conservative — safest — answer.
- e is your margin of error as a decimal, so ±5 percentage points is 0.05.
If you're surveying a known, finite population of size N — a company, a customer list, a graduating class — the requirement drops:
n = n₀ / (1 + (n₀ − 1) / N)
The result is always rounded up, because 217.5 responses means you need 218.
Two worked examples
Unknown or very large population. At 95% confidence, ±5 points, p = 50%: n₀ = 1.96² × 0.25 / 0.05² = 0.9604 / 0.0025 = 384.16, which rounds up to 385 responses. This is the famous "about 400" figure — and note that it holds whether your population is 50,000 or 50 million. Population size barely matters once it's large.
A 500-person company. Same settings, but N = 500: n = 384.16 / (1 + 383.16 / 500) = 384.16 / 1.766 = 217.5, so 218 responses. The finite population correction nearly halves the requirement — good news for internal surveys.
Sample sizes for common scenarios
At 95% confidence and a ±5-point margin of error:
| Population size | Responses needed |
|---|---|
| 100 | 80 |
| 500 | 218 |
| 1,000 | 278 |
| 10,000 | 370 |
| 100,000+ | 383-385 |
The pattern is diminishing returns: beyond a population of roughly 1,000, the required sample barely grows. Surveying a city of 100,000 takes about the same effort as surveying a town of 10,000. The flip side is that small populations reward you — and at the extreme, the math stops being the point. For a 30-person team, don't sample at all: survey everyone, and use a tool like our eNPS calculator to read the result.
Completed responses, not invitations
The number this calculator gives you is completed responses. Not everyone you invite will answer — typical survey response rates run around 20-30%, and often lower for cold audiences. If you need 385 completes at a 25% response rate, plan to invite roughly 1,540 people.
You can attack this from both sides: invite more people, or raise the rate. Shorter surveys, a clear subject line, good timing, and a reminder or two make a real difference — our guide on how to increase your form response rate covers the tactics that reliably work. And if you're unsure what to ask in the first place, the survey question generator can draft your questions for you.
Common sample size mistakes
- Surveying only engaged users. Hitting 385 responses means little if they all come from your most active, happiest segment. A smaller sample drawn evenly from your whole population beats a large one drawn from the people easiest to reach.
- Stopping early because results "look clear". Early responses are the least representative — the most enthusiastic people answer first. If the calculator says 218, collect 218, even if the trend at 60 looks obvious.
- Treating sample size as a quality guarantee. The formula only controls random sampling error. A biased or leading question produces confidently wrong answers at any n; no sample size rescues a bad questionnaire.
- Ignoring subgroups. If you plan to compare departments or customer tiers, each segment needs enough responses on its own. An overall n of 400 split ten ways leaves every comparison underpowered.
Once your responses are in, close the loop: run your numbers through the margin of error calculator to see the precision you actually achieved.