How many people do you need to survey?
Enter your population, the confidence level you want and the margin of error you can live with — the calculator returns the sample size you need.
How many people do you need to survey?
Share of the population
Calculate sample size
The larger the sample, the smaller the margin of error.
Leave empty if the group is very large or unknown.
Sample needed
370answers
n₀ = z² · p · (1 − p) / e², then corrected for the size of the population.
Collect enough answers to stand behind the result
With empirio.ai you share your survey by link, QR code or email invitation, and you can see at any moment how far you still are from your target.
- Share by link, QR code or email
- Watch responses arrive in real time
- Remind only the people who have not answered yet
What makes a sample representative?
Representative means the people you surveyed mirror the population in the characteristics that matter for your question. Sample size determines precision; how you select people determines bias. A large but skewed sample gives you precisely wrong answers — both have to be right.
How is sample size calculated?
The formula is n₀ = z² · p · (1 − p) / e². Here z is the value from the normal distribution for your confidence level (1.96 at 95 %), p is the expected share and e is the margin of error you accept. When the population is known and finite, the result is corrected downwards with n₀ / (1 + (n₀ − 1) / N). Without an estimate of your own, set p to 50 %: variance is at its maximum there, which keeps the calculation on the safe side.
Typical sample sizes
At 95 % confidence and a ±5 % margin of error you need around 385 answers — and that barely changes whether the population is 100,000 or ten million. It surprises people, but it follows directly from the formula: past a certain size the population hardly matters. The reverse also holds: in a small group the number drops sharply, and a population of 500 needs only about 218 answers for the same precision.
Guide values at 95 % confidence and a ±5 % margin
| Population | Answers needed |
|---|---|
| 100 | 80 |
| 500 | 218 |
| 1,000 | 278 |
| 10,000 | 370 |
| 1,000,000 | 385 |
Common questions
Why does a million people not need more answers than 100,000?
Because the precision of an estimate depends on the size of the sample, not the size of the population. Past roughly 20,000 people the required number barely moves.
What does the confidence level mean?
It states how often the calculated interval contains the true value if you repeated the survey many times. At 95 % that is 19 times out of 20. A higher level demands a larger sample.
Which expected share should I enter?
50 % if you have no prior knowledge. Variance peaks there, so the calculation is conservative. If an earlier survey told you the share is around 20 %, enter that and you will need fewer answers.
Do abandoned responses count?
No. The number refers to complete, usable answers. Plan a buffer and factor in the response rate you expect.