How to use it
- Choose the confidence level: 90%, 95% (the usual default) or 99%.
- Enter the margin of error you can accept, for example ±5 percentage points.
- Leave the expected proportion at 50% unless earlier research gives you a better estimate.
- Add the population size if your target group is small and countable, such as your B2B customers or members.
- Optionally, enter the expected response rate to see how many invitations to send.
Formula and logic
The calculator first works out the sample for a very large population:
n₀ = z² · p(1 − p) / e²
Here z is the z-score for the confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), p is the expected proportion as a decimal and e is the margin of error as a decimal, so 0.05 for ±5 points. With p = 0.5 and e = 0.05 at 95% confidence, n₀ = 384.2, which rounds up to 385.
If you enter a population size N, the finite population correction reduces the requirement:
n = n₀ / (1 + (n₀ − 1) / N)
For a customer base of 2,000, the 385 falls to 323. Finally, if you enter an expected response rate r, the number of invitations is n / r. Assuming a 20% response rate, 385 completed interviews require 1,925 invitations.
How to read the result
The table shows how quickly the required sample grows as you ask for more precision (95% confidence, p = 0.5, large population):
| Margin of error | Completed interviews |
|---|---|
| ±10 points | 97 |
| ±5 points | 385 |
| ±4 points | 601 |
| ±3 points | 1,068 |
| ±2 points | 2,401 |
Halving the margin of error roughly quadruples the sample, so decide in advance how precise the decision really needs to be. The precision also applies to the whole sample only: if you want to compare regions, age groups or customer types, each subgroup needs its own adequate sample, and that is what usually drives the total.
The formula assumes a simple random sample. Quotas, weighting and online panels reduce the effective sample, so treat the result as a minimum. If only part of the population qualifies for the survey, the incidence rate increases the number of people you must screen, not the number of completes. To check the precision of a sample you already have, use the margin of error calculator.
Frequently asked questions
Why is 385 such a common sample size?
It is the result of the formula at 95% confidence, a ±5-point margin of error and the most cautious assumption p = 0.5, for a large population. It became a convention because many decisions are comfortable with that precision. It is not a rule: if you need to compare several subgroups, 385 in total will be far too small, and for a rough exploratory reading, fewer may do.
Does a bigger population need a bigger sample?
Only up to a point. Once the population runs into the tens of thousands, it barely affects the result: for a population of 10,000, the calculator returns 370 instead of 385. What matters is the absolute number of interviews, not the share of the population interviewed. The correction makes a real difference only for small, countable populations, such as a few hundred business customers.
How many respondents do I need per subgroup?
Apply the same logic to each subgroup you intend to report separately. If you want each of four regions read to ±10 points, every region needs around 100 completed interviews, so the total depends on how many cells you plan to compare. Our guide on sample size for surveys works through subgroup planning with examples.
What if my target group is hard to reach?
The required number of completes stays the same, but the effort to reach them rises. With a low incidence or a low response rate, many more people must be contacted and screened, which affects the timeline and the budget. If you are planning such a study, request a proposal and we will estimate the feasibility of the sample before fieldwork starts.
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