In this article
You almost never need to ask everyone. A well-chosen sample of a few hundred or a few thousand people can describe a very large group with a known amount of error. The calculator turns three choices into one number: how precise you want to be, how sure you want to be and how varied you expect the answers to be.
The three dials
The common formula is n = z² × p × (1 − p) ÷ e², where z is 1.96 for 95% confidence, p is the expected proportion and e is the margin of error.
Where 385 comes from
- 1Pick the numbersz = 1.96 (95% confidence), p = 0.5, e = 0.05.
- 2Top of the formula1.96² × 0.5 × 0.5 = 3.8416 × 0.25 = 0.9604.
- 3Bottom of the formula0.05² = 0.0025.
- 4Divide and round up0.9604 ÷ 0.0025 = 384.16, so you need **385** responses.
Always round up. 384 would fall just short of the target.
Smaller margin, much bigger sample
Precision follows a square-root law. To cut the margin of error in half you need four times the responses. The curve below is why most surveys settle for ±3% to ±5%.
| Margin of error | Responses needed (95%) | Compared with ±5% |
|---|---|---|
| ±10% | 97 | about a quarter |
| ±5% | 385 | baseline |
| ±3% | 1,068 | 2.8 times |
| ±2% | 2,401 | 6.2 times |
| ±1% | 9,604 | 25 times |
Going from ±5% to ±1% means asking about 25 times as many people.
The last bar is so tall that the first two look tiny. That is the point: the last bit of precision is the costliest.
The line drops fast at first and then flattens. The jump from 100 to 400 responses roughly halves the error; the jump from 2,500 to 10,000 only takes off one point.
- Sharpunder 3%
- Usable3–6%
- Roughover 6%
A rough guide only. Close races and small differences need a sharper margin than a general 'how many people like this' question.
How sure do you want to be?
A higher confidence level means you accept fewer surprises, but it costs responses. 95% is the common default; 99% is used when the cost of being wrong is high.
Moving from 95% to 99% asks for about 70% more people for the same margin of error.
Does population size matter?
For large groups, no. Surveying a town of 100,000 needs about the same 383 responses as a country of 100 million. For small groups there is a finite population correction: n = n₀ ÷ (1 + (n₀ − 1) ÷ N), where n₀ is the basic answer (384.16) and N is the population.
For a class or a company of 200 people you need 132 answers (66% of them). For 100,000 people you need 383, which is less than half a percent.
- Must respond132
- Can stay silent68
Small groups need a high response share. In a tiny group it is often simpler to ask everyone.
When you already know the answer will be lopsided
The 50% assumption is the safest, because it gives the largest sample. If you are confident that only about 10% of people will say yes, you need fewer. Do not use this shortcut unless you really have evidence.
| Expected share | Responses for ±5% (95%) |
|---|---|
| 50% (unknown, safest) | 385 |
| 30% | 323 |
| 20% | 246 |
| 10% | 139 |
| 5% | 73 |
The formula uses p × (1 − p), which is biggest at 50%.
A short checklist
- Decide the margin of error you can live with, such as ±5%.
- Choose the confidence level. Use 95% unless there is a reason not to.
- Use 50% for the expected share if you have no good estimate.
- Enter your population, especially if it is under a few thousand people.
- Divide by your expected response rate to know how many invitations to send.
Questions people ask
What sample size do I need for a survey?
For a large population, 385 responses give a ±5% margin of error at 95% confidence. For ±3% you need about 1,068, and for ±1% about 9,604.
Why is 385 so common?
It comes from the formula n = z² × p × (1 − p) ÷ e² with 95% confidence (z = 1.96), a 50% expected split and a 5% margin of error, which gives 384.16, rounded up to 385.
Does population size matter for sample size?
Only for small groups. Beyond a few thousand people the required sample barely changes. For small populations a finite population correction reduces the number you need.
What is margin of error?
It is the range around your result in which the true value is expected to lie at your chosen confidence level. A result of 60% with ±5% means the real figure is likely between 55% and 65%.
What confidence level should I use?
95% is standard. Use 90% for quick, low-stakes checks and 99% when a wrong conclusion would be costly, remembering that higher confidence needs more responses.
Can a large sample still be wrong?
Yes. If the people who answer are not representative of the group, for example only volunteers or only one region, a large sample gives a precise but biased result.