About the Sample Size Calculator
A sample size calculator tells you how many responses a survey needs to achieve a chosen margin of error at a chosen confidence level. It is the calculation that decides whether a study can support conclusions, and it is best done before collecting any data rather than after.
The formula
n = z² · p(1 − p) / e²z is the critical value for your confidence level — 1.96 at 95 percent. p is the expected proportion, and e is the margin of error as a decimal. A finite population correction reduces n when the population is small.
How to use this calculator
- 1Enter your Confidence Level (90=90%, 95=95%, 99=99%). The field starts at
95, which you can overwrite. - 2Enter your Margin of Error (%). The field starts at
5, which you can overwrite. - 3Enter your Population Size (0=infinite). The field starts at
0, which you can overwrite. - 4Enter your Expected Proportion (%). The field starts at
50, which you can overwrite. - 5Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Confidence Level (90=90%, 95=95%, 99=99%) | 95 |
| Margin of Error (%) | 5 |
| Population Size (0=infinite) | 0 |
| Expected Proportion (%) | 50 |
Result
Required Sample Size: 385
Z-Score: 1.96
Population: Infinite
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
Precision is expensive because the requirement grows with the square of the margin of error. Halving the margin from 5 to 2.5 percentage points quadruples the sample needed. This is why national polls settle around 1,000 respondents: it delivers roughly a 3 percent margin, and pushing to 1 percent would demand nearly 10,000.
The result depends far less on population size than most people expect. Above roughly 20,000 people, the population barely affects the sample needed — 1,000 respondents give about the same precision for a city of 100,000 as for a country of 300 million. Representativeness, not raw size, is what determines whether a sample is trustworthy.
Things worth knowing
- Use p = 0.5 when you have no prior estimate. It maximises required sample size, so the result is conservative.
- Oversample to allow for non-response. A 30 percent response rate means inviting three times your target.
- Margin of error applies to the whole sample. Analysing subgroups needs enough responses within each subgroup.
- A large sample cannot fix a biased sampling method. Non-random selection produces confidently wrong answers.
- For comparing two groups rather than estimating one proportion, use a power calculation instead.
Frequently asked questions
How many people do I need to survey?+
For a 95 percent confidence level and a 5 percent margin of error, about 385 responses regardless of population size above roughly 20,000. Tighter margins require substantially more.
What does margin of error mean?+
The range within which the true population value likely falls. A result of 60 percent with a 5 percent margin means the true figure is probably between 55 and 65 percent.
Does population size matter?+
Only for small populations. Below a few thousand, the finite population correction meaningfully reduces the sample needed. Above about 20,000 the effect is negligible.
What confidence level should I use?+
95 percent is the convention in most research. 90 percent needs a smaller sample but accepts more uncertainty; 99 percent needs a much larger one and is reserved for high-stakes decisions.