Enter your confidence level, margin of error, and expected proportion to get the minimum sample size for a reliable result.
Margin of error is the range around your survey result that the true population value is likely to fall within. A 5% margin of error on a result of 60% means the true figure is likely between 55% and 65%.
The term p×(1−p) in the sample size formula is maximized when p=50%, so using 50% as your estimate produces the largest, most conservative required sample size. If you have a genuine prior estimate of the proportion (say, from a pilot survey), using it instead can lower the required sample size.
It adjusts your required sample size downward when your sample would make up a meaningful fraction of a small, known total population — surveying 500 people out of a population of 600 needs a smaller correction-adjusted sample than the base formula suggests. For large or unknown populations, the correction has negligible effect, which is why the population size field is optional.
Yes. Higher confidence levels use a larger z-value (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), and since the required sample size scales with the square of the z-value, moving from 95% to 99% confidence noticeably increases the sample you need for the same margin of error.
Worked example: at 95% confidence (z=1.96), a 5% margin of error, and the conservative 50% proportion estimate: n = (1.96² × 0.5 × 0.5) / 0.05² = 0.9604/0.0025 ≈ 384.16, rounded up to 385 — the classic "385 respondents" figure widely cited for a 95%/±5% survey with no known population size.
For 95% confidence, a 5% margin of error and an assumed proportion of 0.5, the required sample is 385. That figure turns up constantly in survey work, and it comes straight from 1.96² × 0.25 ÷ 0.05².
The 0.5 matters: p(1−p) is largest at 0.5, so assuming it produces the most conservative — largest — sample size. If you genuinely expect a lopsided proportion, say 0.1, the required sample falls substantially. When you have no prior information, 0.5 is the safe assumption.
Margin of error scales with the square root of sample size, so improvements cost disproportionately. Halving the margin of error requires quadrupling the sample. Going from 5% to 2.5% takes you from 385 responses to roughly 1,537.
This is why most published polling settles around 3-4%: below that, cost rises faster than the usefulness of the extra precision.
Sample size depends far less on population size than intuition suggests. Sampling a town of 50,000 and a country of 50 million needs almost the same number of responses. The finite population correction only matters when your sample is a large fraction of the whole — roughly above 5% — at which point the required number falls.
People routinely over-sample large populations because it feels wrong that 385 could represent millions. Statistically it can.
This is the important caveat. Sample size controls random error only. A biased sampling method produces a confidently wrong answer, and a bigger biased sample produces a more confidently wrong answer.
Non-response is the usual culprit: if the people who reply differ systematically from those who don't, your effective sample is not random however large it is. Plan for the response rate — needing 385 completed responses at a 20% response rate means contacting around 1,925 people. Draw the sample itself with the Random Number Generator, and turn the results into a range with the Confidence Interval Calculator.
Once you have the sample, the Confidence Interval Calculator gives the margin of error and the Z-Score Calculator the critical values behind it. For drawing the sample itself, use the Random Number Generator.