Sample Size Calculator
Calculate the required survey sample size for a given confidence level, margin of error and expected proportion.
Precise
A ±5% margin of error is where your survey's precision lands — the tighter that margin, the larger the sample size it takes to earn it (that's why 385 respondents are needed here).
Tightening the margin of error or raising the confidence level both push the required sample size up — that's the core tradeoff behind every survey design.
ƒShow your work
- 1Z-score for 95% confidence = 1.96
- 2n₀ = z²×p(1−p) / e² = 1.96² × 0.5 × 0.5 / 0.05² = 384.2
- 3No population size entered, so no finite-population correction is applied.
- 4Round up to a whole respondent count: 385
About the Sample Size Calculator
Sample size math answers a very practical question before you run a survey or study: how many people do you actually need to talk to for the results to be trustworthy? Ask too few and your margin of error balloons; ask more than you need and you've wasted time and budget collecting responses that barely tighten the result any further.
This is the calculator behind market research surveys, academic studies, political polling, and product feedback forms — anywhere someone needs to say, credibly, 'we surveyed enough people that this result reflects the broader population within a stated margin of error.'
The required sample size depends on how tight you want your margin of error, how confident you want to be in the result, and — perhaps less intuitively — on the expected proportion itself, since a rough 50/50 split needs a larger sample than a lopsided one to pin down accurately.
How it’s calculated
The core formula is n = z²×p(1−p) / e², where z is the z-score for your chosen confidence level, p is the estimated proportion (as a decimal), and e is your target margin of error (also as a decimal). Higher confidence and tighter margins both push z or shrink e, which pushes the required sample size up.
p(1−p) is largest when p = 0.5, which is why 50% is the most conservative (largest sample-requiring) estimate to use when you genuinely don't know what proportion to expect — it guarantees you won't undersize the survey.
When you're sampling from a small, known population rather than an effectively infinite one, a finite population correction shrinks the required sample size, since surveying a larger share of a small group naturally yields more certainty per respondent.
Frequently asked questions
What sample size do I need for a survey?
It depends on your target margin of error and confidence level — a common starting point is a 95% confidence level with a 5% margin of error, which typically calls for a sample in the low hundreds regardless of how large the overall population is, unless that population itself is small.
Why does the population size barely matter for large populations?
Once a population is large relative to the sample, sampling a bit more or less of it changes the required sample size only marginally — the required n converges toward the same value whether the population is 100,000 or 100,000,000. It only shrinks noticeably when the population itself is small.
What confidence level and margin of error should I use?
95% confidence with a 5% margin of error is the most common default across market research and academic surveys, though tighter margins (like 3%) or higher confidence (99%) are used when the decision riding on the result matters more.
Why does using 50% for the expected proportion give the largest sample size?
The math term p(1−p) peaks at p = 0.5, so a roughly even split in your population is the hardest case to pin down precisely — using 50% when you're unsure guarantees your sample size is large enough no matter what the true proportion turns out to be.
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