Find the survey sample size you need from your confidence level, margin of error, and population — for a proportion or a mean, with population correction.
Pick a scenario, then adjust the confidence level, margin, and population.
Uses the standard Cochran formula. An expected proportion of 50% gives the largest, safest sample size; results round up to whole respondents. For complex study designs, consult a statistician.
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Before you run a survey or study, you need to know how many people to sample — enough for reliable results, but not so many that you waste time and money. This calculator finds your required sample size from three inputs: your confidence level (how sure you want to be), your margin of error (the ± precision you'll accept), and your expected proportion. It handles surveys of a proportion (like 'what % will vote yes') and estimates of a mean, applies a finite population correction when your group is small, and can also work backwards to tell you the margin of error for a sample you already have. For a typical survey at 95% confidence with a ±5% margin, you need about 385 responses.
The standard formula for a proportion is Cochran's: n₀ = z² × p(1−p) ÷ e². Here z is the z-score for your confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), p is the expected proportion, and e is the margin of error as a decimal. When you have no estimate for p, use 0.5 — it produces the largest, safest sample size. For example, at 95% confidence (z = 1.96), p = 0.5, and a ±5% margin (e = 0.05): n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² ≈ 385. If your population is small, the finite population correction reduces the number: n = n₀ ÷ [1 + (n₀−1)/N]. For estimating a mean instead of a proportion, the formula is n = (z × σ ÷ E)², where σ is the standard deviation and E is the margin of error in the same units. Common benchmarks at 95% confidence and p = 0.5: ±5% needs 385, ±3% needs 1,068, and ±1% needs 9,604.
Cochran's Sample Size Formula
Size a customer or market survey for a target margin of error.
Find how many voters to poll for a ±3% margin at 95% confidence.
Determine the sample needed for a thesis, dissertation, or research paper.
Pick an inspection sample size from a production batch (small-population FPC).
Size a study to estimate a mean within a set margin using the standard deviation.
Work out the margin of error for a survey you've already run.
Get enough responses for reliable results without over-sampling and wasting resources.
Size a study whether you're measuring a percentage or estimating an average.
Automatically reduces the sample when you're surveying a small, known population.
Find the sample size you need, or the margin of error for a sample you already have.
A sensitivity table and chart show how the sample grows as you demand more precision.
No signup — the standard statistical formulas, done for you.
Use Cochran's formula for a proportion: n = z² × p(1−p) ÷ e². Plug in the z-score for your confidence level (1.96 for 95%), your expected proportion p (use 0.5 if unsure), and your margin of error e as a decimal. This calculator does it for you and applies a population correction if needed.
For a typical survey at 95% confidence with a ±5% margin of error, you need about 385 responses regardless of how large the overall population is. Tightening the margin to ±3% raises it to about 1,068. Enter your own confidence and margin above for an exact number.
There's no single 'good' number — it depends on the precision you need. 385 is enough for ±5% at 95% confidence; many national polls use ~1,000 for roughly ±3%. More responses narrow the margin of error, but with diminishing returns.
About 385 respondents, using a conservative expected proportion of 50%. If you're sampling a small, known population, the finite population correction can lower that — for example, a population of 500 needs only about 217.
Margin of error is the ± range around your result that reflects sampling uncertainty. A ±5% margin on a 60% result means the true value is likely between 55% and 65%. A larger sample produces a smaller margin of error.
Usually no. For large populations, the required sample size barely changes, so you can leave it blank. The population size only matters when your sample would be a large fraction (roughly 10%+) of a small population — then the finite population correction reduces the number you need.
It's an adjustment that lowers the required sample size when you're sampling a meaningful share of a small population, because each response tells you proportionally more. The formula is n = n₀ ÷ [1 + (n₀−1)/N], where N is the population size.
Because p = 0.5 maximizes p(1−p), it produces the largest required sample size. Using 50% when you don't have a prior estimate guarantees your sample is big enough no matter what the true proportion turns out to be.