How many completed responses do you actually need? Set your confidence level and margin of error below. The same math serves as a market research sample calculator or a polling one; the formula does not care what the study is about.
Assumes the most conservative case (a 50/50 split on the question you care about most), so this is a safe upper bound — a real result skewed further from 50/50 needs fewer completes for the same margin of error.
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Sample size is the number of completed responses a study needs for its margin of error, and the calculator above runs on a formula you can check by hand. The standard sample size formula (Cochran's):
Three inputs. z is the z-score of the confidence level (1.96 at 95%, 1.645 at 90%, 2.576 at 99%). p is the expected share giving a particular answer: set it to 0.5 unless you know better, because 0.5 maximizes the variance and therefore the required sample, which is the safe direction to be wrong in. e is the margin of error as a decimal. Worked at 95% confidence and ±5%: n₀ = 1.96² × 0.25 / 0.05² = 384.16, rounded up to 385, the number behind every “you need about 400” rule of thumb in survey research.
For a small, known population (your own customer list, a company's employees), the determination of sample size adds one step, the finite population correction: n = n₀ / (1 + (n₀ − 1) / N). With a population of N = 800, the 385 above becomes 385 / (1 + 384/800) ≈ 260 completes. This is why surveying a small list needs meaningfully fewer responses than the general-population math suggests, and it is the correction the calculator applies when you enter a population size.
Three corrections the formula does not show, and where real sample size calculation goes wrong. Invitations are not completes: divide the required completes by your expected response rate: needing 385 at a 25% response rate means inviting roughly 1,540 people (honest rate benchmarks by audience are in survey response rates). Subgroups need their own math: a 400-complete study reads its 80-person subgroup at about ±11 points, so size the sample for the smallest group the report must quote, not the topline. Weighting shrinks the sample after the fact: the formula assumes equal weights, and raking to population targets always costs precision: the effective base after weighting is the honest n, a haircut explained in survey weighting. And if the study compares two groups or two message arms rather than measuring one number, the margin of error on the difference runs about 1.4× a single group's margin; the arm-budgeting math is worked through in political message testing.
Cochran's formula: n = z² × p(1−p) / e², where z is the z-score of the confidence level (1.96 at 95%), p is the expected proportion (0.5 as the conservative default), and e is the margin of error as a decimal. At 95% confidence and ±5% it gives 385 completes. For a known small population, apply the finite population correction n = n₀ / (1 + (n₀−1)/N). An 800-person list drops the requirement to about 260. Then divide by your expected response rate to get the number of invitations.
95% is the standard choice for most market research and opinion polling; it is the industry default. Use 99% for high-stakes decisions where being wrong is costly, or 90% for a quick directional read where speed matters more than precision.
±5% is typical for general population studies. Tighter margins (±3% or better) are worth the extra sample for close races or high-stakes decisions: political horse-race polling usually wants ±3% or tighter. Looser margins (±7-10%) are fine for quick directional reads or hard-to-reach niche audiences where every extra complete is expensive.
For large or effectively unlimited populations (the general public, a broad consumer base), it barely changes the required sample at all. It matters more for small, finite audiences: surveying your own customer list of 800 people needs meaningfully fewer completes than an unlimited-population calculation would suggest.
No. A large but unrepresentative or low-quality sample can be worse than a smaller, well-screened one. Clean screeners, quota management, and speeder/straightliner detection matter as much as raw sample size. This calculator tells you the floor; data quality determines whether you can trust what you collect.
Comparing survey platforms? Wavefield vs. Qualtrics · Wavefield vs. SurveyMonkey · Read quota sampling vs. random sampling, how to analyze survey results or what survey programming involves. The calculated n assumes equal weights; survey weighting explains the effective-base haircut. Also: question types · data collection methods
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