Sample Size Calculator

n₀ = z² × p(1−p) ÷ e², where z is the z-score for your confidence level, p is the expected proportion, and e is the margin of error as a decimal.

p defaults to 0.5 because that maximises p(1−p) and therefore gives the largest, safest sample. Use a different value only if you have a solid prior estimate.

When you supply a population size N, the finite population correction applies: n = n₀ ÷ (1 + (n₀ − 1)/N). For a 500-person company this often halves what you need.

Survey sample size for a percentage ("what share of customers would renew?") comes from Cochran's formula. You need three inputs: the confidence level, which sets the z-score (1.645 for 90%, 1.96 for 95%, 2.576 for 99%); the margin of error e you can live with, as a decimal; and the expected proportion p. The calculator above fixes p at 0.5, because p(1−p) is largest there, so the answer is the most cautious one.

Step one is the sample size for a very large population: n₀ = z² × p(1−p) ÷ e². Step two, only if you know the population size N, is the finite population correction: n = n₀ ÷ (1 + (n₀ − 1) ÷ N). Always round up — you cannot collect 0.16 of a response.

n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² = 3.8416 × 0.25 ÷ 0.0025 = 384.16, so 385 responses. That is where the familiar "about 400 responses" advice comes from.

Now say the survey goes to a company of 500 employees. n = 384.16 ÷ (1 + 383.16 ÷ 500) = 384.16 ÷ 1.766 = 217.5, so 218 responses. The correction matters because 385 would be 77% of everyone.

Illustration: you have 1,200 active customers and want ±3% at 95% confidence. n₀ = 3.8416 × 0.25 ÷ 0.0009 = 1,067.1. With the correction, n = 1,067.1 ÷ (1 + 1,066.1 ÷ 1,200) = 1,067.1 ÷ 1.888 = 565.1, so 566 responses — nearly half the list. Relax to ±4% and the answer drops to 401.

If you have a solid prior estimate that is far from 50%, you can use it by hand. Expecting about 20% to say yes: 3.8416 × 0.2 × 0.8 ÷ 0.0025 = 245.9, so 246 instead of 385. Only do this if the estimate comes from real earlier data; if the true figure turns out nearer 50%, your margin will be wider than you planned.

Completed responses. The formula assumes every sampled person answers, so the number it returns is what must arrive, not what you send. To plan invitations, divide by the response rate you actually expect for this audience and channel: needing 385 responses at a 25% response rate means inviting 1,540 people; at 10% it means 3,850. Our survey response rate calculator measures the rate from a past survey, and the survey invitation planner turns a completion target into invitation scenarios.

The harder problem is who does not respond. If the people who ignore your survey differ from those who answer — less engaged customers, busier staff — sending more invitations produces a bigger sample with the same bias. Sample size controls random error only. Reminders, a short questionnaire and a clear reason to answer do more for accuracy than padding the invite list.

The calculator's answer applies to the whole sample. If you plan to report results by department, region or plan tier, each of those groups needs its own adequate sample, and a subgroup of 60 inside a sample of 400 carries a margin of about ±12.7 points at 95% confidence, not ±4.9.

Plan from the smallest group you intend to report. Illustration: to give four departments ±10% each, you need roughly 97 responses per department (fewer if a department is small enough for the population correction to apply), so about 390 in total, spread evenly. Pew Research Center does not publish subgroup estimates based on fewer than 100 interviews, which is a sensible floor for anything you plan to present.

The formula assumes a probability sample: everyone in the population had a known, non-zero chance of being selected, and you chose people at random. A link posted on social media, a website pop-up that anyone can answer, or a panel of people who signed up to take surveys is a non-probability sample. The American Association for Public Opinion Research (AAPOR) says the margin of sampling error does not apply to opt-in online surveys and other non-probability polls — so a "required sample size" for them has nothing solid underneath it.

This is not a theoretical worry. In a 2023 comparison, Pew Research Center found that opt-in online samples averaged 5.8 percentage points of absolute error against benchmarks, versus 2.6 points for probability-based panels, and the gap was wider for young adults and Hispanic adults. More opt-in responses did not close it.

Three other cases where the calculator is the wrong tool. Small populations: for a team of 50 you need 45 answers for ±5%, so just survey everyone and chase response rate. Comparing two groups or two versions: that needs a power calculation, which depends on the size of the difference you want to detect; the A/B test significance calculator is the closer fit. Qualitative research: interview studies are sized by when new themes stop appearing, not by a margin of error.

Once you know the target, the form settings should protect it. In Zunoform you can close a form automatically when it reaches a response count, so a survey stops at the planned sample instead of running on; turn on one response per person so the same respondent is not counted twice; and keep partial responses on (the default) to see where people drop off. Anonymous mode stores no IP address, user agent or location for that form, which can lift honesty on sensitive questions. Hidden fields record which invitation channel each response came from, so you can check whether one channel is over-represented. The Free plan allows 500 responses a month; larger samples need Pro (5,000) or Business (25,000).