Free calculator
Sample size calculator
Plan minimum survey completes for one population proportion under a simple random sample story: pick a confidence level, a margin of error (half-width for p̂), and an expected proportion p (use 0.5 when unsure). Optionally enter a finite population size N for the usual correction—or switch tabs to read the margin of error from a completed n. Google Sheets and Excel use NORM.S.INV(1 − α/2) for the same z we derive here.
When to use this calculator
Quick SRS planning for one proportion before you field a short survey or mirror the same logic in a workbook—transparent z, not a full statistics suite.
- Ballpark how many completes you need for a target margin of error at 90%, 95%, or 99% confidence.
- Compare conservative p = 0.5 vs a prior proportion to see how much n drops when the event is rarer or more common.
- Apply a finite population correction when your audience is a known small N (e.g. employees, members).
- Read the approximate margin of error after fieldwork when you already know n and p.
Under a normal approximation for a single proportion p̂, the Wald half-width is E ≈ z √( p(1−p) / n ) for a very large population. Solving for n gives n₀ = z² p(1−p) / E². With a finite population N, a common correction is n = n₀ / (1 + (n₀ − 1)/N); we ceil the result as a practical minimum count.
Confidence → z
For two-sided level (1 − α), z is chosen so Φ(z) = 1 − α/2. This page solves z numerically from the same Φ used on the z-score calculator (bisection on normalCdf).
Solve for n
Given E (margin as a fraction), n₀ = z² p(1−p) / E². With N, apply the correction above; without N, use n₀ directly. Displayed n is ceil of the continuous value.
Margin from n
The second tab uses E = z √( p(1−p)/n ) when N is omitted, and E = z √( p(1−p)/n × (N−n)/(N−1) ) when N is supplied—matching the same SRS variance factor as many textbook survey calculators.
We do not implement cluster design effects, Wilson or exact binomial planning, two-sample tests, or power curves—use dedicated study-design software when you need those models.
When you already have data and want a two-sided Wald interval (or mean z/t intervals), open the confidence interval calculator.
To standardize one raw x against μ and σ, use the z-score calculator (**z** there is a **data** standard score, not the **critical value** tabulated here—same symbol, different job).
FAQs cover p = 0.5, finite N, clinical power, and A/B tools so expectations stay clear.
Google Sheets & Excel
The critical z for a two-sided (1 − α) confidence level satisfies Φ(z) = 1 − α/2. In English function names, =NORM.S.INV(1-α/2) returns z when α = 1 − confidence (enter α as a decimal in the cell). Pair with your own p and n cells if you rebuild the Wald half-width in the sheet.
=NORM.S.INV(0.975)Replace 0.975 with 1 − α/2 for other confidence levels.
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Frequently asked questions
What does this sample size calculator estimate?
It estimates a minimum integer sample size n to survey a single proportion with a Wald / normal margin of error at your chosen two-sided confidence—plus an optional finite population correction. It is a planning aid for SRS-style thinking, not a guarantee of precision in real field conditions.
Why is p = 0.5 the default?
The variance factor p(1−p) is largest at 0.5, so using 0.5 gives a conservative (larger) n when you do not yet have a better guess. If you expect a rarer outcome, enter a smaller p (still strictly between 0 and 1) to reduce required n for the same margin.
When should I enter a population size N?
When your list is a real finite universe (employees, members, accounts) and sampling without replacement is the right mental model. Leave N blank when the population is large relative to n so the extra factor is negligible.
Is the second tab a “margin of error calculator”?
Yes—the Margin of error tab uses the same p, N, and confidence assumptions to report an approximate half-width from a completed n.
Can I use this for clinical trial sample size?
Not in v1. Clinical designs usually need power for tests, dropouts, and multi-arm plans—use G*Power, your biostatistics team, or trial-design software instead of this Wald-only proportion planner.
Does this replace an A/B test sample size calculator?
No. A/B tools often target minimum detectable effect on conversion with different assumptions. This page is one proportion, SRS framing—good for simple surveys, not lift-test engines.
How do I get sample size for a mean when I only have σ?
That is a different formula (mean CI width with σ or t). Start from the confidence interval calculator for mean intervals; this page stays on proportions only in v1.
What sampling assumptions are baked in?
The math matches common simple random sample textbook presentations for p̂ with a normal critical value z. Stratified, cluster, or quota designs usually need design effects not modeled here.
Which spreadsheet function matches z here?
In English Excel and Google Sheets, NORM.S.INV(1-α/2) with α = 1 − confidence (as a decimal). Localized function names differ by language pack—use Insert function to find the same inverse normal in your install.
Is this professional survey advice?
No—results are educational and depend on the inputs you choose. Nonresponse, weighting, mode effects, and legal constraints can all change what “enough” means in practice.