Sample Size Calculator
Wald sample size for a proportion. n = z^2 p (1-p) / e^2. Optional finite N. Educational, not a survey product and not a power analysis for a mean.
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How to compute a Wald sample size
- Enter z greater than 0. 1.96 is the usual two-sided 95% normal value. You type z. This page does not look up a table.
- Enter proportion p from 0 to 1. 0.5 maximizes p(1-p) and is the conservative default.
- Enter margin of error e greater than 0 as a proportion, so 5 percentage points is 0.05.
- Optional: type a finite population N greater than 1. Read n, n rounded up, and the finite rows when N is set. Educational only.
Wald sample size for a proportion
Educational n from z, p, and margin e
| Formula | n = z^2 p (1-p) / e^2 |
|---|---|
| Default | z = 1.96, p = 0.5, e = 0.05 |
| Finite correction | n / (1 + (n-1)/N) when N > 1 |
| Rounded n | ceil of the Wald n |
| z source | You type z. No inverse-normal table is loaded. |
| Scope | Educational Wald. Not a survey product. |
What this sample size page computes
The Wald formula sizes a simple random sample for a binary proportion at a chosen z and margin of error. It is a classroom identity, not Cochran with finite fpc as a product default, and not a clustered or stratified design. Power for a mean, an odds ratio, or a two-sample test is out of scope.
How n is computed
n = z^2 p (1-p) / e^2. z and e must be greater than 0. p must sit from 0 to 1 inclusive. The page also ceils n. If you type a population N greater than 1, finite n is n / (1 + (n-1)/N), then that value is ceiled too. Convert a confidence level to z yourself. The z-score page standardizes one observation. It does not invert a normal tail into z for this form.
Wald, p = 0.5, and related z jobs
p = 0.5 is the usual conservative pick because p(1-p) peaks there. Wilson and Agresti-Coull intervals change how you report a proportion after you sample. They do not change this n formula. Design effect, nonresponse, and finite surveys with complex weights need a statistician. This page stays on the Wald identity.
Use cases
A methods-class check that 1.96, 0.5, and 0.05 produce n near 385. A planning sketch before you talk to a survey vendor. Not a replacement for IRB sample-size language or a vendor quote.
Limits
No inverse-normal lookup. No clusters. No two-sample power. Blank N skips finite correction. Educational only. CZNull does not receive the numbers.