Use this calculation to reproduce a defined quantitative method when the observations, units, sampling process, and assumptions match the method shown here.

Proportion

Required number. Expected proportion p, strictly between 0 and 1 (use 0.5 for maximum variance).

Margin of error

Required number. Desired margin of error E on the proportion.

z score

Optional number. Two-sided critical z value; defaults to 1.96 (95% confidence).

The cited overview of Statistics supplies background for the terminology and domain context used by this tool.^[1]

Two-sided sample size for estimating a proportion: n = p*(1-p)*(z/E)^2 with z defaulting to 1.96. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Required sample size

Returned integer. Ceiling of the exact requirement.

Exact sample size

Returned number. Unrounded n = p*(1-p)*(z/E)^2.

• A numerical result does not by itself establish data quality, causation, representativeness, independence, distributional fit, or practical significance.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

Inspect the underlying data, visualize its distribution, report uncertainty and sample size, and compare the result with a robust or domain-specific method where appropriate.

• Sample Size for Mean Calculator

  Two-sided sample size for estimating a population mean: n = (z*sigma/E)^2 with z defaulting to 1.96.

• Fisher's Exact Test

  Compute the two-sided Fisher exact p-value for a 2×2 contingency table with fixed margins. Tables above 10,000 total observations are rejected to bound exact enumeration.

• Permutation Test Calculator

  Exact two-sided permutation test on the difference of two group means; all C(nA+nB, nA) group assignments of the pooled sample (each sample capped at 8 values) are enumerated deterministically.