Sample Size For Estimating A Proportion

Estimate the number of binary observations needed to bound a proportion or nonconformance rate by a target margin of error.

Concept

Results

Enter inputs and select Calculate to display reviewed results.

Inputs

Confidence level *

Target margin of error *

Use conservative p = 0.5

Use when no defensible prior proportion is available.

Estimated proportion *

Ignored when conservative mode is selected.

Formula & Variables

n ≥z_1-α/2²p(1 - p)E²

n: Sample size; [1]
p: Planning proportion; [1]
E: Margin of error; [1]

Assumptions

Each observation is a binary Bernoulli trial.
Observations are independent.
Margin of error is an absolute proportion, such as 0.04 for four percentage points.

⚠ Limitations

Does not plan power for detecting a specified change.
Rare-event and acceptance-sampling workflows may need exact/binomial, reliability, or standards-based methods.