KIMRA

Research toolsStudy design

Sample size for estimating a proportion

Calculates how many participants are required to estimate a single proportion — a prevalence, a response rate, a proportion of patients meeting a criterion — to within a stated absolute precision at a chosen confidence level.

Between 0 and 1. If you have no prior estimate, use 0.5 — it gives the largest, safest sample.

Half the width of the confidence interval you want. 0.05 means ±5 percentage points.

Leave blank for a large or unknown population. Supplying it applies the finite population correction.

The sample is inflated so that the target is still met after losses.

Results

Participants required
385
Before rounding
384.15
Critical value (z)
1.959964

Round up, never down. Recruiting one fewer than the calculated number means the study is under-powered by design.

When to use it

  • Planning a cross-sectional prevalence survey.
  • Estimating a single rate where the aim is precision rather than comparison.
  • Justifying a sample size in a protocol or an ethics application.

Formula

n = z²  ×  p(1 − p)  /  d²

  z = the two-sided normal critical value for the confidence level
      (1.959964 at 95%)
  p = the proportion you expect to observe
  d = the absolute precision you want, i.e. the half-width of the
      confidence interval

Finite population correction, when the population size N is known:

  n_adj = n / ( 1 + (n − 1)/N )

Inflation for anticipated non-response at rate r:

  n_final = ceil( n_adj / (1 − r) )

Worked example

A prevalence survey where no prior estimate exists, so the most conservative assumption is used.

Expected proportion
0.50
Absolute precision
0.05 (±5 percentage points)
Confidence level
95%

n = 384.15, so 385 participants.

With 385 participants, an observed prevalence of 50% would carry a 95% confidence interval of roughly 45% to 55%.

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