PUBLIC LIBRARY / CALCULATOR

Sample size for estimating a proportion

Estimates people needed to measure prevalence or another proportion with specified precision under simple random sampling.

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Check the population, units and version. The result shows the formula or classification; it does not make an automatic treatment decision.

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Method · Limits of application

WHO/Lwanga–Lemeshow 1991: single proportion, finite-population correction, attrition, ceiling;95% z1.959964

Use an expected proportion and an absolute margin of error, in the indicated units, to estimate a proportion under simple sampling. Confidence level is not the statistical power of a comparison. Finite-population correction assumes a defined population; it does not automatically incorporate clusters, stratification or a design effect. Inflation for losses increases recruitment but does not remove nonresponse bias. The normal approximation and the full WHO 1991 manual have not been validated for every design by this interface.

Conditions of use

Check the population, units, inclusion and exclusion criteria, and version in the original source. A result alone does not establish a diagnosis, discharge decision or prescription.

Documented parameters

Expected proportion (if unknown, use 50%) · %
Absolute margin of error (precision) · points %
Confidence level
Population size (optional, for a finite population) · people
Anticipated losses and refusals (optional) · %

3/3 reference cases checked. Numerical tests are not clinical validation.

Sources and documentation

Documented formula

Transcribed from the source or a recorded revision; this is not a clinical recommendation.

n₀ = z² × p × (1 − p) / d²; z = 1.645 (90%), 1.96 (95%) or 2.576 (99%); d = absolute error margin.

Finite population (N): n = n₀ / [1 + (n₀ − 1) / N]. Attrition: n_final = n / (1 − attrition proportion). All values round upward.

Numerical precision: For 95% calculation, z=1.959964;1.96 above is rounded display. The reference-case correction is recorded in catalogue provenance.

References

Identifier: tamanho-amostral-proporcao

Original clinical content: Brazilian Portuguese.

Method version

WHO/Lwanga–Lemeshow 1991: single proportion, finite-population correction, attrition, ceiling;95% z1.959964

tamanho-amostral-proporcao@native-2026-10-05+59b35f7a2057

Source for the active edition

The bibliographic edition identifies the source. By itself, it proves neither full conformity of the formula nor clinical approval.

Synthetic cases checked (3)

Synthetic cases for checking the implementation, with no patient data.

Case 1

reference-001

Inputs

Expected proportion (if unknown, use 50%): 20 %
Absolute margin of error (precision): 5 points %
Confidence level: 95%

{
  "p": 20,
  "d": 5,
  "conf": "95"
}

Expected result

{
  "n0": 245.853368402944,
  "final": 246
}

Actual result

{
  "n0": 245.85336840294397,
  "n": 245.85336840294397,
  "final": 246
}

Case 2

reference-002

Inputs

Expected proportion (if unknown, use 50%): 50 %
Absolute margin of error (precision): 5 points %
Confidence level: 95%
Population size (optional, for a finite population): 1,000 people

{
  "p": 50,
  "d": 5,
  "conf": "95",
  "pop": 1000
}

Expected result

{
  "n0": 384.15,
  "final": 278
}

Actual result

{
  "n0": 384.14588812959994,
  "n": 277.7334563377639,
  "final": 278
}

Case 3

reference-003

Inputs

Expected proportion (if unknown, use 50%): 50 %
Absolute margin of error (precision): 5 points %
Confidence level: 95%
Anticipated losses and refusals (optional): 10 %

{
  "p": 50,
  "d": 5,
  "conf": "95",
  "perdas": 10
}

Expected result

{
  "main": "428"
}

Actual result

{
  "n0": 384.14588812959994,
  "n": 384.14588812959994,
  "final": 428
}

Code and reproducibility

This tool’s code on GitHub

Download code and tests

Sources, version and reproduction instructions

README

Local installation

Code license: Apache-2.0

Guidelines and conditions

This repository’s license applies to the code. Third-party instruments, questionnaires, data and models remain subject to their owners’ conditions.

The code tests are technical checks. Clinical approval and professional translation review are recorded separately.

Relationship with cancer research

Support for research — context required

Planning to estimate a proportion. It relates to the mission only when the question and data concern a population of oncological interest.

Applications: Epidemiology