Sample Size Calculator for Prevalence Studies
Calculate required sample size for cross-sectional prevalence studies using standard formulas. Includes design effect correction for cluster sampling.
Determining an adequate sample size before conducting a prevalence survey is a fundamental step in study design. An undersized sample produces estimates with unacceptably wide confidence intervals, while an oversized sample wastes resources and may expose more participants to unnecessary data collection burden. This calculator implements the standard single-proportion formula for cross-sectional prevalence studies, with optional corrections for cluster sampling design effects and anticipated non-response.
The formula is used in nutrition surveys (SMART methodology, MICS, DHS), disease burden assessments, and programme coverage evaluations. When a two-stage cluster design is used - as in most field surveys in low-income settings - the simple random sampling formula systematically underestimates the required sample size. The design effect (DEFF) correction accounts for the intracluster correlation that arises when sampled units within a cluster are more similar to each other than to units in other clusters.
Use 50% if the true prevalence is unknown - this produces the largest (most conservative) sample size.
The ± width of the confidence interval around the estimate. Typically 5% for national surveys; 3–4% for sub-national estimates.
DEFF = 1.0 assumes simple random sampling. For two-stage cluster designs, SMART methodology recommends DEFF = 2.0 for anthropometric indicators; 1.5 is common for health and nutrition coverage indicators.
Inflate the sample to account for refusals, absences, and incomplete questionnaires. 10% is standard; field surveys in difficult settings may use 15–20%.
Formula: Cochran WG (1977). Sampling Techniques, 3rd ed. Wiley, New York. Design effect framework: Kish L (1965). Survey Sampling. Wiley, New York. SMART methodology reference: Action Against Hunger / SMART (2017). Standardised Monitoring and Assessment of Relief and Transitions (SMART) Methodology, v2. For MICS and DHS survey design see UNICEF MICS Programme and ICF International DHS Programme technical documentation.