Sample size to estimate a proportion or apparent prevalence with specified precision

Input Values


Calculates the sample size required to estimate a proportion (or prevalence) with a specified level of confidence and precision.

Inputs are the assumed or estimated value for the proportion, the desired level of confidence, the desired precision of the estimate and the size of the population for limited population sizes. The desired precision of the estimate (also sometimes called the allowable or acceptable error in the estimate) is half the width of the desired confidence interval. For example if you would like the confidence interval width to be about 0.1 (10%) you would enter a precision of +/- 0.05 (5%).

The program outputs the sample sizes required to estimate the true value with the desired precision and confidence, for both an infinite population and for a population of the specified size. If population size is left blank or zero, only the sample size for an infinite population is calculated.

Note: Adjustment for finite population size may underestimate required sample size unless this is also taken into account when estimating variance and resulting confidence interval.

Sample size is calculated using the formula:

n = (Z2 × P(1 – P))/e2

  • Z = value from standard normal distribution corresponding to desired confidence level (Z=1.96 for 95% CI)
  • P is expected true proportion
  • e is desired precision (half desired CI width).

For small populations n can be adjusted so that n(adj) = (Nxn)/(N+n). Adjustment for finite population size is described by Thrusfield M, 2005. Veterinary Epidemiology, 2nd Edition, Blackwell Science, Oxford, UK (p 183).

Estimated true proportion:
Desired precision (+/-):
Confidence level:
Population size (for finite populations):

Sample size to estimate a simple proportion (apparent prevalence)

Analysed: Fri Oct 18, 2019 @ 08:58


Estimated Proportion 0.5
Desired precision of estimate 0.05
Confidence level 0.95
Population size 1000


Sample size required for specified inputs

Large population 385
Population = 1000 278

Sample sizes for varying prevalence and precision values

 AP = 0.01   AP = 0.02   AP = 0.05   AP = 0.1   AP = 0.2  AP = 0.5 
Precision = 0.01 381 753 1825 3458 6147 9604
Precision = 0.02 96 189 457 865 1537 2401
Precision = 0.05 16 31 73 139 246 385
Precision = 0.1 4 8 19 35 62 97
Precision = 0.2 1 2 5 9 16 25

Download excel file of results



  Home  |   About this site  |   Glossary   |   References   |   Links  

This site was created by Ausvet with funding from a range of sources.
It provides a range of epidemiological tools for the use of researchers and epidemiologists, particularly in animal health.
Please send any comments, questions or suggestions to Evan Sergeant
© 2019 Ausvet