Survey Sample Size Calculator
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Determine the required survey sample size when population variance and acceptable margin of error are uncertain.
NOTEAbout This Model
## Determine the required survey sample size when population variance and acceptable margin of error are uncertain. This model estimates **Final Sample Size** based on uncertain inputs: Margin Of Error, Population Variance Estimate. Run the simulation to see the distribution of possible outcomes.
VARIABLEPopulation Variance Estimate
triangular(0.1, 0.3, 0.5)
Estimated variance of the population characteristic. For proportions, max variance occurs at p=0.5 (var=0.25).
population_variance_estimate
VARIABLEMargin Of Error
beta(2, 18.8)
Acceptable error range (2% to 10%). Smaller margin requires significantly larger samples.
margin_of_error
FORMULAZ Score
1.960
Critical value from standard normal distribution (Z-score) for a two-tailed 95% confidence level. 1.96 is the standard constant.
z_score
FORMULARequired Sample Size Raw
(pow(z_score, 2) * population_variance_estimate) / pow(margin_of_error, 2)
Standard formula for sample size: N = (Z^2 * Variance) / E^2. Since population is assumed large/infinite, finite population correction is omitted.
required_sample_size_raw
FORMULAFinal Sample Size
ceil(required_sample_size_raw)
Ensures the output is a whole number of respondents.
final_sample_size
OUTPUTFinal Sample Size
final_sample_size
Total survey responses needed to achieve the desired margin of error. Accounts for expected response rate—if your response rate is uncertain, the distribution widens.
What is Carlo?
Carlo is a visual tool for Monte Carlo simulation. Model uncertainty by dragging probability distributions, connecting them visually, and running thousands of scenarios instantly.