Sample Size Calculator

What Is Sample Size?

Sample size is the number of observations or measurements needed in a study to achieve a specified level of statistical precision. Proper sample size determination is crucial for ensuring that study results are reliable and that resources are used efficiently. Too small a sample may fail to detect real effects, while too large a sample wastes resources without meaningful gains in precision.

The required sample size depends on four key factors: the desired confidence level, the acceptable margin of error, the expected variability in the population, and the total population size (for finite populations).

Sample Size Formula

For finite populations, apply the correction factor:

Where Z is the Z-score for the desired confidence level, p is the estimated proportion, E is the margin of error, and N is the population size.

Factors Affecting Sample Size

Factor	Effect on Sample Size
Higher confidence level	Increases sample size
Smaller margin of error	Increases sample size
Higher variability (p near 50%)	Increases sample size
Smaller population	Decreases sample size (finite correction)

Common Sample Sizes

Margin of Error	90% CL	95% CL	99% CL
1%	6,765	9,604	16,587
3%	752	1,068	1,844
5%	271	385	664
10%	68	97	166

Frequently Asked Questions

Why is 50% used as the default proportion?

Using p = 50% produces the maximum sample size for any given confidence level and margin of error. This is the most conservative estimate and is appropriate when you do not have prior knowledge about the population proportion. Using a proportion closer to 0% or 100% would yield a smaller required sample.

Does population size matter?

Population size has a diminishing effect. For large populations (over 20,000), the finite population correction has negligible impact. For small populations, the correction significantly reduces the required sample size because you are surveying a larger fraction of the total population.