Sample Size Calculator
Determine the required sample size for surveys and statistical studies.
A sample size calculator determines how many observations you need for statistically significant survey or experiment results.
Examples
General survey
Small population
Tight margin
Frequently Asked Questions
Why use 50% for population proportion?
What is the finite population correction?
How does margin of error affect sample size?
Quick Tips
- •Double-check your inputs — small errors lead to incorrect results.
- •Use 50% for population proportion when you have no prior estimate, as it gives the most conservative sample size.
- •Specify the population size for small populations to benefit from the finite population correction.
A sample size calculator determines how many observations you need for statistically significant survey or experiment results.
How to Use This Calculator
Select the desired confidence level, enter the margin of error (as a percentage), population proportion, and optionally the total population size. The calculator determines the minimum sample size needed.
Understanding the Formula
n = Z² × p × (1-p) / E². With finite population correction: n_adj = n / (1 + (n-1)/N).
Examples
General survey
95% confidence, 5% margin, 50% proportion: n = 1.96² × 0.5 × 0.5 / 0.05² = 385
Small population
Same parameters with population 500: n = 385 / (1 + 384/500) = 218
Tight margin
99% confidence, 2% margin: n = 2.576² × 0.25 / 0.0004 = 4,148
Frequently Asked Questions
Why use 50% for population proportion?
Using 50% gives the maximum (most conservative) sample size. If you have prior knowledge about the proportion, use that for a potentially smaller required sample.
What is the finite population correction?
When sampling from a limited population, the required sample size can be reduced. The correction adjusts for the fact that sampling a larger fraction of the population provides more information.
How does margin of error affect sample size?
Halving the margin of error roughly quadruples the required sample size, since E appears squared in the denominator.
Assumptions & Limitations
- Assumes a standard normal distribution for the z-score lookup.
- Assumes simple random sampling from the population.
- Assumes exact input values; rounding in inputs propagates to results.