Sample Size Calculator
Calculate the required sample size for a survey or experiment based on confidence level, margin of error, and population size.
Inputs
Results
Sample Size Formula
For an infinite population: n = Z² × p(1−p) / e². For a finite population: n_adj = n / (1 + (n−1)/N). Z = 1.96 for 95% confidence. Margin of error e = 5% means results are accurate within ±5%. Use p = 0.5 for the most conservative estimate.
What is the Sample Size Calculator?
The Sample Size Calculator determines exactly how many people you need to survey in order to get mathematically significant results. It is a mandatory tool for sociologists, political pollsters, and market researchers who cannot practically survey an entire population.
How It Works (Formula)
The required sample size depends on three variables: the total Population Size, the Margin of Error (how much you allow the results to vary), and the Confidence Level (usually 95%, which corresponds to a Z-score of 1.96).
$$ n = \frac{Z^2 \times p(1-p)}{E^2} $$
Cochran's formula for determining sample size for an infinite population.
How to Use It
Enter the total population size if known. Select your desired Confidence Level and acceptable Margin of Error. The calculator will output the absolute minimum number of respondents you need to achieve statistically valid data.