Mathematics
Sample Size Calculator
Determine the minimum number of people you need to survey or test to get statistically significant results.
How to Use
- Select your Confidence Level. 95% is the standard for most surveys and scientific studies.
- Enter your Margin of Error. A 5% margin means if 60% answer "Yes", you can be confident the true answer is between 55% and 65%.
- Enter your total Population Size if known. If you are surveying a city of 1 million people, you can leave this blank (treated as infinite).
- The calculator determines exactly how many responses you need to collect.
Formula
Infinite Population Sample Size (n):
n = [z² × p(1-p)] / e²
Finite Population Correction:
n' = n / [1 + ((n-1)/N)]
Where:
z = Z-score (1.96 for 95% confidence)
p = Population proportion (defaults to 0.5 for max variance)
e = Margin of error as decimal
N = Population size
n = [z² × p(1-p)] / e²
Finite Population Correction:
n' = n / [1 + ((n-1)/N)]
Where:
z = Z-score (1.96 for 95% confidence)
p = Population proportion (defaults to 0.5 for max variance)
e = Margin of error as decimal
N = Population size
A Sample Size Calculator is vital for market research, surveys, and A/B testing. It tells you mathematically how many people you need to include in your study to ensure your results represent the overall population and aren't just random chance.