Calculate the minimum sample size needed for a survey or study, based on confidence level, margin of error, and population size.
This tool calculates the minimum number of survey respondents or study participants needed to achieve statistically reliable results, based on your desired confidence level, margin of error, and population size. It's essential for planning surveys, market research, and scientific studies before data collection begins.
Sample Size = (Z² × p × (1-p)) ÷ E², where Z is the z-score for your desired confidence level, p is the estimated proportion (0.5 is used when unknown, as it maximizes required sample size), and E is the margin of error. For finite populations, a correction factor is applied to adjust the result downward.
Enter your desired confidence level (commonly 95%), acceptable margin of error (commonly 5%), and population size (if known), and the calculator returns the minimum required sample size.
Example: For a large population, a 95% confidence level, and a 5% margin of error, the required sample size is approximately 385 respondents.
Why is 385 such a common sample size number? It's the standard result for a 95% confidence level and 5% margin of error with an unknown population proportion (p = 0.5) and a very large or unlimited population size — a frequently cited benchmark in survey research.
Does a bigger population always need a bigger sample? No — beyond a certain population size, the required sample size levels off and grows very slowly, because sample size for a fixed margin of error depends more on the desired precision than the total population.
What is margin of error? It's the range within which the true population value is expected to fall, expressed as a plus-or-minus percentage around your survey results.
Should I always use p = 0.5 if I don't know the expected proportion? Yes, using 0.5 is the conservative, safe choice since it produces the largest possible required sample size, ensuring your study is adequately powered regardless of the actual proportion.
How does confidence level affect required sample size? Higher confidence levels (like 99% instead of 95%) require larger sample sizes, since more certainty demands more data.