Calculator tool
How this calculator works
Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.
What this estimate assumes
The calculator estimates sample size for a proportion using a conservative response proportion of , which gives the largest required sample when the true proportion is unknown:
Where is the confidence-level z-score and is the margin of error as a decimal. If a finite population is entered, the tool applies a finite-population correction so the requirement can shrink when the population itself is not large.
What sample size does not fix
A large sample cannot repair biased sampling, low response quality, poor question wording, or a non-representative frame. The result is a mathematical target for a simple random-sample design, not a guarantee that a survey will be trustworthy.
Frequently asked questions
Why does the calculator use p = 0.5?
When the true proportion is unknown, 0.5 is conservative because it produces the largest required sample size for a given confidence level and margin of error.
What happens when I enter a finite population?
The calculator applies a finite-population correction, which can reduce the required sample when the population is not extremely large.
Does a larger sample remove all survey error?
No. It reduces random sampling error, but it does not cure biased recruitment, misleading questions, or poor response coverage.
Why do tighter margins of error need more responses?
Because estimating more precisely requires more information. Reducing the allowed error makes the denominator smaller, which raises the needed sample size.
