Sample Size Calculator
How many survey responses you need for a given confidence level and margin of error
Using 50% expected proportion gives the most conservative (largest) sample size — safe to use whenever you don't already have a good estimate.
Frequently Asked Questions
Determining how many survey responses are needed for a given confidence level and margin of error is the planning-stage counterpart to the Confidence Interval Calculator — rather than analyzing an already-collected sample, this calculator answers the upstream question of how large a sample needs to be before data collection even begins.
Why required sample size depends on confidence level and margin of error together
A larger sample size generally produces a narrower confidence interval (more precision) for the same confidence level — but the specific sample size needed to achieve a target margin of error depends on both the desired confidence level and how tight that margin of error needs to be, with tighter (smaller) margins of error and higher confidence levels both independently pushing the required sample size upward. This relationship isn't linear — cutting the target margin of error in half doesn't just double the required sample size, it roughly quadruples it, since sample size requirements scale with the square of the margin of error, not directly with it. This is exactly why survey designers often have to make a practical tradeoff between achievable sample size and desired precision, rather than simply specifying an arbitrarily tight margin of error.
A worked example
Halving the target margin of error for a survey (making the results twice as precise) doesn't require twice as many respondents — it requires roughly four times as many, since the underlying formula's sample-size requirement scales with the square of the precision improvement, not linearly with it, which is exactly why very high-precision surveys become disproportionately expensive to run as the required margin of error shrinks.
How this connects to your other statistical calculations
Once a survey is actually run using a properly calculated sample size, the Confidence Interval Calculator analyzes the resulting data — the two calculators are companion tools for the planning and analysis stages of the same underlying statistical process, using the same confidence-level and margin-of-error concepts from opposite directions.
Common mistakes
Requesting an arbitrarily tight margin of error without considering the resulting sample-size requirement is a common planning mistake — because required sample size scales with the square of the precision target, a seemingly modest tightening of the desired margin of error can push the required sample size to an impractically large number, and checking this tradeoff before committing to a target precision avoids an unrealistic survey design.