Sample Size Calculator
Required sample size: 0
The Formula Behind This Calculator
This calculator uses the standard formula for estimating a population proportion: n0 = (Z2 × p × (1 - p)) / E2, where Z is the z-score for your chosen confidence level, p is the estimated proportion (use 50% if you have no prior estimate, since it produces the most conservative, largest sample size), and E is your acceptable margin of error expressed as a decimal. If you supply a known, finite population size N, the calculator applies the finite population correction: n = n0 / (1 + (n0 - 1) / N), which reduces the required sample size when the population itself is small relative to n0. Results are always rounded up to the nearest whole person, since a fractional respondent isn't possible.
Why 50% Is the "Safe" Default for Sample Proportion
The term p(1-p) in the formula is maximized when p = 0.5, which is why researchers who don't have a prior estimate of the true proportion default to 50% — it guarantees the calculated sample size is large enough regardless of what the real proportion turns out to be. If you already have a rough estimate (say, from a pilot study or prior research showing the true rate is closer to 10% or 90%), using that value instead will typically shrink your required sample size, since p(1-p) is smaller further from 0.5.
Confidence Level, Margin of Error, and Related Tools
The confidence level describes how often, if you repeated the survey many times, the true population proportion would fall inside your margin of error — it is not the probability that this one specific survey is correct. If you need to work backward from a completed survey's data to a confidence interval, or want to double check the z-score for an unusual confidence level, see the confidence interval calculator and the z-score calculator.
Frequently Asked Questions
What sample proportion should I use if I don't know it in advance?
Use 50%. The term p(1-p) in the sample size formula reaches its maximum at p = 0.5, so assuming a 50% proportion produces the largest, most conservative sample size estimate that stays valid no matter what the true proportion actually is.
Do I need to enter a population size?
Only if your population is small and finite (for example, surveying all 800 employees at a company). Leave it blank for large or effectively unlimited populations (like all adults in a country) - the calculator will use the standard infinite-population formula, since the finite population correction has negligible effect once the population is much larger than the calculated sample size.