Calculate the survey sample needed to estimate a population proportion at a chosen margin of error and confidence level. The calculation begins with the standard proportion formula and then applies a finite population correction when a population size is supplied. Use an expected proportion of 50% when you have no prior estimate because it produces the most conservative sample requirement.
Initial n₀ = z²p(1−p)/e². With finite population N, n = n₀/[1+(n₀−1)/N]. Required counts are rounded upward.
The primary result is conditional on the values and statistical assumptions entered. Read the secondary results to understand uncertainty, workload, or design sensitivity before making a decision.
This planning estimate is not a substitute for a study protocol, domain review, or a method chosen for the final data distribution.
For a population of 10,000, a 5% margin, 50% expected proportion, and 95% confidence, n₀ is 384.15 and the finite-population requirement rounds up to 370 responses.
The calculator uses a standard statistical approximation. Small samples, highly skewed outcomes, or model misspecification can make the estimate less accurate.
Yes. A 90% setting gives a narrower interval or lower sample requirement, while a 95% setting provides more conservative coverage.
Use zero only where the input allows it. A rate calculation still needs a positive total or a defined prior so that division by zero is avoided.
No. It summarizes uncertainty or planning assumptions; study design, randomization, measurement quality, and confounding still matter.
Keep rates and intervals at the shown precision, but round required counts upward because a fraction of a sample or processing unit is not usable.
| Item | How it is used |
|---|---|
| Observed or planned sample | Sets the available evidence or workload. |
| Uncertainty setting | Controls interval width or rejection threshold. |
| Variability or rate | Translates the sample into uncertainty, power, or capacity. |