DIY Cost Tools
Sample Size Calculator
MATH & STATISTICS CALCULATOR
Estimate a survey sample size using confidence level, margin of error, expected proportion, optional population size, and response rate.
How it works
The calculator uses the normal-approximation sample-size equation and applies a finite-population correction when a population is entered.
Formula
n₀ = z²p(1−p) ÷ e²
Finite population: n = n₀ ÷ (1 + (n₀−1)/N)
Important limits
- The formula assumes a probability sample and a proportion estimate.
- Design effects, clustering, weighting, nonresponse bias, subgroup analysis, and measurement error can require a larger sample.
- Rounding up does not correct biased sampling.
Frequently asked questions
Why use 50% for expected proportion?
When the true proportion is unknown, 50% produces the largest conservative sample under this formula.
What does response rate change?
It changes invitations needed, not the number of completed responses required.
What affects a sample-size estimate
Sample size depends on the confidence level, margin of error, expected proportion or variability, and population size. When the expected proportion is unknown for a yes/no outcome, 50% is often used because it produces a conservative, larger sample.
The calculation assumes a suitable sampling method and independent observations. A large sample cannot correct selection bias, poor question wording, nonresponse bias, or measurements that do not represent the target population. Increase the invited sample when some people are unlikely to respond, and consider design effects for clustered or weighted surveys. For medical, safety, regulatory, or high-cost research, have a statistician review the outcome definition, power, expected effect size, and analysis plan before collecting data.
Review notes
The tool shows the uncorrected estimate, finite correction, and response-rate adjustment separately. Last reviewed September 30, 2026.