Sample Size Calculator
Determine how many respondents you need for a proportion estimate, adjusting for finite population when necessary.
Use 50% for a conservative estimate when unsure.
Leave blank for large or unknown populations.
Z critical value: 1.960
Initial sample size (infinite population): 385
How to Use This Calculator
- Select a confidence level and margin of error for your survey or study.
- Provide an expected proportion (50% is conservative when the true value is unknown).
- Optionally enter population size to apply finite population correction.
- Use the reported sample size to plan recruitment or data collection.
Formula
n₀ = (z² × p × (1 − p)) / e²
Finite population correction: n = n₀ × N / (n₀ + N − 1)
Where z is the z-score for the desired confidence, p is expected proportion, e is margin of error, and N is population size.
Full Description
Sample size calculations balance precision, confidence, and practicality. This calculator targets proportion estimates, making use of the normal approximation and optional finite population correction to adjust for smaller populations.
Higher confidence levels and expected variability (p near 0.5) increase required sample size; larger margins of error decrease it.
Frequently Asked Questions
What if I don’t know the expected proportion?
Use 50%. It yields the largest sample size and is a safe starting point when planning.
Can this calculator handle means instead of proportions?
No. Use sample size formulas involving standard deviation when estimating means.
Why adjust for finite populations?
When sampling without replacement from a small population, fewer responses are needed to reach the same precision.
Does this account for design effects?
No. For complex samples (clustered or stratified), multiply the calculated sample size by the design effect.