Sample Size Proportion
Calculator
Results
- Required sample size
- 384.159999
- Rounded sample size
- 385
Statistical results
| Required sample size | 384.159999 |
| Rounded sample size | 385 |
formula-map diagram
- Required sample size
- 384.159999
- Rounded sample size
- 385
Statistical relationship
Formula
n = z² × p × (1 − p) / E²= 384.16
Note
This is a simplified model: it applies the displayed standard formula to the summary values you entered and assumes their underlying conditions (independence, normality, correct sampling) hold. It does not analyse a real data set. Check the assumptions before relying on the result.
More in Statistics and probability
See all →Frequently asked questions
What is this calculator solving for?+
It tells you how many respondents or observations you need to estimate a population proportion within a chosen margin of error and confidence level. It's the reverse of the margin-of-error calculation: instead of computing error from a given n, it computes the n needed for a target error.
Why do I need to guess the expected proportion before collecting data?+
The required sample size depends on how variable the outcome is expected to be, and proportions near 50% have the most variability. If you don't have a prior estimate, using 50% is the conservative choice because it produces the largest, safest sample size.
Why does assuming 50% give the largest required sample size?+
The variance of a proportion, p(1−p), is maximized when p = 0.5. Any proportion further from 0.5, like 10% or 90%, has lower variance and therefore needs a smaller sample to reach the same precision.
How much does raising the confidence level increase the needed sample size?+
It increases the required n substantially, since the confidence multiplier (the z-value) grows for higher confidence levels and that value is squared in the formula. Going from 95% to 99% confidence can increase your required sample size by nearly 75%.
Does this calculator account for the total population size?+
The basic version assumes an effectively infinite or very large population, which is accurate for most national or large-scale surveys. For small, finite populations, a finite population correction can reduce the required sample size further, since you can't sample more people than exist.