# Sample size calculator for needs assessments and KAP surveys

The following calculator will help you find an appropriate sample size for a needs assessment survey, a KAP survey, or any other kind of survey intended to provide a "snapshot" of a population at a given point in time. The results of the survey can be used to draw conclusions about the population as a whole, and can provide useful inputs on the design and planning of interventions. To measure change over time in the same population, see our Baseline and endline sample size calculator.

## Formulas

This calculator uses the following formula to find the required sample size:

$$n=\frac{m}{1+\frac{m-1}{N}}$$

Where $$m$$ is the sample size required for a large population, and $$N$$ is the actual population size.

The required sample size for a large population is:

$$m=\frac{z^2_{\alpha/2}\hat{p}(1-\hat{p})}{\epsilon^2}$$

Where $$\hat{p}$$ is the expected proportion in the population, $$\epsilon$$ is the allowable margin of error, and $$z^2_{\alpha/2}$$ is the z-Score that corresponds to the 95% confidence level.

For a proof of this formula, see Penn State's excellent Introduction to mathematical statistics course.