Enter the population proportion, confidence level, and desired margin of error to calculate the sample size needed for a population proportion estimate.

**Required Sample Size:**

## Understanding Sample Size Calculation for Proportion

This calculator uses the following formula to determine the sample size required to estimate a population proportion within a specified margin of error and confidence level:

where:

- \( n \) = Sample size
- \( Z \) = Z-score associated with the confidence level
- \( p \) = Population proportion
- \( E \) = Margin of error

### Real-Life Example: Estimating Support for a Policy

Suppose you want to estimate the percentage of voters who support a new policy, with a 95% confidence level and a margin of error of 5%. If you have no prior estimate, you can use a proportion of 0.5 to maximize sample size.

Here’s the step-by-step calculation:

**Step 1:**Set the values: confidence level = 95%, margin of error = 5%, population proportion (p) = 0.5.**Step 2:**Find the Z-score for a 95% confidence level (Z ≈ 1.96).**Step 3:**Use the formula:$$ n = \frac{{(1.96)^2 \cdot 0.5 \cdot (1 - 0.5)}}{{(0.05)^2}} = 384.16 $$**Interpretation:**You would need a sample size of at least 385 people to estimate the proportion of supporters within a 5% margin of error.

Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.