Sample Size Proportion Calculator
Calculate sample size proportion with clear inputs, formula guidance, and practical result checks.
Sample Size Proportion measurements
Enter your values, then calculate.
Result
How to calculate sample size proportion
This calculator finds the required sample size for a survey targeting a specific margin of error, based on expected proportion and desired precision at a 95% confidence level.
How the calculation works
Sample size = (1.96² × Expected proportion × (1 − Expected proportion)) ÷ Margin of error².
Example
An expected 40% proportion with a desired 4% margin of error: (1.96²×0.4×0.6)÷0.04² = (3.8416×0.24)÷0.0016 = 0.922÷0.0016 ≈ 576.
Frequently asked questions
How is Result calculated?
Result = pow(1.96, 2) × ([Expected proportion] ÷ 100) × (1 − [Expected proportion] ÷ 100) ÷ pow([Desired margin of error] ÷ 100, 2).
Is the Sample Size Proportion Calculator free to use?
Yes — every calculator on Simple Calculator Tools is free, runs in your browser, and does not require an account.
Sample Size Proportion Calculator
Sample size = (1.96² × Expected proportion × (1 − Expected proportion)) ÷ Margin of error².
Let's understand your sample size proportion result.
Calculate a result above and this guide will help you interpret it using this calculator's own formula and explanation.
Pro Tips for Sample Size Proportion
- Using 50% as the expected proportion produces the most conservative (largest) required sample size when you have no prior estimate, since p×(1-p) is maximized at p=50%.
- A smaller desired margin of error requires a substantially larger sample, since margin of error is squared in the denominator — the relationship is not linear.
Common Sample Size Proportion Mistakes to Avoid
- Assuming a small reduction in target margin of error requires only a proportionally small increase in sample size, when the actual relationship is much steeper due to the squared term.
When to Use This Calculator
This calculator finds the required sample size for a survey targeting a specific margin of error, based on expected proportion and desired precision at a 95% confidence level.