How to calculate sample size
The sample size needed for a proportion is n = z² × p(1 − p) ÷ e², rounded up to a whole respondent. With z = 1.96 (95%), p = 0.5 and a margin of error e = 0.05, that is 3.8416 × 0.25 ÷ 0.0025 = 384.16, which rounds up to 385. For a numeric outcome you need an estimate of the spread first, which is where the standard deviation calculator comes in.
How to use this calculator
Enter the z-score for your confidence level, your expected proportion (use 0.5 if unsure), and your target margin of error as a decimal. The result is always rounded up so the margin is met. To check the margin a sample actually gives, use the margin of error calculator.
Choosing your inputs
Use p = 0.5 for the safest (largest) sample size when the true proportion is unknown. A smaller margin of error or a higher confidence level both increase the sample needed. To build the final estimate, see the confidence interval calculator.
Frequently asked questions
- How do I calculate sample size?
- Use n = z² × p(1 − p) ÷ e², then round up. With z = 1.96, p = 0.5, e = 0.05 you need 385 respondents.
- Why round up?
- You can't survey a fraction of a person, and rounding up guarantees the margin of error is met.
- What proportion should I assume?
- If you don't know it, use 0.5, which gives the largest and safest sample size.
- How do I get a smaller margin of error?
- Lower the target margin e, which increases the required sample size sharply because it depends on 1 ÷ e².
- Do I need a bigger sample for a bigger population?
- Barely — the formula does not include population size at all, so polling a city and polling a country need almost the same sample. A finite population correction only makes a real difference when your sample would exceed roughly 5% of the population.