Sample Size Calculator
Calculate the required sample size for estimating a population proportion with a specified confidence level and margin of error.
This is NOT a Power Analysis
This calculator determines sample size for estimating a population proportion (e.g., survey research). It is not suitable for determining sample size for hypothesis testing.
For correlation, regression, ANOVA, moderation, mediation, experiments, and other hypothesis-testing designs, sample size should generally be determined using an appropriate power analysis rather than this proportion-based formula.
Calculator Inputs
e.g., 5 for ±5 percentage points
Use 50% if unknown (most conservative)
Leave blank for very large or unknown populations
Formula
Infinite Population
n₀ = Z² × p × (1 − p) / E² Where: Z = z-score for the confidence level p = expected proportion (0 to 1) E = margin of error (0 to 1)
Finite Population Correction
n = n₀ / (1 + (n₀ − 1) / N) Where: n₀ = sample size for infinite population N = total population size
The FPC reduces the required sample size when the population is small and known, because sampling a larger proportion of the population provides more information.
When to Use This Calculator
This calculator is appropriate for:
- Survey research estimating population percentages
- Market research and opinion polling
- Quality assurance sampling plans
- Any study estimating a proportion with a confidence interval
Not for Hypothesis Testing
If you are designing an experiment, clinical trial, or any study that tests a hypothesis (e.g., “Is treatment A better than treatment B?”), you need a power analysis, not this calculator. Power analysis accounts for effect size, significance level (α), and statistical power (1 − β), which are not considered here.
Worked Example
A university wants to survey students about satisfaction. They want 95% confidence with ±5% margin of error. They don't know what to expect, so they use p = 50%. The university has 5,000 students.
Step 1: Infinite population
n₀ = (1.96)² × 0.5 × 0.5 / (0.05)²
= 3.8416 × 0.25 / 0.0025
= 0.9604 / 0.0025
= 384.16
→ 385 (rounded up)
Step 2: Finite population correction
n = 385 / (1 + (385 − 1) / 5000)
= 385 / (1 + 384/5000)
= 385 / 1.0768
= 357.6
→ 358 (rounded up)The university needs 358 responses (instead of 385) because the finite population correction accounts for surveying a meaningful fraction of the 5,000-student population.
Common Sample Sizes
| Confidence | MOE | p | n |
|---|---|---|---|
| 95% | ±5% | 50% | 385 |
| 95% | ±3% | 50% | 1,068 |
| 95% | ±1% | 50% | 9,604 |
| 99% | ±5% | 50% | 664 |
| 90% | ±5% | 50% | 271 |
All values assume an infinite (very large) population and the most conservative proportion estimate (p = 50%).