Sample SizeCalculator
Determine the minimum required sample size for statistical significance in surveys, clinical trials, and A/B tests.
Survey & Research Requirements
Required Sample Size
Sample Size Calculator - Free Survey & Research Cohort Sizing Tool: Determine required survey sample sizes with finite population correction. Fast, free, and secure client-side execution in your browser.
How to Use the Sample Size Calculator
Define Margin of Error
Select your acceptable error tolerance (commonly ±3% for political polling or ±5% for consumer surveys).
Choose Confidence Level
Pick 95% standard confidence, 99% for rigorous clinical research, or 90% for quick preliminary studies.
Set Population Proportion
Keep 50% for maximum variance (most conservative sample size), or enter a known baseline percentage.
Apply Population Size
Input total population size to apply the Finite Population Correction (FPC) if studying a small closed group.
Sample Size Determination: Cochran’s Formula and Finite Population Correction
Determining the appropriate sample size is a pivotal preliminary step in any quantitative research endeavor, survey design, or experimental clinical trial. Under-sizing a study leads to insufficient statistical power, rendering genuine experimental effects undetectable. Conversely, over-sizing squanders financial capital, organizational labor, and participant time while detecting clinically inconsequential trivial differences.
Cochran’s formula provides the standard mathematical framework for determining sample size in proportion studies: n0 = (Z² × p(1 − p)) / e², where Z is the critical value for the chosen confidence level, p is the estimated population proportion, and e is the desired margin of error. Setting p = 0.50 yields p(1 − p) = 0.25, which represents maximum mathematical variance and produces the most conservative (largest) recommended sample size.
A common misconception in survey methodology is that sample size must scale proportionally with population size. For large populations (e.g., millions of national voters), the required sample size plateaus: a sample of approximately 384 respondents provides a ±5% margin of error at a 95% confidence level whether the population is 100,000 or 300 million.
When sampling from a small, defined finite population (such as employees of a 500-person company), the Finite Population Correction (FPC) formula significantly reduces sample size requirements without compromising statistical rigor. Applying FPC accounts for the fact that sampling a large percentage of a finite pool progressively exhausts remaining variability.
Key Advantages & Analytical Value
Cochran's Formula Standard
Employs universally recognized statistical formulas for survey and cohort sizing.
Finite Population Correction
Reduces survey respondent requirements for small closed populations automatically.
Conservative 50% Default
Guarantees adequate statistical power by maximizing variance parameters.
Multi-Confidence Tiers
Instantly compare 90%, 95%, and 99% confidence sample volume demands.
Confidential Research
Calculate clinical and market research parameters privately on your local browser.
Real-Time Reactivity
Watch sample sizes adjust dynamically as margin of error inputs are adjusted.
Frequently Asked Questions
Under Cochran’s formula, 384 is the exact sample size needed to achieve a ±5% margin of error at a 95% confidence level for an infinite population with maximum variance (p = 0.50).
FPC is a mathematical adjustment applied when the sample size exceeds 5% of the total population, reducing the required sample size because a substantial portion of the population is being surveyed.
Sample size is inversely proportional to the square of the margin of error. Halving your margin of error (e.g., from 4% to 2%) quadruples your required sample size.
Use 50% (0.50). This produces the maximum possible product p(1 - p) = 0.25, ensuring your sample size is sufficiently large regardless of the actual outcome.
Yes. If you need 400 completed responses and your historical survey response rate is 20%, you must distribute invitations to at least 2,000 individuals (400 / 0.20).