Sample Size Calculation Equation Calculator
Estimate the minimum sample size for proportions using confidence level, margin of error, and expected proportion.
Understanding the Sample Size Calculation Equation
Sample size calculation for proportions is a cornerstone of survey design, market research, and statistical quality control. The equation estimates how many observations are needed to achieve a target margin of error at a chosen confidence level. This calculator uses the standard formula for proportions and applies finite population correction when a population size is provided.
The Core Equation
The initial sample size (n0) for an infinite population is: n0 = (Z² × p × (1 − p)) ÷ E²
- Z is the z-score based on the confidence level (90%, 95%, or 99%).
- p is the estimated proportion of the attribute in the population.
- E is the desired margin of error (as a decimal).
Finite Population Correction
When the total population size is known and not extremely large, apply: n = n0 ÷ (1 + (n0 − 1) / N)
This adjustment reduces the required sample size because the population is finite, improving efficiency without sacrificing precision.
Practical Example
Suppose you want a 95% confidence level, a ±5% margin of error, and estimate the proportion at 50%. The unadjusted sample size is about 384. If the population size is 20,000, the corrected sample size becomes approximately 377.
When to Use This Calculator
- Designing customer satisfaction surveys and market studies.
- Estimating defect rates in quality assurance.
- Determining required sample sizes for compliance or audit checks.