Sample Size Calculator
Determine the required sample size for a survey or experiment based on population size, confidence level, and desired margin of error. Includes finite population correction.
About this Calculator
Determine the required sample size for a survey or experiment based on population size, confidence level, and desired margin of error. Includes finite population correction.
Formula & Calculations
Formula
n₀ = (z² × p(1−p)) / e²; n = n₀ / (1 + (n₀−1)/N) (with finite population correction)Where:
- N=Population size (total number of individuals in the group)
- z=Z-score for the chosen confidence level
- e=Margin of error (as a proportion, e.g., 0.05 for 5%)
- p=Estimated proportion (default 0.5 for maximum sample size)
- n=Required sample size
Assumptions
- When the population proportion p is unknown, p = 0.5 is used to maximize the required sample size (most conservative approach).
- The finite population correction (FPC) adjusts the sample size downward when sampling from a small population.
- Confidence level and margin of error are specified as percentages.
- Results assume simple random sampling.
Calculation Examples
Example 1
z = 1.96, p = 0.5, e = 0.05. n₀ = (1.96² × 0.5 × 0.5) / 0.05² = 384. With FPC: n = 384 / (1 + 383/10000) ≈ 370.
Example 2
z = 2.576, n₀ = (2.576² × 0.25) / 0.03² = 1844. With FPC for small population: n ≈ 395.
Frequently Asked Questions
Why is p = 0.5 used when the true proportion is unknown?
The expression p(1−p) is maximized when p = 0.5, giving p(1−p) = 0.25. This yields the largest possible required sample size, making it the most conservative assumption and ensuring your sample will be large enough regardless of the true proportion.
What is finite population correction and when is it needed?
Finite population correction (FPC) adjusts the sample size downward when you are sampling from a relatively small population. As a rule of thumb, use FPC when your sample size would be more than 5% of the population. For very large populations, the correction is negligible.