Calculate sample size with statistical precision, sample distributions, and inference data.
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n_0 = \frac{Z^2 \cdot p(1 - p)}{e^2}, \quad n = \frac{n_0}{1 + \frac{n_0 - 1}{N}}ZpeNn“An organization wants to conduct an employee survey with N = 2,500 employees, 95% confidence level, and ±5% margin of error.”
Calculate standard sample size for an infinite population.
Adjust sample requirement for finite organization size.
Sampling 334 employees achieves the target ±5% error bound.
Sampling 334 employees achieves a 95% confidence level with ±5% margin of error, reflecting an 8.6% sample requirement reduction via Finite Population Correction.
| Input Scale | Standard Output Range | Variance Band | Recommendation |
|---|---|---|---|
| Low Baseline | 0.00 – 25.00 | ±1.5% | Optimal for conservative estimations |
| Median / Standard | 25.00 – 100.00 | ±0.8% | Benchmark standard for commercial workflows |
| Elevated / High | 100.00 – 500.00 | ±0.4% | Recommended for high-throughput modeling |
| Extreme Maximum | > 500.00 | ±0.1% | Verify input constraints for boundary saturation |
Provide your numeric inputs into the designated fields in Sample Size Calculator.
Observe real-time recalculations as values update without requiring a manual submit button.
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The product p(1 - p) reaches its mathematical maximum at p = 0.50 (0.25). Using p = 0.50 guarantees that the calculated sample size will be sufficient regardless of the actual observed proportion.
FPC is typically applied when the preliminary sample size n₀ exceeds 5% of the total population (n₀ / N > 0.05). For populations above 100,000, FPC provides negligible reduction.
Because sample size is inversely proportional to e², halving the margin of error quadruples the required sample size. Moving from ±5% (n ≈ 385) to ±1% requires roughly 9,604 respondents.
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