Determine the minimum sample size needed to estimate a population proportion or population mean with a given confidence level and margin of error.
Estimates sample size to determine a population proportion p within margin of error E.
Formula: n = z²·p·(1−p) / E²
| Parameter | Value |
|---|---|
| Confidence Level | 95% |
| Critical value (z*) | 1.96 |
| Proportion (p) | 0.5 |
| 1 − p = q | 0.5 |
| Margin of Error (E) | ±0.05 (5.0%) |
| Unadjusted n₀ | 385 |
| Required n | 385 |
| Margin of Error | n (95% CI) | n (99% CI) |
|---|---|---|
| ±1% | 9,604 | 16,587 |
| ±2% | 2,401 | 4,147 |
| ±3% | 1,067 | 1,843 |
| ±4% | 600 | 1,037 |
| ±5% | 384 | 664 |
| ±10% | 96 | 166 |
Determine the right sample size for your survey or study with our free calculator, balancing statistical confidence against practical constraints.
Sample Size = (Z² × p × (1-p)) / e², where Z is the z-score for your confidence level, p is your estimated proportion (use 0.5 if unknown, which maximizes required sample size), and e is your margin of error.
50% produces the largest possible required sample size for a given confidence and margin of error, making it the safe, conservative choice when you have no prior estimate.
Common survey margins of error range from 3-5%, tighter margins require larger samples, so this is often a practical trade-off against cost and feasibility.
For very large populations, it has minimal effect on required sample size; for smaller, finite populations, a finite population correction can reduce the required sample size.
95% is the most common standard for survey research, though 90% or 99% may be appropriate depending on how much precision your specific use case requires.