Calculate the required sample size for surveys, experiments, and statistical studies. Determine how many participants you need for reliable results.
Sample Size
385
Infinite population
Required Sample Size
385
With 95% confidence and ±5% margin of error, you need 385 samples.
n = (Z² × p × (1-p)) / E²
Sample sizes for proportion estimates with 50% expected proportion
| Margin of Error | 90% CI | 95% CI | 99% CI |
|---|---|---|---|
| ±1% | 6,766 | 9,604 | 16,590 |
| ±2% | 1,692 | 2,401 | 4,148 |
| ±3% | 752 | 1,068 | 1,844 |
| ±5% | 271 | 385 | 664 |
| ±10% | 68 | 97 | 166 |
80%
1.282
85%
1.440
90%
1.645
95%
1.960
99%
2.576
99.9%
3.291
Sample Size
385
Infinite population
Sample size formula: n = (Z^2 * p * (1-p)) / E^2, where Z is z-score for confidence level (1.96 for 95%), p is expected proportion (use 0.5 if unknown), E is margin of error. For finite populations, adjust: n_adj = n / (1 + (n-1)/N). Example: 95% confidence, 5% margin of error needs ~385 samples.
Sample size is the number of observations or respondents needed in a study to achieve reliable statistical results. Proper sample size ensures sufficient statistical power to detect effects and provides results with desired precision. Sample size calculation balances accuracy, resources, and practical constraints.
Quick-start with common scenarios
Test your skills with practice problems
Practice with 6 problems to test your understanding.
Explore similar calculators
Sample size formula: n = (Z^2 * p * (1-p)) / E^2, where Z is z-score for confidence level (1.96 for 95%), p is expected proportion (use 0.5 if unknown), E is margin of error. For finite populations, adjust: n_adj = n / (1 + (n-1)/N). Example: 95% confidence, 5% margin of error needs ~385 samples.
Sample size is the number of observations or data points collected in a study. A larger sample size generally provides more precise estimates and greater statistical power. The required sample size depends on desired confidence level, margin of error, and population variability.
Margin of error is the range within which the true population value is likely to fall. A 3% margin of error means results could vary ±3% from the sample estimate. Smaller margins require larger sample sizes.
95% is the standard in most research. Use 90% for preliminary studies or when resources are limited. Use 99% when high precision is critical (medical research, quality control). Higher confidence requires larger samples.
When sampling from a small, known population, you can reduce sample size because you're sampling a larger proportion. If sampling more than 5% of population, use the correction: n_adjusted = n / (1 + (n-1)/N).
Use 50% (0.5) as a conservative estimate. This maximizes sample size and ensures adequate precision regardless of actual proportion. If you have pilot data or similar studies, use those estimates instead.
Last updated: 2025-01-15
Sample Size
385
Infinite population