Sample Size Calculator

Calculate the required sample size for surveys, experiments, and statistical studies. Determine how many participants you need for reliable results.

Required Sample Size

Sample Size

385

Infinite population

Confidence Level95%
Margin of Error±5%
Z-Score1.960

Calculation Type

Parameters

5%
1%20%
50%
1%99%

Result

Required Sample Size

385

With 95% confidence and ±5% margin of error, you need 385 samples.

Calculation Details

n = (Z² × p × (1-p)) / E²

Z-Score (95% confidence)1.96
p (proportion)0.5
E (margin of error)0.05
Base sample size (n₀)385

Quick Reference Table

Sample sizes for proportion estimates with 50% expected proportion

Margin of Error90% CI95% CI99% CI
±1%6,7669,60416,590
±2%1,6922,4014,148
±3%7521,0681,844
±5%271385664
±10%6897166

Z-Scores for Confidence Levels

80%

1.282

85%

1.440

90%

1.645

95%

1.960

99%

2.576

99.9%

3.291

Required Sample Size

Sample Size

385

Infinite population

Confidence Level95%
Margin of Error±5%
Z-Score1.960

?How Do You Calculate Sample Size?

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.

What is Sample Size?

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.

Key Facts About Sample Size

  • Formula: n = (Z^2 * p * (1-p)) / E^2
  • Z-scores: 90% = 1.645, 95% = 1.96, 99% = 2.576
  • Use p = 0.5 for maximum sample size (most conservative)
  • Smaller margin of error = larger sample needed
  • Higher confidence level = larger sample needed
  • Finite population correction reduces sample size
  • 95% confidence, 5% margin: ~385 for large populations
  • Doubling precision (halving error) quadruples sample size

Quick Answer

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.

Frequently Asked Questions

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