Sample Size Calculator Determine the right sample size for your survey or experiment — with confidence levels, margins of...

Sample Size Calculator

Determine the right sample size for your survey or experiment — with confidence levels, margins of error, and population adjustments.

Proportion (Percentage)

Mean (Average)

Finite Population

A/B Testing

Confidence Level (%) 90% 95% 99%

Margin of Error (%)

Expected Proportion (%)

Confidence Level (%) 90% 95% 99%

Margin of Error

Standard Deviation

Confidence Level (%) 90% 95% 99%

Margin of Error (%)

Population Size

Expected Proportion (%)

Confidence Level (%) 90% 95% 99%

Statistical Power (%)

Baseline Rate (%)

Min. Detectable Effect (%)

385

Required Sample Size

95%

Confidence Level

±5%

Margin of Error

Proportion

Calculation Type

Sample Size Formulas

Proportion

n = Z²·p(1-p)/E²

Mean

n = Z²·σ²/E²

Finite Population

n_adj = n/(1 + (n-1)/N)

A/B Testing

Based on power analysis

Interpretation

—

Sample Size vs Confidence Level

Sample Size Fundamentals

Sample size is the number of observations or replicates to include in a statistical sample.

Key Concepts**:

• Confidence Level**: Probability that the true population parameter falls within your confidence interval
• Margin of Error**: Maximum expected difference between sample estimate and true population value
• Population Size**: Total number of individuals in your target population
• Expected Proportion**: Your best guess of the percentage for your key metric

Why It Matters**:

• Too small: Results may not be statistically significant
• Too large: Wastes resources and time
• Just right: Achieves desired precision with optimal resources

✅ Rule of Thumb**: For unknown populations, use 50% as your expected proportion (most conservative estimate).

Common Sample Size Mistakes

⚠️ Avoid these critical errors:

• Ignoring non-response rates**: Actual required sample = calculated sample / expected response rate
• Using wrong confidence level**: 95% is standard, but 99% may be needed for medical studies
• Overestimating precision**: Smaller margins of error require exponentially larger samples
• Forgetting finite population correction**: Essential when sample >5% of population
• Confusing power with confidence**: Power is about detecting effects, confidence is about precision

✅ Best Practices**:

• Always account for expected non-response (typically add 20-30%)
• Use conservative estimates (50% proportion) when uncertain
• Consider your minimum detectable effect size carefully
• Validate your sample size calculation with a statistician for critical studies

Real-World Applications

Sample size calculations are essential in:

• Market Research**: Customer satisfaction surveys, product testing
• Academic Research**: Clinical trials, social science studies
• Quality Control**: Manufacturing defect rates, process monitoring
• Elections**: Polling and exit surveys
• Website Testing**: A/B testing for conversion optimization

📊 Example Use Cases**:

• Customer Survey**: 95% confidence, ±5% margin → 385 responses needed
• Clinical Trial**: 99% confidence, ±3% margin → 1,843 patients needed
• Small Population**: 500 employees, 95% confidence, ±5% margin → 217 employees needed
• A/B Test**: Detect 10% improvement with 80% power → 14,000 visitors per variant

How to Use This Calculator

➡️ Proportion (Percentage)

"Survey with 95% confidence, ±5% margin" → 385 samples

➡️ Mean (Average)

"Estimate average with σ=10, ±2 margin" → 97 samples

➡️ Finite Population

"Survey 10,000 people with ±5% margin" → 371 samples

➡️ A/B Testing

"Detect 10% improvement with 80% power" → 14,000 per group

Note: All calculations use standard statistical formulas. For A/B testing, we use a two-proportion power analysis with equal group sizes.