Sample Size Calculator
Calculate the required sample size for surveys, experiments, and research studies. Ensure your results are statistically significant and representative.
Common values: 5% (standard), 3% (more precise), 10% (less precise)
Understanding Sample Size
What is Sample Size?
Sample size is the number of participants or observations needed in a study to achieve statistically valid results. A larger sample size generally provides more reliable and precise results, but requires more time and resources.
Key Parameters Explained
- Population Size: Total number of individuals in the group you're studying. For very large populations (>100,000), you can leave this blank.
- Confidence Level: How confident you want to be that the true value falls within your margin of error. 95% is standard for most research.
- Margin of Error: The acceptable range of error in your results. 5% means your results could be off by ±5 percentage points.
- Proportion: Expected percentage with the characteristic you're measuring. Use 50% when unsure (provides maximum sample size for safety).
When to Use This Calculator
- Planning surveys (customer satisfaction, market research)
- Designing experiments and clinical trials
- Academic research studies
- Quality control sampling
- A/B testing and usability studies
Real-World Example
A company wants to survey employees (population: 5,000) about job satisfaction with 95% confidence and ±5% margin of error. Using 50% expected proportion, they need approximately 357 responses. This ensures their survey results represent the entire workforce with statistical validity.
Common Trade-offs
- Higher confidence (99% vs 95%): Requires larger sample size
- Lower margin of error (3% vs 5%): Requires larger sample size
- Larger population: Only slightly increases sample size (levels off)
- Unknown proportion: Use 50% to be conservative (largest sample)
Important Considerations
- Account for non-response rates (plan for 20-30% more than calculated)
- Ensure random sampling for representative results
- This calculator assumes simple random sampling
- For complex designs (stratified, cluster), consult a statistician
Formula
For infinite/unknown population:
n = (Z² × p × (1-p)) / E²
For finite population:
n = (Z² × p × (1-p)) / E² / (1 + (Z² × p × (1-p)) / (E² × N))
Where:
- n = required sample size
- Z = Z-score for confidence level
- p = expected proportion (as decimal)
- E = margin of error (as decimal)
- N = population size
Educational Purpose Disclaimer
This calculator is provided for educational purposes only. Results should not be used as the sole basis for critical decisions. Always verify important calculations independently and consult qualified professionals when needed.