Sample Size Calculator
Determine the optimal number of respondents needed for your survey or experiment to achieve statistically significant results with specified confidence level and margin of error.
Results
Enter your parameters and click "Calculate" to see results.
About Sample Size Calculator
The Sample Size Calculator helps you determine the optimal number of respondents needed for your survey or experiment to achieve statistically significant results. It calculates the required sample size based on your desired confidence level, margin of error, population size, and response distribution.
Key Concepts
Understanding these statistical concepts will help you use the calculator effectively:
Confidence Level
The confidence level represents the probability that your sample accurately reflects the attitudes of your population. Common confidence levels are 90%, 95%, and 99%. A 95% confidence level means that if you were to conduct the same survey 100 times, the results would be within the margin of error 95 times.
Margin of Error
The margin of error indicates the maximum difference you expect between your sample results and the true population value. A smaller margin of error requires a larger sample size but provides more precise results.
Population Size
This is the total number of people in the group you're trying to study. For large populations (over 100,000), the exact size has little effect on the sample size calculation.
Response Distribution
This is the expected percentage of respondents selecting a particular answer. When unsure, using 50% provides the most conservative (largest) sample size estimate.
How to Use the Calculator
Follow these steps to determine your required sample size:
- Select your confidence level: Typically 90%, 95%, or 99%
- Enter your margin of error: Common values are 3%, 5%, or 10%
- Enter your population size: The total number of people in your target group
- Enter the response distribution: Use 50% if unsure
- Click "Calculate Sample Size": View your required sample size
Sample Size Formula
The calculator uses the following formula to determine sample size:
Sample Size = (Z² × p × (1 - p)) / e²
Where:
- Z is the Z-score (based on confidence level)
- p is the response distribution (as a decimal)
- e is the margin of error (as a decimal)
For finite populations, the formula is adjusted with a correction factor.
Practical Considerations
When planning your survey, consider these practical aspects:
- Higher confidence levels require larger sample sizes
- Smaller margins of error require larger sample sizes
- For populations over 100,000, the exact size has minimal impact
- Response rates affect your required initial sample size
- Stratified sampling may require larger overall samples