Sample Size Calculator
Calculate the optimal sample size for surveys, research studies, and statistical analysis
Calculate Sample Size
How confident you want to be in your results
Acceptable error in your results (typically 3-5%)
Expected percentage with the characteristic (use 50% if unknown)
Sample Size Results
Good sample size - provides reliable results
Formula used: n = (Z² × p × (1-p)) / e²
Parameters: Z = 1.96, p = 0.50, e = 0.050
Survey Distribution Planning
Account for response rates when distributing your survey:
Example Calculation
Market Research Survey
Objective: Measure customer satisfaction rate
Confidence Level: 95% (Z = 1.96)
Margin of Error: ±3%
Expected Proportion: 70% satisfied (conservative estimate)
Population: Large (infinite)
Calculation
n = (Z² × p × (1-p)) / e²
n = (1.96² × 0.70 × 0.30) / 0.03²
n = (3.84 × 0.21) / 0.0009
n = 0.8064 / 0.0009
n = 897 respondents
Common Sample Sizes
Pilot Study
Minimum for basic statistics
Exploratory research
Small Survey
±10% margin at 95% confidence
Internal assessments
Standard Survey
±5% margin at 95% confidence
Market research
Large Survey
±3% margin at 95% confidence
National polls
Sample Size Tips
Use 50% proportion when unsure for maximum sample size
Higher confidence levels require larger samples
Smaller margins of error need more respondents
Consider response rates when planning distribution
Finite population correction reduces required sample
Understanding Sample Size Calculation
What is Sample Size?
Sample size is the number of observations or participants included in a study. It determines the statistical power of your research and the precision of your results. A properly calculated sample size ensures your study can detect meaningful effects while being cost-effective.
Key Components
- •Confidence Level: How certain you want to be (95% is standard)
- •Margin of Error: Acceptable level of uncertainty in results
- •Sample Proportion: Expected percentage with the characteristic
- •Population Size: Total size of your target group
Formula Explanation
n = (Z² × p × (1-p)) / e²
For surveys and proportions
- n: Required sample size
- Z: Z-score for confidence level (1.96 for 95%)
- p: Expected sample proportion (0.5 = 50%)
- e: Margin of error (0.05 = 5%)
Note: For finite populations, apply finite population correction (FPC) to reduce the required sample size.
Statistical Power
Larger samples increase your ability to detect true effects and reduce Type II errors.
Cost Efficiency
Optimal sample sizes balance statistical requirements with research budget constraints.
Precision
Adequate samples provide more precise estimates with narrower confidence intervals.