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Online Sample Size Calculator
Calculate the minimum sample size needed for your survey or study with our easy-to-use online tool. Achieve desired confidence levels and margins of error for accurate statistical results.
Sample Size
385
Margin of Error
9.8%
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What Is This Tool?
This calculator estimates the required minimum sample size to accurately represent a population proportion in surveys, experiments, or statistical studies. It uses a standard formula that incorporates your chosen confidence level, estimated proportion, and margin of error.
How to Use This Tool?
- Enter the Z-score corresponding to your confidence level (for example, 1.96 for 95%)
- Input the estimated proportion (p) of the population or use the default 0.5 if unknown
- Specify your desired margin of error (e) as a decimal (e.g., 0.05 for 5%)
- Click the calculate button to obtain the minimum required sample size (n)
- Use the resulting sample size to plan your survey or study accordingly
Key Features
- Estimates sample size based on confidence level, estimated proportion, and margin of error
- Uses a precise statistical formula for population proportion sample size estimation
- Supports common confidence levels with corresponding Z-scores (e.g., 1.96 for 95%)
- High-precision floating-point calculations ensure accurate results
- Easy to use browser-based interface with quick calculation
Examples
- For 95% confidence (Z = 1.96), estimated proportion p = 0.5, and margin of error e = 0.05: n = (1.96² × 0.5 × 0.5) / 0.05² = 384.16, rounded to 385
- Adjust the margin of error to see how sample size requirements change for tighter or looser precision
- Change the estimated proportion if prior knowledge of the population differs from 0.5
Common Use Cases
- Determining sample sizes for academic research surveys
- Planning polling studies to reflect population opinions accurately
- Designing medical and clinical study sample sizes
- Calculating samples for product testing or market research
- Ensuring statistically valid sample sizes in social science experiments
Tips & Best Practices
- Use a default estimated proportion of 0.5 when the true proportion is unknown to maximize sample size for safety
- Select an appropriate confidence level reflecting your study's required rigor
- Choose a realistic margin of error balancing precision and sample size feasibility
- Consider the population size and whether a finite-population correction might be needed
- Verify inputs carefully to ensure accurate calculation results
Limitations
- Assumes that the sample is obtained through random sampling methods
- Formula applies best to large populations; small populations may require additional corrections
- Does not account for population variability outside the estimated proportion parameter
- Does not consider design effects or non-response rates in surveys
Frequently Asked Questions
- What does the Z-score represent in the formula?
- The Z-score corresponds to the confidence level selected for the study, such as 1.96 for a 95% confidence interval.
- Why is the estimated proportion often set to 0.5?
- Using 0.5 as the estimated proportion maximizes the required sample size, ensuring the calculation is conservative when the actual proportion is unknown.
- What is the margin of error?
- The margin of error is the maximum allowed difference between the sample proportion and the true population proportion, expressed as a decimal.
- Can I use this calculator for very small populations?
- The formula assumes a large population size. For small populations, additional finite-population corrections may be required for accurate results.
Key Terminology
- Z-score
- A value representing the desired confidence level used in the sample size formula, such as 1.96 for 95% confidence.
- Estimated Proportion (p)
- An estimate of the segment of the population with the attribute of interest, often set to 0.5 if unknown.
- Margin of Error (e)
- The allowable difference between the sample proportion and the true population proportion, expressed as a decimal.
- Sample Size (n)
- The minimum number of observations needed to achieve the desired confidence and precision in a study.