Key Takeaways
- Sample size determines how many observations are needed for statistical significance
- Higher confidence levels require larger samples
- Smaller margins of error require larger samples
- For unknown proportions, use 50% for maximum sample size (conservative approach)
- Finite population correction reduces required sample when population is known and small
What Is Sample Size?
Sample size is the number of observations or respondents needed in a study to make statistically valid conclusions about a larger population. Proper sample size calculation is crucial for research validity - too small and your results may be unreliable, too large and you waste resources.
The sample size depends on several key factors: your desired confidence level, acceptable margin of error, expected population proportion, and total population size. Understanding these relationships helps you design effective surveys and research studies.
The Sample Size Formula
n = (Z2 * p * (1-p)) / E2
For finite populations where sample exceeds 5% of total population, apply the finite population correction:
nadj = n / (1 + ((n-1) / N))
How to Calculate Sample Size (Step-by-Step)
Determine Your Confidence Level
Choose how confident you want to be in your results. Common levels are 90% (Z=1.645), 95% (Z=1.96), or 99% (Z=2.576). Higher confidence means larger sample size.
Set Your Margin of Error
Decide how much error is acceptable. A 5% margin means results could be off by 5 percentage points. Smaller margins require larger samples.
Estimate Population Proportion
If you have prior data, use that proportion. If unknown, use 50% (0.5) which gives the maximum sample size and is the most conservative approach.
Apply the Formula
For 95% confidence, 5% margin, 50% proportion: n = (1.962 * 0.5 * 0.5) / 0.052 = 385 respondents
Adjust for Finite Population (if needed)
If your population is known and relatively small, apply the finite population correction to reduce the required sample size.
Z-Scores for Common Confidence Levels
| Confidence Level | Z-Score | Use Case |
|---|---|---|
| 80% | 1.282 | Exploratory research, quick polls |
| 85% | 1.440 | Preliminary studies |
| 90% | 1.645 | Market research, business decisions |
| 95% | 1.960 | Most common - scientific studies, surveys |
| 99% | 2.576 | Medical research, critical decisions |
How to Use This Calculator
Enter the required values in the input fields above and click "Calculate" to get your result. Use the "Reset" button to clear all fields and start over.
Understanding the Result
This calculator provides the minimum sample size needed to achieve your desired confidence level and margin of error. For surveys, plan to collect more responses than the calculated minimum to account for incomplete or invalid responses.
Frequently Asked Questions
When the true population proportion is unknown, 50% (p=0.5) produces the maximum variance (p*(1-p) = 0.25), requiring the largest sample size. This is the most conservative approach - if you use 50% and your actual proportion differs, you'll have more precision than required, but never less.
Confidence level tells you how often your interval would contain the true value if you repeated the study. Margin of error is the range around your estimate. For example, "95% confident the result is 45% plus or minus 5%" means in 95 out of 100 samples, the true value would be between 40-50%.
Use the finite population correction when your sample size exceeds 5% of the total population. For example, surveying 400 people from a population of 5,000 (8%) warrants correction. For large populations (over 20,000), the correction makes little practical difference.
Multiply your calculated sample size by an adjustment factor. If you expect a 60% response rate, divide your required sample by 0.6. For example, if you need 385 complete responses: 385 / 0.6 = 642 people to contact initially.
For most general surveys, 385 respondents provides 95% confidence with a 5% margin of error. National polls typically use 1,000-1,500 respondents. Subgroup analysis requires larger samples - if analyzing 5 subgroups, you may need 5x the base sample.