Sample Size Calculator
Determine the ideal sample size for surveys and research studies. Adjust for population size, confidence level, and margin of error.
Sample Size
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Recommended Sample Size
264
1.645 (90% confidence) · 10,000 (medium population)
Formula & Calculation
Step 1: Infinite Population Formula
n₀ = Z² × p × (1-p) / E²
n₀ = 1.645² × 0.5 × 0.5 / 0.05²
n₀ = 271
Step 2: Finite Population Correction
n = n₀ / (1 + (n₀ − 1) / N)
n = 264
Sample Size by Margin of Error
| Margin | ±1% | ±2% | ±3% | ±4% | ±5% | ±10% |
|---|---|---|---|---|---|---|
| n | 4,036 | 1,447 | 700 | 406 | 264 | 68 |
The Formula
The sample size formula determines how many survey responses are needed for statistically significant results. Z is the Z-score for your confidence level (1.96 for 95%), p is the estimated proportion (0.5 is most conservative), E is the margin of error, and N is the population size. The finite population correction adjusts the sample size when the population is small.
Variable Definitions
Z-Score
1.645 for 90% confidence, 1.96 for 95%, 2.576 for 99%. Higher confidence levels require larger Z-scores and larger samples.
Proportion
Estimated response proportion. 0.5 = 50% (most conservative estimate, gives the largest sample size). If you know the approximate proportion, use it.
Margin of Error
The acceptable error range, e.g., 0.05 for ±5%. Smaller margins require larger sample sizes.
Population Size
Total size of the group being studied. For very large populations (>100,000), the infinite population formula dominates.
How to Use This Calculator
- 1
Enter your total population size (the group you want to study).
- 2
Select your desired confidence level (95% is the standard for most research).
- 3
Set your acceptable margin of error (5% is common for market research).
- 4
Review the recommended sample size and the margin comparison table showing how sample size changes with different margins.
- 5
Remember: the calculated number is the number of COMPLETED responses you need, not the number of surveys sent (account for non-response rates).
A sample is a subset of the population used to estimate population parameters
Understanding the Concept
Sample size determination is critical in market research, UX research, clinical trials, and opinion polling. A sample that is too small may fail to detect real effects (false negative), while one that is too large wastes time and money. The 95% confidence level is the industry standard — it means that if you repeated the survey 100 times, the results would fall within the margin of error 95 times out of 100. The formula uses p = 0.5 (maximum variability) by default, which gives the most conservative (largest) sample size estimate. If you have prior knowledge that the proportion is near 0.2 or 0.8, the required sample size would be smaller. The finite population correction (FPC) adjusts the sample size downward when the sample is a significant fraction of the population. For populations over 100,000, the FPC has minimal effect and the infinite population formula dominates. Remember that the calculated number is the number of completed responses needed — if you expect a 20% response rate, you need to invite five times as many participants.
Frequently Asked Questions
Sources & References
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