Statistical Sample Size Calculator
Calculate the required sample size for surveys using Confidence Level and Margin of Error. Includes Z-score logic and population adjustments.
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Respondents needed
Impact of Error Margin on Sample Size
About
In market research and academic studies, surveying an entire population is rarely feasible. Researchers must select a subset - a sample - that accurately represents the whole. This calculator uses Cochran's Sample Size Formula to determine the minimum number of respondents needed to achieve statistical significance.
Key metrics include the Confidence Level (how sure you can be that the result is accurate) and the Margin of Error (the range of deviation). It helps budget for surveys by finding the "sweet spot" between precision and cost.
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sample size
margin of error
z-score
Formulas
The sample size n is calculated as:
n = Z2 ⋅ p1−pe2
Where:
- Z: Z-score (from Confidence Level)
- p: Population Proportion (usually 0.5)
- e: Margin of Error (decimal)
Reference Data
| Confidence Level | Z-Score | Typical Use Case |
|---|---|---|
| 80% | 1.28 | Preliminary market research |
| 90% | 1.645 | Political polling (Low budget) |
| 95% | 1.96 | Academic/Scientific Standard |
| 99% | 2.576 | Medical/Pharma Studies |
Frequently Asked Questions
A proportion of 50% yields the maximum possible sample size required, making it the most conservative estimate. If you have prior data suggesting a 90% vs 10% split, you can adjust this, but 50% is the standard safety margin.
For small populations, the formula adjusts using the Finite Population Correction (FPC). This reduces the required sample size because each person surveyed represents a larger chunk of the total group.