Sample Size Calculator
Calculate the required sample size for survey polls or quantitative research, or solve for the margin of error of an existing sample.
* 50% is standard default providing the most conservative (maximum) sample size.
385 participants
1.95996
Not Required ❌
Margin of Error Sensitivity Ledger (95% Confidence)
| Sample Size (n) | Margin of Error (E) | Audit Status |
|---|---|---|
| 100 | ±9.7998% | Alternative Projection |
| 250 | ±6.1979% | Alternative Projection |
| 385 | ±4.9944% | ★ Solver Selection |
| 500 | ±4.3826% | Alternative Projection |
| 1000 | ±3.099% | Alternative Projection |
Statistical Audit Workings
The Importance of Sample Size in Statistics
In research and surveying, it is rarely possible to collect data from every member of a target population. Instead, we select a representative subset—a sample. The size of this sample determines the precision of our estimates.
Confidence Levels and Margin of Error
The accuracy of a survey is defined by two key metrics:
- Confidence Level: The probability that the sample results reflect the true population parameters. A 95% confidence level means that if the survey were repeated 100 times, the results would fall within the margin of error in 95 cases. This is mapped to a critical Z-score (1.96 for 95%).
- Margin of Error (MOE): The maximum expected difference between the true population parameter and the sample estimate (e.g. plus or minus 5%).
Finite Population Correction (FPC)
When sampling from a relatively small, known population (such as a company with 500 employees), the sample size represents a significant percentage of the total. In these cases, the Finite Population Correction (FPC) formula reduces the required sample size, since each survey response contains a larger share of the total population data.
Frequently Asked Questions About Sample Size
Why is 50% used as the default expected proportion in surveys?
Using a 50% expected proportion (p = 0.50) yields the maximum possible variance since p * (1 - p) reaches its maximum value of 0.25 at this point. This provides the most conservative (largest) required sample size. If the actual proportion is higher or lower, a smaller sample size would actually achieve the same margin of error.
When should I use the Finite Population Correction (FPC)?
You should use the Finite Population Correction when your sample size represents more than 5% of your total population size (n/N > 0.05). The correction adjusts the variance down because sampling a large portion of a finite population increases precision.
How does the margin of error affect the required sample size?
The sample size is inversely proportional to the square of the margin of error. This means that if you want to cut the margin of error in half (e.g., from 10% to 5%), you must increase your sample size by four times to maintain the same level of confidence.
Does this include finite population correction?
Yes. Calculate required sample size with margin of error and FPC for accurate research design.