Sample Size Calculator

1. Enter your population size (N): This is the total number of people in the group you want to study. For example: 1,000 students enrolled at a university, 500 employees at a company, or 3,200 registered teachers in a region. If your population is unknown or very large (e.g., all internet users), enter a large number like 1,000,000.

2. Choose your confidence level: This is how sure you want to be that your results represent the population. 95% is standard for most theses. Use 99% for medical or high-stakes research. 90% is acceptable for exploratory studies.

3. Set your margin of error: This is how much error you are willing to accept. 5% is standard. A smaller margin (e.g., 3%) requires a larger sample. A larger margin (e.g., 8%) allows a smaller sample but less precision.

4. Expected proportion (advanced): This is the estimated percentage of your population that has the characteristic you are studying. If you are unsure, leave it at 50%, which gives the most conservative (largest) sample size. If prior research suggests the proportion is around 20% or 80%, you can adjust it to get a smaller, more efficient sample.

5. Review all three results: The calculator shows Yamane, Cochran, and Krejcie & Morgan side-by-side so you can compare and choose the method your supervisor prefers.

6. Follow the recommendation: The calculator suggests which method to cite based on your parameters and field of study.

7. Add a non-response buffer: Always distribute 10-15% more questionnaires than your minimum sample size to account for incomplete or unreturned surveys.

Determining the correct sample size is one of the most important decisions in research design. A sample that is too small may fail to detect significant effects, while an unnecessarily large sample wastes resources and time.

The Three Methods

Yamane (1967) provides the simplest calculation for general research. It is widely used in academic institutions, particularly in Asia. However, it assumes a 95% confidence level and 50% variability, so it cannot be adjusted for other confidence levels.

Cochran (1977) is the most flexible and internationally recognized method. It allows you to adjust the confidence level, margin of error, and expected proportion. It also includes a finite population correction factor, making it accurate for both small and large populations.

Krejcie & Morgan (1970) is the most cited sample size reference in education, psychology, and social science research. At 95% confidence with 50% proportion, it gives the same result as Cochran, which serves as a useful cross-validation.

Why Do Large Populations Always Give ~400?

You may notice that for very large populations (50,000+), the sample size stabilizes around 380-400 regardless of population size. This is mathematically expected: as the population grows, the formula converges to a fixed value determined only by the confidence level and margin of error. At 95% confidence and 5% margin, Yamane converges to 400 and Cochran converges to 384. This is why many studies with large populations simply use approximately 400 respondents.

Important Notes

All three methods assume simple random sampling. If you are using stratified, cluster, or multistage sampling, consult your research methodology textbook for appropriate adjustments. The sample sizes calculated here represent the minimum required; always add a 10-15% buffer to account for non-response.