Sample Size Calculator

Choosing the right sample size is one of the most important steps in any research project. Survey too few people and your results may be unreliable; survey too many and you waste time, money, and effort. The sample size calculator above gives you the minimum number of respondents you need for your chosen confidence level and margin of error — adjust any value and the result updates instantly.

What Is Sample Size?

Sample size is the number of responses or observations you collect from a larger population. Because studying an entire population is rarely practical, researchers measure a representative sample and use it to draw conclusions about the whole group. A well-chosen sample size keeps your study accurate while staying realistic to carry out. The larger and more representative your sample, the more confident you can be that your findings reflect the true population.

How to Use the Sample Size Calculator

The calculator has two modes. Use Proportion when your outcome is a percentage or a yes/no answer (for example, the share of people who prefer a product). Use Mean when you are measuring a continuous value such as age, income, or test scores. Then fill in the following:

• Confidence level – how sure you want to be that the true value falls within your margin of error. 95% is the standard choice in most research.
• Margin of error – the range of error you can accept around your result, written as a plus-or-minus value (for example, ±5%).
• Expected proportion or standard deviation – your best estimate of the result. For proportions, use 50% if you are unsure, because it produces the largest and safest sample. For means, enter the standard deviation from a previous study or pilot.
• Population size (optional) – the total number of people in the group you are studying. Leave it blank for very large or unknown populations; enter a number to apply the finite population correction.

Sample Size Formula

For estimating a proportion, the calculator uses Cochran’s formula:

n₀ = Z² × p(1 − p) / e²

Here Z is the z-score for your confidence level (1.96 for 95%), p is the expected proportion, and e is the margin of error. When you enter a finite population size (N), the result is adjusted with the finite population correction:

n = n₀ / (1 + (n₀ − 1) / N)

For estimating a mean, the calculator uses:

n = (Z × σ / e)²

where σ is the standard deviation and e is the margin of error in the units of your measurement.

Factors That Affect Sample Size

• Confidence level: A higher confidence level (such as 99% instead of 95%) requires a larger sample.
• Margin of error: A smaller margin of error means a larger sample. Cutting the margin of error in half roughly quadruples the sample needed.
• Variability: The more varied the responses (a proportion near 50%, or a large standard deviation), the larger the sample required.
• Population size: For small, finite populations the required sample is reduced. For large populations, sample size barely changes once the population passes a few tens of thousands.

Sample Size Reference Table

The table below shows the sample size needed at a 95% confidence level with an expected proportion of 50% (the most conservative case) for a large population. Create this as a Table block in WordPress:

Margin of error	Sample size
±10%	97
±5%	385
±3%	1,068
±2%	2,401
±1%	9,604

This is why so many professional surveys aim for around 385 respondents: it delivers a ±5% margin of error at 95% confidence.

Worked Example

Suppose you want to survey university students at a campus of 8,000 people, with 95% confidence and a ±5% margin of error. Using 50% as the expected proportion, the unadjusted sample is 385. Applying the finite population correction for N = 8,000 brings the required sample down to about 367 respondents. The calculator does this adjustment automatically when you enter the population size.

Common Mistakes to Avoid

• Forgetting to round up. Sample size is always rounded to the next whole person, never down.
• Using a margin of error that is too small for your resources, which can make a study impractical.
• Ignoring expected response rates. If you expect only half of invitees to respond, invite roughly twice your target sample.

Frequently Asked Questions

What is a good sample size for a survey?
For most general surveys, around 385 respondents gives a ±5% margin of error at 95% confidence, regardless of how large the population is. Smaller margins of error require larger samples.

How does the confidence level affect sample size?
A higher confidence level demands a larger sample. Moving from 95% to 99% confidence noticeably increases the number of respondents you need for the same margin of error.

Do I need to know my population size?
Not always. For large or unknown populations you can leave it blank. Entering a finite population size only reduces the required sample, which is helpful for smaller, well-defined groups.

Why is 50% used as the default expected proportion?
A proportion of 50% represents the highest possible variability, so it produces the largest sample size. Using it ensures your study is adequately powered even when you cannot estimate the true proportion in advance.

What sample size do I need for 95% confidence and a 5% margin of error?
For a large population, you need 385 respondents. For smaller populations the number is lower, and the calculator above adjusts it automatically.

Conclusion

A correct sample size is the foundation of credible research. Use the calculator above to plan your study, then refer to the formulas and table to understand and explain your numbers. Whether you are running a survey, an experiment, or a thesis project, getting the sample size right ensures your conclusions are both reliable and defensible.