Sample Size Calculator

Free Sample Size Calculator by ResRef

Getting Sample Size Right

Sample size refers to the number of individuals, observations, or data points included in a study. Choosing the right sample size ensures your findings are statistically valid, representative of the population, and suitable for publication.

A study with too few participants risks producing unreliable results, while an unnecessarily large sample wastes time, money, and resources. Calculating sample size in advance helps researchers achieve the right balance between accuracy and efficiency.

Sample size should always be estimated at the design stage of your research—before collecting any data. Early planning ensures that your study is ethical, minimizes participant burden, and maximizes the quality of your outcomes.

Calculate your sample size

Confidence level Margin of error (e) — % Estimated proportion (p) Population size (N) — optional

Sample size

Uses n₀ = (z² · p · (1 − p)) / e² and n = n₀ / (1 + n₀ / N) when N is provided.

Definitions of Key Terms

Population size (N):

The total group you want to study (e.g., all patients in a hospital, all students in a university).

Margin of error (e):

The range within which the true population value is likely to fall. Smaller margins need larger samples.

Confidence level (z):

How sure you are that the sample represents the population (commonly 90%, 95%, 99%).

Estimated proportion (p):

The assumed percentage of the population with a certain characteristic (often 0.5 when unknown).

Key Insights for Sample Size Calculator

Guidelines / Best Practices

• A higher confidence level → larger sample.
• A smaller margin of error → larger sample.
• Use p = 0.5 when the true proportion is unknown (gives the maximum sample size).
• For very small populations, sample size may approach the population size itself.

Example Calculations

• Large city population (500,000, 95%, 5% margin): Sample size ≈ 384.
• Small company survey (300 employees, 80%, 10% margin): Sample size ≈ 37.

Most Popular Questions about Sample Size Calculator

What is a good sample size?

There is no single “one-size-fits-all” number. The right sample size depends on your study’s objectives, the variability in your population, and the level of precision you want. For many surveys, a sample of around 385 is considered adequate for large populations at 95% confidence and 5% margin of error.

Why use 95% confidence?

A 95% confidence level is the global research standard because it strikes a balance between statistical accuracy and practicality. It means that if you repeated the study many times, 95% of the time the results would reflect the true population values.

Do I always need the population size?

Not always. If your target population is very large or unknown, you can leave the population size blank. The formula will still provide a reliable estimate because sample size levels off at a certain point and does not keep increasing indefinitely.

What if my population is very small?

For small populations, the calculator applies a correction factor to avoid overestimating the needed sample. In some cases, your required sample may approach the full population itself (for example, in studies of small organizations, rare diseases, or niche groups).