Sample Size Calculator — Free Online Calculator
Sample Size Calculator
A G*Power alternative — calculate the required sample size from effect size, alpha and power.
Parameters
Medium effect — the value most commonly used in social science research.
The result will appear here
Enter the parameters and click "Calculate".
Quick Guide
- Cohen's d: 0.2 small, 0.5 medium, 0.8 large effect
- Cohen's f: 0.1 small, 0.25 medium, 0.4 large (ANOVA)
- Pearson r: 0.1 small, 0.3 medium, 0.5 large (Correlation)
- α = 0.05: standard in the social sciences
- Power = 0.80: recommended by Cohen (1988)
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| Achieved Power | — |
| Effect Size | — |
Interpretation
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Reporting in APA Format
Methodology
What Is Power Analysis?
Statistical power (1−β) is the probability of detecting an effect that truly exists. Power analysis calculates the minimum sample size needed to reach the target level (usually 0.80). An insufficient sample leads to missing real effects (Type II error).
Academic Reference
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.
Faul, F. et al. (2007). G*Power 3: A flexible statistical power analysis program. Behavior Research Methods, 39(2), 175–191.
What Is Sample Size?
A sample size calculator determines how many participants a study needs to achieve the desired statistical power. Too small a sample misses real effects (low power); too large a sample wastes resources and can make small differences with no practical importance appear significant. The right sample size is both an ethical and a methodological necessity.
Use it at the research design stage, before you start collecting data. Most thesis examiners and journal reviewers ask for a sample size justification. You can plan for independent-samples t-tests, ANOVA, correlation or chi-square analyses.
Cohen's d effect size: 0.2 small, 0.5 medium, 0.8 large. f (ANOVA): 0.10 small, 0.25 medium, 0.40 large. r (correlation): 0.10 small, 0.30 medium, 0.50 large. Result: The calculated n is the minimum number of participants required per group; adding 10–20% is recommended to cover dropouts and refusals.
Frequently Asked Questions
I don't know the effect size — what should I enter?
Use the effect size reported by similar studies in the literature. If none is available, a medium effect (d = 0.5, f = 0.25) is an accepted, conservative starting point.
I can't reach the calculated sample size — what should I do?
You can target a larger effect size or lower the power to 0.70. State this limitation transparently in your methods section.
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