How this power calculator helps with sample size planning
If your study is too small, you risk missing a real effect. If your study is too large, you spend extra time and money for little gain. This power calculator helps you estimate the required sample size before collecting data, based on your expected effect size, significance level, and desired power.
The calculator is built for a two-group comparison using a standardized mean difference (Cohen's d). This is a common setup for experiments, A/B tests, and many clinical or behavioral studies.
What each input means
1) Effect size (Cohen's d)
Effect size represents how big you expect the difference between groups to be in standard deviation units. Larger effects require fewer participants; smaller effects require more.
- 0.2 → small effect
- 0.5 → medium effect
- 0.8 → large effect
2) Significance level (α)
Alpha is your false-positive risk threshold. A typical value is 0.05. Lower alpha (for example 0.01) increases required sample size.
3) Power (1 − β)
Power is the probability of detecting a true effect of the size you specified. Many researchers target 0.80 or 0.90.
4) One-sided vs two-sided test
Two-sided tests are standard in most research because they allow effects in either direction. One-sided tests can reduce sample size, but only when a directional hypothesis is justified in advance.
5) Allocation ratio and dropout
If group sizes are unequal, enter the ratio n2 / n1. You can also inflate your estimate to account for expected dropout or missing data.
Formula used in this calculator
This page uses a normal approximation for two independent groups with standardized effect size:
Where:
- d = Cohen's effect size
- r = allocation ratio n2/n1
- zα = critical value for α (two-sided uses α/2)
- zpower = normal quantile for the chosen power
Then n2 = r × n1, and both are rounded up to whole participants.
Worked example
Suppose you expect a medium effect (d = 0.5), want α = 0.05, and target 80% power with equal groups. You will generally need about 64 participants per group (about 128 total), before adjusting for dropout.
If you expect 15% attrition, planned enrollment should be increased so the final analyzable sample still meets the power target.
Practical tips for better planning
- Use realistic effect sizes: overestimating effect size leads to underpowered studies.
- Pre-register assumptions: document alpha, power, and analysis approach in advance.
- Account for real-world losses: missing data, noncompliance, and exclusions can reduce effective sample size.
- Consider design complexity: clustered, repeated-measures, or non-inferiority designs may need specialized formulas.
Limitations
This calculator provides a fast planning estimate and is ideal for early study design. For high-stakes projects, use software that matches your exact model (e.g., mixed effects, survival analysis, binary outcomes, or multiple comparisons adjustments).
Bottom line
A good sample size plan protects your conclusions. Use this tool to pick a defensible starting point, then refine with domain-specific assumptions and consultation when needed.