Power Analysis Calculator
Calculate the statistical power of a hypothesis test or determine the required sample size to achieve a desired power level. Essential for study design, grant proposals, and ensuring experiments can detect meaningful effects.
This free online power analysis calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
Standardized effect size. Small = 0.2, Medium = 0.5, Large = 0.8.
Probability of Type I error (false positive). Commonly 0.05 or 0.01.
Number of participants per group in the study.
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Power Analysis Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Power Analysis Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Power Analysis Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Power Analysis Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
- •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
- •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
- •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.
About This Calculator
The Power Analysis Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the statistical power of a hypothesis test or determine the required sample size to achieve a desired power level. Essential for study design, grant proposals, and ensuring experiments can detect meaningful effects. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.
About Power Analysis Calculator
The power analysis calculator helps researchers design studies that are large enough to detect meaningful effects while being efficient with resources. Statistical power is the probability of correctly rejecting a false null hypothesis (1 minus the Type II error rate). An underpowered study wastes resources by being unable to detect real effects, while an overpowered study wastes resources by recruiting more participants than necessary. Power analysis involves four interconnected quantities: effect size, sample size, significance level (alpha), and power. Given any three, you can solve for the fourth. This calculator is essential for grant proposals, IRB submissions, clinical trial design, and any research planning where resources are limited.
The Math Behind It
Formula Reference
Sample Size for Two-Group Comparison
n = 2 * ((z_alpha + z_beta) / d)^2
Variables: z_alpha = critical Z for alpha; z_beta = critical Z for power; d = Cohen's d effect size; n = per-group sample size
Worked Examples
Example 1: Clinical trial sample size
A drug trial expects a medium effect (d = 0.5) and wants 80% power at alpha = 0.05.
You need approximately 63 participants per group (126 total) to detect a medium effect with 80% power.
Example 2: Small effect with 90% power
Detect a small effect (d = 0.2) with 90% power at alpha = 0.05.
You need 526 participants per group (1,052 total). Small effects require very large samples.
Common Mistakes & Tips
- !Performing power analysis after the study is complete (post-hoc power) -- this is circular and uninformative. Power analysis should be done during study planning.
- !Using an unrealistically large effect size to justify a small, convenient sample -- be honest about expected effect sizes based on prior research.
- !Forgetting to account for attrition, non-compliance, and missing data -- inflate the calculated sample size by 10-20% to account for these losses.
- !Confusing the sample size per group with the total sample size -- for two-group comparisons, you need n per group, so total N = 2n.
Related Concepts
Used in These Calculators
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Frequently Asked Questions
What is the minimum acceptable power for a study?
The conventional minimum is 80% power, meaning a 20% chance of missing a real effect. However, many journals and funding agencies now recommend 90% or higher. For confirmatory studies and clinical trials, 90% power is often required. The appropriate power level depends on the consequences of a Type II error in your specific context.
How do I estimate the effect size for my power analysis?
The best approach is to use effect sizes from prior research on the same or similar topics (meta-analyses are ideal). If no prior data exists, conduct a small pilot study. Cohen's benchmarks (0.2 small, 0.5 medium, 0.8 large) are a last resort and may not be appropriate for your specific field or outcome measure.
What is the difference between power and significance?
Significance level (alpha) is the probability of a false positive -- rejecting a true null hypothesis. Power (1-beta) is the probability of a true positive -- rejecting a false null hypothesis. They address different types of errors. Ideally, both alpha should be low and power should be high, but increasing power typically requires larger samples or accepting a higher alpha.