G-Power: Statistical Power Analysis Guide

G-Power (stylized as G*Power) is a free statistical power analysis program developed by researchers at Heinrich Heine University Düsseldorf. In quantitative research design, conducting a prospective power analysis ensures that a study has a sufficient sample size to detect a genuine experimental effect while minimizing unnecessary participant burden and institutional cost. For broader planning frameworks, researchers can consult our overview of sample size for a quantitative study.

Search engines frequently encounter “G-Power” in two entirely separate contexts: academic statistical software and automotive tuning. In scientific research, G-Power refers strictly to the standalone statistical calculator developed by Franz Faul and colleagues, used across the biomedical, behavioral, and social sciences to compute sample sizes, statistical power (1 − β), and critical test boundaries.

What it is used for in research

Statistical power represents the probability that a statistical test will correctly reject a false null hypothesis (1 − β), where β is the probability of committing a Type II error (a false negative). Calculating power before data collection prevents underpowered studies that fail to detect real effects and overpowered studies that waste resources detecting trivial differences. G*Power addresses five distinct statistical test families:

Exact tests: Computes power and sample size for exact binomial tests, Fisher’s exact test for 2 × 2 contingency tables, McNemar tests for paired proportions, and sign tests.
F tests: Covers univariate and multivariate analysis of variance (ANOVA), repeated-measures ANOVA, analysis of covariance (ANCOVA), multiple linear regression (both omnibus tests and R² increase tests), and tests of variance equality.
t tests: Handles two-sample independent means tests, paired-samples means tests, one-sample t-tests against a constant, point-biserial correlations, and linear regression slopes.
χ2 tests: Calculates goodness-of-fit tests, multi-cell contingency table independence tests, and single-sample variance tests.
z tests: Includes logistic regression, Poisson regression, comparisons between independent or dependent correlation coefficients, and generic large-sample normal tests.

Across these test families, G*Power structures evaluations into five operational analysis types, as defined in the official manual (Faul et al., 2023):

A priori analysis: Computes the required total sample size N given the desired significance level (α), target power (1 − β), and the expected population effect size. This is the gold standard for grant proposals, institutional review board (IRB) protocols, and pre-registered study plans. When defining research boundaries, investigators must align this calculation with their designated unit of analysis.
Compromise analysis: Calculates both α and 1 − β simultaneously given a fixed available sample size N, an expected effect size, and a chosen error probability ratio (q = β/α). This mode is used when participant recruitment is constrained by rare clinical populations or budget ceilings.
Criterion analysis: Computes α and the corresponding critical decision cutoff given 1 − β, effect size, and sample size N.
Post hoc analysis: Computes the achieved statistical power (1 − β) after study completion, given the observed α, sample size N, and sample effect size. (Note: Post hoc observed power based directly on observed p-values provides limited diagnostic utility compared to prospective planning).
Sensitivity analysis: Computes the minimum detectable effect size a study can reliably identify, given α, power (1 − β), and available sample size N. For a detailed methodological breakdown, review our guide to sensitivity power analysis.

Install or access (official source only)

G*Power is distributed exclusively through the Department of Psychology at Heinrich Heine University Düsseldorf. Users should download installation archives only from the official university portal (https://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower) to avoid adware or modified bundles hosted on third-party aggregators.

Windows: Version 3.1.9.7 (released March 17, 2020; archive size approximately 20 MB). Compatible with Windows XP, Vista, 7, 8, 10, and 11. Download the ZIP file and extract all contents to a local directory. Launch the program by double-clicking GPowerNT.exe. If an error appears regarding missing runtime components, execute VC_redist.x86.exe (packaged inside the archive) to install the necessary Microsoft Visual C++ redistributable libraries.
macOS: Version 3.1.9.6 (released February 21, 2020; archive size approximately 2 MB). Supports macOS 10.7 through macOS 14. The application is compiled for Intel 64-bit architecture and executes transparently on Apple Silicon hardware via Rosetta 2. The authors report that G*Power 4, featuring a native Apple Silicon architecture, is in development.
Licensing and Security: G*Power is provided free of charge for all academic, institutional, and commercial researchers. Commercial resale or redistribution is prohibited under the author terms of use. The application executes locally on the user machine and does not establish network connections, transfer analytics, or require cloud authentication.

Step-by-step task

The following numbered procedure details how to execute an a priori power analysis to determine the required sample size for a two-group randomized experiment using an independent-samples t-test. This workflow illustrates the standard interface controls in G*Power 3.1:

Launch the software: Open GPowerNT.exe on Windows or G*Power from the macOS Applications folder.
Select the test family: Locate the Test family drop-down menu in the top center of the interface. Select t tests.
Choose the specific statistical test: Click the Statistical test drop-down menu and select Means: Difference between two independent means (two groups).
Set the analysis type: In the Type of power analysis menu, select A priori (compute required sample size - given α, power, and effect size).
Configure Input Parameters:
- Tail(s): Select Two for standard non-directional testing or One if a directional hypothesis is theoretically grounded.
- Effect size d: Enter Cohen’s d directly (for example, 0.50 for a medium effect size). If raw means and standard deviations from prior literature are available, click the Determine => button. In the sliding drawer that opens on the right, input Mean group 1, Mean group 2, and the pooled standard deviation, then click Calculate and transfer to main window.
- α err prob: Specify the significance threshold, typically set to 0.05.
- Power (1-β err prob): Enter the desired statistical power, commonly 0.80 or 0.95 for high-stakes confirmatory research.
- Allocation ratio N2/N1: Set to 1 for equal group sample sizes. If planning unequal sampling (e.g., 2:1 control to treatment ratio), enter 0.5 or 2.0 accordingly.
Run calculation: Click the Calculate button in the bottom right corner.
Examine power curves: Click X-Y plot for a range of values at the bottom of the window to generate visual curves plotting statistical power across varying sample sizes or effect size thresholds.
Log the run: Switch to the Protocol of power analyses tab to review, copy, or export the plain-text audit record of your inputs and outputs. For higher-order multi-group designs, see our guide to factorial designs. For regression modeling, refer to our walkthrough on Cohen’s f² effect size for regression.

Output and how to read it

When the calculation completes, G*Power populates the Output Parameters panel in the lower right and updates the graphical distribution window:

Noncentrality parameter δ: Quantifies the degree to which the distribution under the alternative hypothesis (H1) deviates from the null distribution (H0). For a two-sample t-test with N1 = N2 and equal variances, δ = d × √(N / 4).
Critical t: The critical t-statistic cutoff value. An empirical test statistic exceeding this threshold results in rejecting the null hypothesis at significance level α.
Df: The degrees of freedom for the test, calculated as (N1 + N2 − 2).
Sample size group 1 and Sample size group 2: The minimum number of observational units required in each experimental arm.
Total sample size: The aggregate sample size (N = N1 + N2) required across the complete experiment.
Actual power: The exact statistical power achieved by the computed sample size. Because real-world sample sizes must be whole numbers, G*Power always rounds non-integer participant estimates up to the nearest integer. Consequently, the actual power displayed will equal or slightly exceed the requested nominal power (e.g., 0.8074 rather than 0.8000).
Distribution Plot: The upper pane illustrates two overlapping probability curves: the central distribution under H0 and the noncentral distribution under H1. The shaded red region marks the Type I error area (α), and the shaded blue region marks the Type II error area (β). Right-clicking this plot allows researchers to copy or export high-resolution vector or raster images for manuscripts and grant submissions.

Troubleshooting

Application fails to launch on Windows: If double-clicking GPowerNT.exe returns an error regarding missing dynamic link libraries (such as msvcr100.dll), run VC_redist.x86.exe located directly inside the unzipped G*Power folder to install the required Microsoft Visual C++ runtime.
X-Y plot fails to reflect updated inputs: In Windows release 3.1.9.7, changing input parameters in the main window without pressing Calculate leaves the plot window with stale values. Always click Calculate in the main window before opening or redrawing the plot.
Options button missing on macOS: In macOS release 3.1.9.5 and later, selecting “Hide distributions & control” hides certain advanced option toggles. Re-enable the distribution pane to access test-specific options drawers.
Disabling calculation sound effects: G*Power plays an audio chime upon completing calculations. Users wishing to run the software silently can safely delete or move the .wav audio files located inside the application directory without affecting calculation functionality.
Discrepancies in sensitivity analysis for regression: In logistic and Poisson regression modules, power curves can exhibit non-monotonic behavior under extreme covariate distributions. If the “Actual power” field deviates from the requested value during sensitivity analysis, open the X-Y plot window to inspect the full curve across the parameter range.

Free alternatives

While G*Power remains the most popular standalone desktop application for power calculations in behavioral and biomedical research, several free and open-source alternatives support scriptable, reproducible workflows:

Software / Package	Interface	Primary Strengths	Scripting & Automation	Distribution
*GPower 3.1**	Standalone GUI (Windows, macOS)	5 test families, built-in effect size drawer, interactive central/noncentral plots, protocol logging	GUI only (no CLI or scripting API)	Heinrich Heine University Düsseldorf (Free)
R `pwr` package	R command line / scripts	Comprehensive Cohen (1988) power functions for t-tests, ANOVA, correlations, and proportions	Fully scriptable in R and Quarto/R Markdown workflows	CRAN Open Source (GPL-3)
Python `statsmodels`	Python library / Jupyter	Statistical power classes (`TTestIndPower`, `FTestAnovaPower`, `GofChisquarePower`)	Fully scriptable in Python data science and machine learning pipelines	Open Source (BSD 3-Clause)
WebPower	Web browser and R package	Advanced models including structural equation modeling (SEM), mediation, and multilevel designs	Web GUI and scriptable via `WebPower` R package	Free online tool / CRAN (GPL-2)
jamovi / JASP	Standalone GUI (Win, Mac, Linux)	Integrated `jpower` module with real-time dynamic power estimation alongside primary analyses	GUI-driven with R syntax generation mode	Open Source (GPL / AGPL)

FAQ

What is the meaning of G-Power?

In quantitative scientific research, G-Power (stylized as G*Power) denotes a specialized power analysis software developed by psychologists at Heinrich Heine University Düsseldorf. The “G” historically reflects general power calculations spanning multiple test distributions (exact, F, t, χ2, and z).

Is G-Power a software?

Yes. G*Power is a standalone desktop software application available for Windows and macOS, widely recognized in academic research for calculating necessary sample sizes and statistical power before conducting empirical studies.

What is G-Power BMW and how does it differ from G*Power?

G-POWER (G-POWER GmbH) is an independent German vehicle modification and aftermarket tuning manufacturer specialized in BMW high-performance conversions (such as tuned BMW M3 and M5 models). It shares a homonymous name but has no affiliation with the academic statistical software G*Power created in Düsseldorf.

How much does G-Power cost?

The academic research software G*Power is entirely free for all users, including university faculty, graduate students, and private industry researchers. Commercial resale of the software is prohibited. In contrast, the automotive brand G-Power sells commercial automotive engineering upgrades.

How do I cite G*Power in a scientific publication?

The software authors request citing Faul et al. (2007) for general test families, ANOVA, and t-tests, or Faul et al. (2009) for correlation and regression procedures, both published in the journal Behavior Research Methods.

Sources

Heinrich Heine University Düsseldorf, Department of Psychology. “G*Power: Statistical Power Analyses for Mac and Windows.” Official Software Portal. URL: https://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower (Read 2026-11-07).
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2023). “G*Power 3.1 manual.” Heinrich Heine University Düsseldorf. URL: https://www.psychologie.hhu.de/fileadmin/redaktion/Fakultaeten/Mathematisch-Naturwissenschaftliche_Fakultaet/Psychologie/AAP/gpower/GPowerManual.pdf (Read 2026-11-07).
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). “G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences.” Behavior Research Methods, 39(2), 175-191. URL: https://link.springer.com/article/10.3758/BF03193146 (Read 2026-11-07).
Faul, F., Erdfelder, E., Buchner, A., & Lang, A.-G. (2009). “Statistical power analyses using G*Power 3.1: Tests for correlation and regression analyses.” Behavior Research Methods, 41(4), 1149-1160. URL: https://link.springer.com/article/10.3758/BRM.41.4.1149 (Read 2026-11-07).

G-Power: Statistical Power Analysis and Sample Size Guide