Factor Analysis Calculator

Run an Exploratory Factor Analysis (EFA) on your correlation data to identify latent factors from a set of observed variables. Enter your number of variables, sample size, number of factors, and paste your correlation matrix values — then get back factor loadings, eigenvalues, and variance explained for each factor. Useful for reducing dimensionality and uncovering hidden structure in survey, psychological, or multivariate datasets. Also try the Bootstrap Calculator.

How many observed variables are in your dataset (2–10).

Number of latent factors to extract. Must be less than the number of variables.

Total number of observations in your dataset.

Varimax is the most common orthogonal rotation for EFA.

Pearson correlation between Variable 1 and Variable 2.

Pearson correlation between Variable 1 and Variable 3.

Pearson correlation between Variable 1 and Variable 4.

Pearson correlation between Variable 2 and Variable 3.

Pearson correlation between Variable 2 and Variable 4.

Pearson correlation between Variable 3 and Variable 4.

Results

Factor 1 Eigenvalue

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Factor 2 Eigenvalue

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Variance Explained — Factor 1

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Variance Explained — Factor 2

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Cumulative Variance Explained

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KMO Sampling Adequacy (Approx.)

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Results Table

Frequently Asked Questions

What is Exploratory Factor Analysis (EFA)?

EFA is a statistical technique used to uncover underlying latent factors that explain the pattern of correlations among a set of observed variables. Unlike Confirmatory Factor Analysis, EFA does not require you to specify the factor structure in advance — it lets the data reveal the structure. It is widely used in psychology, social sciences, and market research. See also our find P-Value with Log-Rank Test Calculator.

What is an eigenvalue in factor analysis?

An eigenvalue represents the total variance in all observed variables that is accounted for by a given factor. A commonly used rule of thumb (Kaiser criterion) is to retain only factors with eigenvalues greater than 1.0, since such a factor accounts for at least as much variance as a single observed variable.

What does variance explained mean?

Variance explained (or proportion of variance) tells you what percentage of the total variability across all observed variables is captured by each extracted factor. Higher percentages indicate a more important or informative factor. Cumulative variance shows how much total variance is explained by all retained factors together.

What is the difference between Varimax and Oblimin rotation?

Varimax is an orthogonal rotation that assumes the extracted factors are uncorrelated with each other, simplifying the loading pattern by making each variable load highly on one factor and near-zero on others. Oblimin is an oblique rotation that allows factors to correlate, which may be more realistic when the underlying constructs are related conceptually. You might also find our calculate Structural Equation Modeling Required Minimum Sample Size useful.

What is a factor loading?

A factor loading is the correlation between an observed variable and a latent factor. Loadings range from −1 to +1. A loading above 0.40 (or 0.30 in some conventions) is considered meaningful. High loadings indicate that a variable is a strong indicator of the corresponding factor.

What is communality (h²) in factor analysis?

Communality is the proportion of variance in a given observed variable that is explained by all the retained factors combined. It ranges from 0 to 1, where values close to 1 mean the variable is well-represented by the factor solution and low values suggest the variable may not fit the model well.

What is the KMO (Kaiser-Meyer-Olkin) measure?

The KMO statistic assesses whether your correlation matrix is suitable for factor analysis by measuring sampling adequacy. Values above 0.80 are considered 'meritorious', above 0.70 are 'middling', and below 0.50 are considered unacceptable. A high KMO indicates that patterns of correlations are relatively compact and factor analysis should yield reliable factors.

How many factors should I extract?

Several criteria exist: the Kaiser criterion (eigenvalue > 1), the scree plot elbow point, and the parallel analysis method (most rigorous). As a practical rule, extracted factors should be interpretable and the cumulative variance explained should reach at least 50–60% for social science data. Start with the Kaiser criterion and verify with a scree plot.