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FACTOR ANALYSIS CALCULATOR

Exploratory factor analysis (EFA) calculator with varimax rotation.

Find the factors behind your questionnaire items. Get KMO and Bartlett's test, eigenvalues with a scree plot, principal axis factor loadings with varimax rotation, communalities, variance explained and a write-up.

DATA

One row per respondent, one column per item

PRINCIPAL AXIS

Include a header row with item names. Remove respondents with missing answers first. Aim for at least 5–10 respondents per item.

METHOD

Exploratory factor analysis: KMO, extraction, rotation, and reporting

What is exploratory factor analysis?

Exploratory factor analysis (EFA) looks for a small number of underlying factors that explain the correlations between many questionnaire items. Items that load on the same factor are taken to measure the same construct. Researchers use it to check a new scale's structure before computing Cronbach's alpha for each factor.

Step 1: check the data are suitable

  • KMO (Kaiser-Meyer-Olkin) of .60 or more; .80 or more is good
  • Bartlett's test of sphericity significant (p < .05)
  • Item-level KMO above .50; consider dropping items below that
  • About 5–10 respondents per item, and ideally at least 100–200 in total

Step 2: extract and rotate

R − Ψ ≈ ΛΛᵀ (principal axis factoring, iterated communalities)

Principal axis factoring finds loadings Λ that reproduce the item correlations R after removing each item's unique variance Ψ. Varimax rotation then simplifies the loadings so each item loads mainly on one factor, while keeping the factors uncorrelated.

Worked example: six questionnaire items

50 respondents answered six 5-point items (the sample data).

  1. KMO = .64 (mediocre but acceptable); Bartlett's χ²(15) = 63.18, p < .001.
  2. Two eigenvalues exceed 1 (2.19 and 1.65), so two factors are retained.
  3. After varimax rotation, Q1–Q3 load on factor 1 (.71 to .79) and Q4–Q5 on factor 2 (.55 to .91).
  4. Q6 loads only .37 on factor 2, below the .40 cut-off, so it is a candidate for removal.
  5. The two factors explain 49.4% of the variance.

How to report it (APA style)

“An exploratory factor analysis using principal axis factoring with varimax rotation was conducted on the six items (N = 50). The KMO measure was .64 and Bartlett's test was significant, χ²(15) = 63.18, p < .001. Two factors with eigenvalues above 1 were retained, explaining 49.4% of the variance.” Include the rotated loading table in your appendix or results.

References

  • Costello, A. B., & Osborne, J. (2005). Best practices in exploratory factor analysis. Practical Assessment, Research, and Evaluation, 10, Article 7.
  • Kaiser, H. F. (1974). An index of factorial simplicity. Psychometrika, 39(1), 31–36.
  • Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23(3), 187–200.
  • Bartlett, M. S. (1950). Tests of significance in factor analysis. British Journal of Statistical Psychology, 3(2), 77–85.

ABOUT THIS TOOL

Factor Analysis Calculator

Find the underlying factors in questionnaire items with KMO and Bartlett's test, eigenvalues and a scree plot, principal axis factoring, varimax rotation, communalities and a write-up.

  • Check the structure of a new questionnaire before reliability analysis
  • Decide how many dimensions a scale has
  • Find items that cross-load or load weakly

KEY FUNCTIONS

KMO overall and per itemBartlett's test of sphericityEigenvalues and scree plotPrincipal axis factoring with varimax rotationCommunalities and variance explained
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USE IN YOUR THESIS

Cite this calculator and export your results

APA 7 reference for software or an online tool. Cite the statistical method in your text as well.

SolveGrid. (2026). Factor Analysis Calculator [Online calculator]. https://solvegrid.online/factor-analysis-calculator

LEARN THE METHOD

Guides for this calculator workflow

GUIDELikert scale interpretation: weighted mean rangesBuild the 4-, 5-, and 7-point mean range tables, interpret weighted means, and report Likert results in a thesis.Read →GUIDEHow to choose a statistical testSeparate descriptive statistics, t-tests, correlation, and one-way ANOVA by the question and data type.Read →

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