Cronbach's Alpha Calculator

Paste your item-by-respondent data to compute Cronbach's alpha, item variances, item-total correlations, and a quick interpretation.

Dataset

Rows = respondents, columns = items. Accepts comma, semicolon, tab, or space separation.

How to Use This Calculator

Paste rows of respondent scores into the textarea. Each column represents an item, so keep every row the same length. The calculator handles commas, semicolons, tabs, or spaces.

Click Calculate to refresh the results. The table updates with each item mean, variance, and item-total correlation.

Methodology

Cronbach's alpha compares the sum of the item variances to the variance of the total score. When items are consistent, the total score variance is higher, yielding a larger alpha.

  • The calculator requires at least 2 items and 3 respondents; otherwise the reliability estimate is undefined.
  • Item-total correlations are computed by correlating each item with the total score minus that item.
  • Variance and covariance use sample (n-1) denominators to maintain alignment with the original implementation.

Interpretation Guide

  • ≥ 0.90: excellent internal consistency.
  • 0.80 – 0.89: good.
  • 0.70 – 0.79: acceptable.
  • 0.60 – 0.69: questionable.
  • < 0.60: poor — consider revisiting the item set.

Quick Notes

  • Ensure all values are numeric (e.g., Likert-type responses between 1 and 5).
  • Cronbach's alpha may decrease if you add low-quality items.
  • For subscales, run the calculator on each subset of items separately.

Related Statistics Tools

About the author

Ugo Candido builds educational tools that make transparent financial and statistical models accessible.

Contact: info@calcdomain.com

Editorial policy

CalcDomain content is educational, reviewed for clarity, accuracy, and transparency. Inputs and assumptions remain visible so you can verify how results are produced.

Formulas

Cronbach's alpha: \(\alpha = \frac{k}{k-1}\left(1 - \frac{\sum_{i=1}^k \sigma_i^2}{\sigma_T^2}\right)\)

\(k\): number of items · \(\sigma_i^2\): variance of item i · \(\sigma_T^2\): variance of total scores across respondents.

Citations

NIST — Weights and measureshttps://www.nist.gov/pml/weights-and-measures

FTC — Consumer advicehttps://consumer.ftc.gov/

Changelog
  • 0.1.0-draft — 2026-01-19: Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the methodology.

Verified by Ugo Candido on 2026-01-19 · Version 0.1.0-draft

Verified ✓ Version 0.1.0-draft
Formulas
Citations
Changelog
Version 1.5.0