Cronbach's Alpha Calculator

Cronbach's alpha estimates internal consistency — how closely a set of items measures the same underlying construct. It is the standard reliability coefficient reported for Likert-scale questionnaires in psychology, education, nursing, and management research. The calculator uses the original definition from Cronbach (1951).

Let k be the number of items (columns) and n the number of respondents (rows). For each item i, compute its variance σ²ᵢ across respondents. For each respondent, add their item scores into a total Tⱼ, then compute the variance of those totals, σ²ₜ. The coefficient is:

α = (k / (k − 1)) · (1 − Σσ²ᵢ / σ²ₜ)

Because both variances use the same divisor, the choice of the sample (n−1) or population (n) formula cancels in the ratio — alpha is the same either way, so the toggle only changes the variances shown for reference. Alpha rises when items covary strongly (a large total variance relative to the sum of item variances) and when the scale has more items.

For each item the tool also reports the corrected item-total correlation: the Pearson correlation between that item and the sum of the other k−1 items. Values below about 0.30 mark an item that does not fit the scale — often a poorly worded or reverse-coded question. The alpha-if-deleted column drops each item in turn and recomputes alpha on the rest; when a deleted value exceeds the overall alpha, removing that item would raise reliability, so it is flagged.

An optional standardized alphais derived from the mean of the pairwise inter-item correlations r̄ using α_std = (k·r̄)/(1 + (k−1)·r̄); it is preferred when items sit on different response ranges. Results are interpreted with the George & Mallery (2003) bands — α ≥ 0.9 Excellent down to below 0.5 Unacceptable. Alpha can be negative (typically a mis-keyed item) and, for a constant set of totals, is undefined; the tool reports both cases explicitly rather than showing a misleading zero.

• Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika 16(3): 297–334.
• Tavakol, M. & Dennick, R. (2011). Making sense of Cronbach's alpha. Int. J. Medical Education 2: 53–55.
• pingouin.cronbach_alpha — reference implementation cross-checked for the raw-alpha formula.
• George & Mallery (2003) interpretation bands — summary reference.

Formula and interpretation bands last cross-checked on 2026-07-12. Cronbach's alpha is a stable mathematical definition, so it does not expire; the page is reviewed if the cited references change.