Cronbach Alpha Calculator
Internal consistency from a respondent × item matrix: Cronbach's α, the item variances it is built from, and the drop-one table that tells you which question is pulling the scale apart.
Cronbach Alpha Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Raw alpha on complete matrices — no missing-data handling or imputation
- No factor analysis: α is consistency, not unidimensionality
In short: Eight respondents, three items (9,8,7 / 8,7,6 / 7,7,5 / 9,9,8 / 6,5,5 / 8,6,6 / 7,6,4 / 8,7,7): the item variances are 1.071429, 1.553571, 1.714286 (sum 4.339286) against a total-score variance of 11.410714. Cronbach's α = (3/2)×(1 − 4.339286/11.410714) = 0.929577 — by the conventional reading, excellent internal consistency. The drop-one table earns its keep: removing item 1 would sink α to 0.880734, item 2 to 0.901408, item 3 to 0.915129 — every item is pulling WITH the scale, item 1 hardest. α is a property of THESE answers, not of the questionnaire: the same items can read differently on a different sample.
Formula
α = (k/(k−1)) · (1 − Σᵥᵢ²/ᵥₜₒₜ²)
k is the item count, Σᵥᵢ² the sum of per-item variances, ᵥₜ the variance of the row totals. α approaches 1 when items covary strongly — respondents high on one item are high on the others. The drop-one table recomputes the whole coefficient without each item, which is the practical question every scale author actually asks.
Worked Example
- Enter one respondent per row, items separated by commas, respondents by semicolons.
- Every row must carry the same item count — the matrix has to be a rectangle.
- Read α with the convention named; then read the drop-one table, which is where scale editing happens.
- Remember the read is about THIS sample's answers, not about the questionnaire's soul.
Defaults: 8 × 3 matrix — α = 0.929577, item variances 1.071429/1.553571/1.714286, total variance 11.410714, drop-one αs 0.880734 / 0.901408 / 0.915129. Every deletion lowers α: the items support each other.
Strengths & Limits Of This Model
Where this engine is strong
- Drop-one table computed live for every item
- Rectangle violations refused with the row counts named
Where it stops
- No standardized alpha variant
- No item-total correlation column
Practical Use Cases
Psychometrics
questionnaire scale reliability
Product research
multi-item satisfaction indices
Education
test internal consistency
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Cronbach Alpha Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Is 0.929577 a “good” alpha?
By the conventional bands — 0.9 excellent, 0.8 good, 0.7 acceptable — yes, and the verdict card names those bands as conventions, not laws. The number is a property of this sample's answers: the same items re-run on a broader sample can move bands, which is why the page prints the parts beside the verdict.
What does “alpha if item deleted” tell me?
It recomputes α WITHOUT each item. A deletion that would RAISE α marks an item pulling against the scale — misworded, reversed, or measuring something else. In the defaults every deletion LOWERS α (0.880734, 0.901408, 0.915129 against 0.929577), which is the signature of items supporting each other. The table is where scale editing actually happens.
Does a high alpha prove the items measure one thing?
No — this is the classic misread. α rises with inter-item CORRELATION, but a set of items can correlate because they share a method, a mood, or a single dominant facet riding on top of several constructs. α is evidence of consistency, never proof of unidimensionality; the factor-analysis question is a different instrument entirely.
Can alpha be too high?
Yes — above roughly 0.95 the items are often redundant, near-duplicates wearing different words, and the scale is wasting respondents' time re-measuring the same facet. The goal is a consistent scale with independent information in each item, not a maximum coefficient at any cost.
Why does the matrix have to be a rectangle?
The coefficient is built from per-item variances and row-total variances; a ragged row has no defined item positions, and the arithmetic would silently misalign. The page refuses with the counts named rather than guess which respondent skipped which question — that repair belongs to the analyst, not to a silent default.
Does alpha depend on the number of items?
It does, mechanically: the k/(k−1) factor grows with k, so longer scales read higher with the same average correlation. Comparing alphas across scales of different lengths without noting that is a small dishonesty with a formula attached — compare average inter-item correlation when lengths differ.
What if a respondent gives identical answers to everything?
They contribute zero variance to the items but may still shape the row-total variance, so the coefficient absorbs them honestly. The page refuses only when EVERY row is identical — no variance anywhere means α is 0/0, and printing a number there would be decoration.
Why no standardized alpha here?
Raw alpha uses the items' own variances; the standardized form averages correlations instead and answers a slightly different question when items live on different scales. If your items are already on a shared 1–7 style range, the two land close — the raw form with its drop-one table is the version scale authors actually edit against, so that is what this page ships.