Cronbach's Alpha Calculator
Estimate a survey or test's internal-consistency reliability. Enter respondents × items, get per-item variances, total-score variance, α with a plain-language verdict, contribution diagram and show/hide step-by-step working.
| Item 1 | Item 2 | Item 3 | Item 4 | |
|---|---|---|---|---|
| R1 | ||||
| R2 | ||||
| R3 | ||||
| R4 | ||||
| R5 |
What is Cronbach's alpha?
Cronbach's alpha (α) is a reliability coefficient — it estimates how consistently a group of survey or test items measure the same underlying construct ("customer satisfaction", "extraversion", "algebra ability"). If everyone who agrees with item 1 also tends to agree with items 2, 3 and 4, the items are pulling in the same direction and alpha is high. If responses are scattered across items, alpha is low.
Formally, alpha compares the sum of individual item variances to the variance of the total score. When the items covary strongly, the total-score variance is much bigger than the sum of item variances, and α approaches 1.
Cronbach's alpha, piece by piece
Given — item variances
Alpha compares how much variance lives inside individual items to how much lives in the total score. Compute the sample variance (n − 1 denominator) of each column separately, then add them.
Substitute — total-score variance
Sum each respondent's item scores to get the total score, then take the sample variance of those totals. If items agree, respondents' totals spread out much more than any single column does — that's the whole intuition behind alpha.
Formula — k/(k−1) multiplier
The inner ratio 1 − Σσᵢ² / σ²ₜ is bounded above by 1 − 1/k, so the (k / (k − 1)) factor rescales it into the 0-to-1 range and prevents shorter scales from being unfairly penalised.
Answer — α and reliability band
Combine the three ingredients into α. Values between 0.70 and 0.90 are the usual sweet spot; below that suggests weak inter-item agreement, above 0.95 hints that items may be redundant rather than merely consistent.
How to raise a low alpha
- Recode reverse items. A single reverse-scored item left uncorrected can push alpha to zero or negative.
- Drop items with low corrected item-total correlation (rule of thumb: below 0.30). If an item isn't correlated with the total, it isn't measuring the same construct.
- Add more items measuring the same construct. Alpha rises with k — but only if the new items are relevant.
- Rewrite ambiguous or double-barrelled items. "I enjoy my job and my coworkers" mixes two things and drags alpha down.
Features of this calculator
- Editable data grid — rows are respondents, columns are items. Add/remove rows and columns as needed.
- Pre-filled with a plausible 5 × 4 Likert-style example so you can inspect a working answer immediately.
- Per-item means and sample variances (n − 1 in the denominator).
- Total-score variance and the sum of item variances — the two quantities inside the alpha formula.
- Cronbach's alpha with the substitution written out in full.
- Plain-language reliability verdict using the George & Mallery / Nunnally thresholds — with an explicit warning when α ≥ 0.95 (usually a sign of redundant items).
- Contribution diagram — each item's variance as a bar next to the total-score variance, so you can see at a glance which items contribute most spread.
- Show/hide step-by-step working with your own numbers substituted into every formula.
- Copy the summary as text or download the result panel as a PNG.
Frequently asked questions
+Can alpha be negative?
Yes, if the sum of item variances exceeds the total-score variance. This almost always signals a reverse-coded item that wasn't recoded. Fix the coding and recompute.
+Do I use sample or population variance?
Sample variance (n − 1 in the denominator) — that's the convention this calculator and standard software (SPSS, R's psych::alpha) use.
+How many respondents do I need?
The point estimate is defined for n ≥ 2, but confidence intervals stabilise around n = 100+. For scale-development studies, aim for at least 10 respondents per item where possible.
+Is 0.7 really the magic threshold?
It's a convention, not a law. Nunnally originally proposed 0.7 as adequate for early research and 0.8 for applied use. Some fields accept 0.6 for new scales; others insist on 0.9 for clinical decisions.
+Should I report standardised alpha?
Standardised alpha treats items as z-scored — it's what you'd get if every item had unit variance. Report both when items are on different scales; otherwise the raw formula (this page) is standard.
+Is alpha the same as split-half reliability?
No, but they're related. Alpha equals the average of every possible split-half correlation corrected by the Spearman-Brown formula. It's more stable than any one split.