Cronbach's Alpha Calculator

Cronbach's alpha (α) summarizes how consistently the items of a scale measure the same thing. If a questionnaire has five statements about job satisfaction, a satisfied respondent should tend to score high on all five and a dissatisfied one low on all five. Alpha is high when the items rise and fall together across respondents and low when they do not. Lee Cronbach introduced it in 1951 (Psychometrika 16, 297–334) as a generalization of the Kuder–Richardson formula 20 for items scored right or wrong.

Two facts are worth knowing before you use it. Alpha describes the scores in your sample, not the questionnaire as such: the same questionnaire can give a different alpha in a different group. And it is a coefficient, not a test, so it has no p-value; how well it is known is shown by its confidence interval, which is wide when there are few respondents.

1. Put the scores in the box, one respondent per line and one item per column. Separate the values with commas, spaces or tabs: a block copied from Excel or Google Sheets works as it is. Use a point for decimals, not a comma.
2. Complete every line. All lines must have the same number of values. A missing answer is reported with its line number instead of being skipped or filled in; complete the line or remove that respondent.
3. If some items are worded in the opposite direction ("I often think about leaving" among statements about satisfaction), enter their numbers under Items to reverse-score, with the lowest and highest score the scale allows (1 and 5 on a 1–5 scale).
4. Choose the confidence level and press Calculate Cronbach's Alpha. Up to 2000 respondents and 60 items are accepted. Load example fills in the worked example below.

Here k is the number of items, s²ᵢ the sample variance of item i and s²ₜ the sample variance of the respondents' total scores (both with n − 1 in the denominator), r̄ the mean of the k(k − 1)/2 correlations between pairs of items, n the number of respondents, α̂ the alpha found in the sample and γ = 1 minus the confidence level. The same alpha is 1 − MSₑ/MSₛ, where MSₛ is the mean square between respondents and MSₑ the residual mean square of the two-way ANOVA of respondents by items; it is the consistency intraclass correlation of the mean of the k items, ICC(C,k). The F distribution calculator gives the F quantiles used for the interval.

Ten people rated five statements from 1 (strongly disagree) to 5 (strongly agree). Statements 1 to 4 are worded in the same direction; statement 5 is worded the other way. Load example fills in the data and reverses item 5.

1. Without reversing item 5 alpha is only 0.5914. Item 5 has a corrected item–total correlation of −0.7310: people who agree with statements 1 to 4 tend to disagree with statement 5. Without it alpha would be 0.8753.
2. Reverse item 5. Each score x becomes 1 + 5 − x = 6 − x, so its mean changes from 2.6 to 3.4.
3. Item variances. 1.1667, 1.1667, 1.6, 1.5667 and 0.7111, so Σ s²ᵢ = 6.2111.
4. Variance of the totals. The ten total scores have variance s²ₜ = 21.6556(it was 11.7889 before the reversal).
5. Alpha. α = 5/4 × (1 − 6.2111 / 21.6556) = 1.25 × 0.7132 = 0.8915.
6. Standardized alpha. The mean inter-item correlation is 0.6391 (from 0.3698 to 0.8133), so α_std = 5 × 0.6391 / (1 + 4 × 0.6391) = 0.8985.
7. Item by item. The corrected item–total correlations run from 0.6559 (item 4) to 0.9359 (item 1), and every alpha-if-deleted, from 0.8221 to 0.8896, is below 0.8915: no item is hurting the scale.
8. Interval. With 9 and 36 degrees of freedom, F(0.975) = 2.4922 and F(0.025) = 0.2838, so the 95% interval is 1 − 0.1085 × 2.4922 to 1 − 0.1085 × 0.2838, that is 0.7295 to 0.9692 when the unrounded numbers are used. With only ten respondents the plausible range for alpha is wide.

The most quoted rule of thumb is that of George and Mallery (2003):

A minimum of 0.7 is a widely used convention, usually credited to Nunnally (1978). These labels are conventions, not tests, and two things limit them. First, alpha grows with the number of items even when their quality stays the same, as the table shows for standardized alpha. Second, a very high alpha is not automatically better: Tavakol and Dennick (2011) note that reports of acceptable values range from 0.70 to 0.95, that a maximum of 0.90 has been recommended, and that a value above 0.90 may mean that some items are redundant, testing the same question in a different guise.

Items worded in the opposite direction must be reverse-scored before alpha is computed, otherwise they work against the other items and pull alpha down, sometimes below 0. On a scale from L to H an answer x becomes L + H − x: on a 1–5 scale 1 becomes 5, 2 becomes 4 and 3 stays 3. This calculator reverses only the items you list and reports them in the table, so nothing is changed without your knowing. The result for alpha does not depend on the constant L + H, only on the direction; the lowest and highest score are used to keep the reversed item on the original scale and to check that every score of that item lies on it.

The interval is the one of Feldt, Woodruff and Salih (1987), which pingouin reports and which R's psych package prints next to a second one. It rests on the fact that (1 − α)/(1 − α̂), for the true alpha α, follows an F distribution with n − 1 and (n − 1)(k − 1) degrees of freedom. It uses normal theory and only the mean of the covariances between the items, so with Likert-type answers it is an approximation. The psych documentation notes that its second interval, that of Duhachek and Iacobucci (2004), which also takes the variance of the covariances into account, matches the Feldt interval for large samples and differs from it for small ones, and it recommends bootstrapping if the interval matters. The example in the pingouin documentation (15 respondents, 10 items) gives alpha 0.5917 and a 95% interval of 0.195 to 0.84 (pingouin rounds to three decimals) here as it does there.

• Alpha does not show that a scale is unidimensional. Sijtsma (2009) explains why it is not evidence that the items measure the same thing, and a scale that mixes two constructs can still have a high alpha, especially with many items. Compute alpha for one construct at a time.
• Alpha is a lower bound to reliability, not reliability itself. It equals reliability only when the items are essentially tau-equivalent (Novick and Lewis, 1967), and Sijtsma (2009) stresses that in many cases it is a gross underestimate. The documentation of psych likewise says that alpha underestimates the reliability of a test and overestimates the first factor saturation, and points to omega for a fuller analysis.
• Reverse-score first. In the worked example the same data give 0.5914 and 0.8915 depending on that one step.
• Alpha treats the scores as numbers. It is built from variances and covariances, so it assumes that the steps between answers are about equally large.
• Deleting an item to raise alpha is a judgement, not a rule. An item can lower alpha and still cover a part of the topic that the others miss. Look at its wording first.
• An item that never varies has no correlation with anything. It is kept in the scale and flagged, and its alpha-if-deleted shows what removing it does; psych::alpha drops such items by default, with a warning.
• Missing answers are not filled in or dropped silently. psych and pingouin handle missing values pairwise by default, so their alpha can rest on different respondents for different pairs of items; here every line must be complete, and you decide which respondents to remove.
• Very high or very low k. With two items alpha is a function of one correlation (standardized alpha is then 2r/(1 + r)), and alpha if item deleted does not exist.

All of them use the definitions above, so on complete data they agree with this calculator; they differ in how they treat missing answers and items that never vary. For items scored 0 and 1, alpha is the Kuder–Richardson formula 20 (KR-20), provided the variance of the total scores in KR-20 uses the same divisor as p·q, namely n. With n − 1 there, as some textbooks write it, the number is slightly different.