Cronbach’s Alpha: Formula, Interpretation and a Worked Example
Reviewed by Prof. Dr. Alexander Holtermann · Updated 16 October 2026 · 6 min read
Cronbach’s alpha measures the internal consistency of a scale: how well its items measure the same construct. Values of .70 and above are acceptable.
Key takeaways
- Cronbach’s alpha (α) estimates the reliability of a sum or mean score from several items, based on how strongly the items covary.
- Formula:
α = k / (k − 1) · (1 − Σs²_item / s²_total), with k items, the item variances and the variance of the total score. - Common guidelines: ≥ .90 excellent, ≥ .80 good, ≥ .70 acceptable, below .70 questionable. Very high values (> .95) can signal redundant items.
- Alpha rises with the number of items and the average inter-item correlation, so a high alpha does not prove that a scale is unidimensional.
- Before computing alpha, reverse-code negatively worded items. An uncoded reverse item can push alpha close to zero.
What does Cronbach’s alpha measure?
Questionnaires usually measure a construct such as exam anxiety or motivation with several items rather than one, because single items are unreliable. The items are then combined into a scale score. Cronbach’s alpha (Cronbach, 1951) estimates how reliable this score is in the sense of internal consistency: do the items hang together and measure the same thing?
Technically, alpha estimates the proportion of variance in the scale score that is “true” variance rather than measurement error, under the assumption that all items measure the same construct equally well (tau-equivalence). If that assumption is violated, alpha tends to underestimate reliability. Alternatives such as McDonald’s omega relax it, but alpha remains the most widely reported coefficient in student theses and many journals.
Formula and worked example
Six students answer four exam-anxiety items on a scale from 1 (not at all) to 5 (very much).
α = k / (k − 1) · (1 − Σs²_item / s²_total)
| Student | Item 1 | Item 2 | Item 3 | Item 4 | Total |
|---|---|---|---|---|---|
| 1 | 4 | 4 | 5 | 3 | 16 |
| 2 | 3 | 2 | 3 | 3 | 11 |
| 3 | 5 | 5 | 4 | 5 | 19 |
| 4 | 2 | 3 | 2 | 2 | 9 |
| 5 | 4 | 4 | 5 | 4 | 17 |
| 6 | 3 | 3 | 2 | 3 | 11 |
| Variance | 1.10 | 1.10 | 1.90 | 1.07 | 16.17 |
Item analysis: alpha if item deleted
Two statistics help you find weak items. The corrected item-total correlation is the correlation of an item with the sum of the other items; values below about .30 suggest that the item does not fit. Alpha if item deleted shows what alpha would be without the item; if it is clearly higher than the overall alpha, the item lowers consistency.
| Item | Corrected item-total correlation | Alpha if item deleted |
|---|---|---|
| Item 1 | .95 | .83 |
| Item 2 | .79 | .88 |
| Item 3 | .69 | .93 |
| Item 4 | .80 | .88 |
Interpreting alpha
There is no official cutoff, but these guidelines are widely used. For research comparing groups, .70 is usually acceptable; for decisions about individuals (diagnosis, admissions), .90 or more is expected.
- Alpha depends on the number of items: with an average inter-item correlation of .30, 5 items give α = .68, 10 items .81, 20 items .90.
- Short scales (2 or 3 items) often have low alphas even if they are good; report the mean inter-item correlation (ideal range about .15 to .50) as well.
- Alpha describes your sample, not the questionnaire in general. Always compute it for your own data, even for established scales.
| Alpha | Common interpretation |
|---|---|
| ≥ .90 | excellent (above .95: check for redundant items) |
| .80 to .89 | good |
| .70 to .79 | acceptable |
| .60 to .69 | questionable |
| < .60 | poor; the scale score should not be used without changes |
Reverse-coded items and other pitfalls
Many scales mix positively and negatively worded items (“I feel calm before exams”). These must be reverse-coded before computing alpha: on a 1 to 5 scale, new value = 6 − old value.
- Multidimensional scales: compute alpha separately for each subscale, not for the whole questionnaire.
- Alpha is not validity: a scale can be highly consistent and still measure the wrong construct.
- Alpha is not unidimensionality: with many items, alpha can be high even if there are two distinct factors. Use factor analysis to check structure.
- Single items: alpha cannot be computed for one item; for two items, report the correlation or the Spearman-Brown coefficient.
Other types of reliability
Internal consistency is one of several aspects of reliability. Which one you need depends on your measurement.
| Type | Question | Coefficient |
|---|---|---|
| Internal consistency | Do the items of a scale measure the same thing? | Cronbach’s α, McDonald’s ω |
| Test-retest reliability | Are scores stable over time? | Correlation or ICC between two time points |
| Split-half reliability | Do two halves of the test agree? | Spearman-Brown corrected correlation |
| Inter-rater reliability | Do different coders or raters agree? | Cohen’s kappa, ICC, Krippendorff’s alpha |
How to report Cronbach’s alpha
Report alpha in the methods section where you describe each scale, with two decimals and no leading zero. Mention the number of items and, if you removed or recoded items, say so.
Doing this in SPSS, R, JASP or jamovi
Reverse-code negatively worded items before you run the analysis in any program. All programs give the same alpha for the same items.
| Program | How to run it |
|---|---|
| SPSS | Analyze → Scale → Reliability Analysis; Model: Alpha; Statistics: Scale if item deleted |
| R | psych::alpha(df[, c("item1", "item2", "item3")]) |
| JASP | Reliability module: choose Cronbach’s α (and McDonald’s ω) and item statistics |
| jamovi | Factor → Reliability Analysis |
Frequently asked questions
What is a good Cronbach’s alpha?
For research purposes, .70 or higher is usually considered acceptable, .80 good and .90 excellent. Values above .95 may indicate that some items are almost identical.
What do I do if my Cronbach’s alpha is low?
First check whether reverse-coded items were recoded. Then look at corrected item-total correlations and alpha if item deleted. Consider whether the scale is multidimensional and should be split into subscales.
Can Cronbach’s alpha be negative?
Yes, if items correlate negatively on average, which almost always means that reverse-coded items were not recoded or the data contain errors.
How many items do I need for Cronbach’s alpha?
At least two, but alpha becomes more meaningful with three or more. Because alpha increases with the number of items, short scales naturally have lower values.
Is Cronbach’s alpha the same as validity?
No. Alpha measures reliability (consistency). Validity asks whether the scale measures what it is supposed to measure and needs other evidence.
Sources and further reading
- Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297–334.
- Howell, D. C. (2013). Statistical Methods for Psychology (8th ed.). Wadsworth Cengage Learning.
Your university’s examination regulations and style guide always take precedence.
Related articles
- Reliability and validityReliability means a measure gives consistent results; validity means it measures what it is meant to. A measure can be reliable without being valid.
- Likert scaleA Likert scale measures attitudes with several agreement items, usually rated from 1 (strongly disagree) to 5 or 7 (strongly agree), combined into one score.
- Questionnaire designA good questionnaire starts from your research question, uses validated scales, neutral wording and a logical order, and is pilot tested before launch.
- Inter-rater reliabilityInter-rater reliability shows how consistently two or more coders apply the same codes. Cohen’s kappa corrects for chance; κ above 0.60 is usually acceptable.
- Levels of measurementVariables are nominal, ordinal, interval or ratio. The level decides which averages, charts and statistical tests you are allowed to use.
- Statistics software comparedSPSS and Stata are menu- or command-based commercial packages, R and Python are free code, JASP and jamovi are free point-and-click. Choose by field and task.
