Cronbach's Alpha Calculator
Internal consistency from an item count, the sum of item variances, and total score variance.
What it does
Cronbach's alpha estimates how consistently a set of items measures the same thing. It compares the amount of variance contributed by the individual items with the variance of the total score.
The inputs are simple but easy to misunderstand: the number of items, the sum of the item variances, and the variance of the summed score. All three must come from the same sample and the same scoring rules.
The defaults describe five items whose variances add to 4.0 and a total score variance of 10. The multiplier is 1.25, the items account for 40.0% of the total variance, and alpha is 0.750, which is usually called acceptable.
Alpha is a lower bound under strict assumptions, not a complete reliability study. It can be high because items are redundant, and it can be low even when a scale has more than one useful factor. Report the sample, the item count, and any reverse coding with the coefficient.
How to use
- Enter the number of scored items in the scale.
- Compute the variance of each item and add those variances.
- Compute the variance of each person's total score.
- Enter the sum of item variances and the total score variance.
- Press Calculate to see alpha and the item variance share.
- Check that reverse-worded items were recoded before you took the variances.
Formula
- k
- Number of items in the scale.
- sum of item variances
- The variances of the individual item scores, added together.
- total score variance
- The variance of the summed score across respondents.
- alpha
- Estimated internal consistency, usually between 0 and 1.
Alpha can be negative when item variances are large relative to the total score variance, which often signals negatively covarying or reverse-coded items. A value above 1 is possible with this formula and points to a data or scoring problem rather than a better scale.
Worked example
Example: five items, item variances 4.0, total variance 10
Defaults: 5 items, sum of item variances 4.0, total score variance 10.
- Multiplier: k / (k - 1) = 5 / 4 = 1.250.
- Item share: 4.0 / 10 = 0.400, or 40.0 %.
- Inside the bracket: 1 - 0.400 = 0.600.
- Alpha: 1.250 x 0.600 = 0.750.
- The value falls in the Acceptable band for this simple guide.
- The total score variance is larger than the item variance sum, so the items covary in a useful direction.
Reference table
| Alpha | Common label |
|---|---|
| 0.90 or higher | Excellent |
| 0.80 to 0.89 | Good |
| 0.70 to 0.79 | Acceptable |
| 0.60 to 0.69 | Questionable |
| Below 0.60 | Poor |
| 0.750 | The example: acceptable |
Limits
- Assumes items are continuous and roughly tau-equivalent, with equal true-score loadings.
- Does not test whether the scale is unidimensional.
- Depends on the sample and can change across populations.
- A short scale can have a modest alpha even when its items are useful.
Common mistakes
- Treating alpha as proof of validity.
- Forgetting to reverse-code negatively worded items.
- Dropping items only to push alpha above 0.70.
- Computing alpha on a scale that mixes unrelated constructs.
- Reporting alpha without the sample size and scoring rules.
Try it yourself
Quick checks. Answers sit tucked under each question.
What is alpha for 10 items, a variance sum of 9, and total variance of 30?
The multiplier is 1.111, the item share is 30.0 %, and alpha is 0.778, in the Acceptable band.
What is alpha for 6 items, a variance sum of 8, and total variance of 20?
The multiplier is 1.200, the item share is 40.0 %, and alpha is 0.720.
What happens when the item variances sum to 12 but the total variance is only 10?
The item share is 120.0 % and alpha is -0.267. That pattern suggests negative covariance or a scoring error.
Questions
What does Cronbach's alpha measure?
It estimates the internal consistency of a set of items, meaning how closely related the items are as a group.
Is a higher alpha always better?
No. Very high alpha can mean items are redundant. A short, broad scale can be useful with a lower alpha.
Should alpha be above 0.70?
That is a common guide, not a law. The acceptable level depends on the stakes and the number of items.
Why did my alpha come out negative?
Item variances may be large relative to the total, often because some items are reverse-coded or measure a different direction.
Does alpha work for a single item?
No. Internal consistency needs at least two items, and this tool requires a whole number from 2 to 100.
Can I compare alpha across studies?
Only with care. Sample composition, item count, and scoring all affect the coefficient.
Sources
- Bland and Altman, statistics notes on Cronbach's alpha
- SOCR, University of Michigan, Cronbach's alpha