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Cronbach's Alpha Calculator
Cronbach's alpha asks a simple question: do the items on your questionnaire hang together well enough to be summed into one score? Paste your responses below, one row per respondent and one column per item, and read the alpha, its 95% confidence interval, a per-item breakdown showing which items help or hurt, and a flag for any reverse-worded item. Everything is checked against R's psych::alpha(), and stays in your browser.
I want to measure my scale's internal consistency
α = -
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How these numbers are computed
1 - (1 - alpha) * qf(p, n-1, (n-1)(k-1)) at each tail. It uses an F distribution, so small samples give wide intervals. Standardized alpha replaces the covariances with correlations, the value you would get after z-scoring every item.
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How to read Cronbach's alpha
Alpha summarises how consistently a set of items measures the same thing. Read the point estimate, its interval and the item table together, not the headline number alone.
0.9 and up is excellent, 0.8 to 0.9 good, 0.7 to 0.8 acceptable, 0.6 to 0.7 questionable, and below 0.6 poor. Aim for 0.7 or more for a research scale, and treat a value above 0.95 as a hint of redundant items rather than a badge of quality.
Alpha is estimated from a sample. The 95% Feldt interval shows how much it could move in another sample of the same size. A wide interval, common with small samples, means the point estimate is less certain than it looks.
Each item's corrected item-total correlation and alpha-if-dropped tell you which items pull their weight. A negative item-total correlation almost always means a reverse-worded item you need to recode before scoring.
What each number means
| Statistic | What it tells you | In R |
|---|---|---|
| Raw alpha | Internal consistency from the covariance matrix; report this when items share a response scale. | alpha(x)$total$raw_alpha |
| Standardized alpha | Alpha from the correlation matrix, as if every item were z-scored first. | $total$std.alpha |
| 95% CI (Feldt) | Plausible range for the population reliability, from an F distribution. | alpha.ci(a, n, k) |
| Average interitem r | Mean correlation between item pairs; roughly 0.15 to 0.50 is healthy for a broad scale. | $total$average_r |
| G6 (lambda 6) | Guttman's lambda 6, an alternative reliability estimate based on squared multiple correlations. | $total$"G6(smc)" |
| Item-total r | Corrected correlation of each item with the sum of the rest; negative flags a reverse item. | $item.stats$r.drop |
| Alpha if dropped | Alpha with one item removed; a rise means the item is hurting the scale. | $alpha.drop$raw_alpha |
| Spearman-Brown | Predicts reliability if you lengthen or shorten the test by a factor. | (m*a)/(1+(m-1)*a) |
The calculator reports every row of this table for your data. Raw and standardized alpha coincide when all items have similar variance and diverge when they do not.
Frequently asked questions
What is a good Cronbach's alpha value?
A common rule of thumb: 0.9 and above is excellent, 0.8 to 0.9 is good, 0.7 to 0.8 is acceptable, 0.6 to 0.7 is questionable, 0.5 to 0.6 is poor and below 0.5 is unacceptable. Most published scales aim for at least 0.7. Very high values, above about 0.95, can signal that items are near-duplicates, so treat a very high alpha as a prompt to check for redundancy rather than a mark of quality.
Does a high alpha mean my scale is unidimensional?
No. Alpha measures internal consistency, not dimensionality. It rises as you add items and as items become more redundant, so a multidimensional scale with many items can still return a high alpha. Alpha also assumes tau-equivalence, that every item measures the same latent trait with equal weight. To confirm your items measure one thing, run an exploratory or confirmatory factor analysis, and use alpha to describe consistency once dimensionality is established.
Raw alpha or standardized alpha, which do I report?
Raw alpha comes from the covariance matrix and reflects items on their original scales, so report it when your items share a common response format, the usual case for a Likert questionnaire. Standardized alpha comes from the correlation matrix and suits items on different scales or a scoring plan that standardizes items first. When item variances are similar the two barely differ; this calculator shows both so you can see whether they agree.
How do I handle reverse-worded items?
A reverse-worded item correlates negatively with the rest of the scale, dragging alpha down and showing up as a negative corrected item-total correlation. Recode it before scoring: on a 1 to 5 scale, replace each response x with 6 minus x. This calculator flags items with a negative item-total correlation and offers a one-click reverse that recodes the item against the scale maximum and recomputes alpha instantly. A cluster of negative correlations, rather than a single one, may instead mean the scale is not measuring a single construct.
How should I handle missing responses?
Listwise deletion drops any respondent who skipped even one item and computes alpha on the fully complete rows; it is the default here and matches psych with use = complete.obs. Pairwise deletion uses every available pair for each covariance, keeping more data but risking an internally inconsistent correlation matrix. Use listwise when missingness is light and random, and consider pairwise or a proper imputation when listwise would discard a large share of the sample.
Does this match R's psych::alpha()?
Yes. Raw and standardized alpha, Guttman's lambda 6, the average interitem correlation, the per-item statistics, alpha-if-dropped and the Feldt confidence interval are each verified against psych::alpha() across more than twenty matrices, including reverse-coded items, missing data under both deletion rules, near-constant and constant items, two-item scales and scales with more items than respondents, agreeing to at least seven significant figures.
Does a high Cronbach's alpha mean my scale is unidimensional?
No. Alpha measures internal consistency, not dimensionality. It rises as you add items and as items become more redundant, so a multidimensional scale with many items can still return a high alpha. Alpha also assumes tau-equivalence, that every item measures the same latent trait with equal weight. To confirm your items measure one thing, run an exploratory or confirmatory factor analysis; use alpha to describe consistency once dimensionality is established.
How is the raw alpha different from the standardized alpha?
Raw alpha is computed from the covariance matrix and reflects the items on their original scales, so it is the value to report when items share a common response format. Standardized alpha is computed from the correlation matrix, which is what you get after z-scoring every item, and is appropriate when items are on different scales or when you plan to standardize before scoring. When all items have similar variances the two are close. This calculator shows both.
What does the 95% confidence interval for alpha mean?
Alpha is a sample estimate, so it comes with sampling error. The interval shown here is the Feldt confidence interval, which uses an F distribution with degrees of freedom based on the number of respondents and items. A 95% interval means that, across repeated samples, an interval built this way would contain the true reliability about 95% of the time. Narrow intervals come from large samples; small samples can produce surprisingly wide intervals even when the point estimate looks reassuring.