Cronbach's Alpha Calculator
Estimate the internal-consistency reliability of a scale.
How Cronbach's alpha works
Cronbach's alpha estimates the internal-consistency reliability of a multi-item scale — how well the items hang together as measures of the same underlying construct. Higher values indicate the items are more consistently measuring the same thing.
This calculator uses the standardized formula, built from the number of items and their average inter-item correlation — the version used when you have summary statistics rather than the full raw item-by-respondent data matrix.
As a standardized measure, it assumes item variances are roughly equal. If you have the raw response data and item variances differ substantially, a covariance-based alpha calculated directly from that data may differ slightly from this estimate.
The formula
α = k·r̄ ÷ (1 + (k−1)·r̄)
k is the number of items and r̄ is the average correlation between all pairs of items. More items at the same average correlation increase alpha — the same logic behind the Spearman-Brown prophecy formula.
Worked example
10 items, average inter-item correlation of 0.30
α = 10 × 0.30 ÷ (1 + 9 × 0.30) = 3.0 ÷ 3.7 ≈ 0.81 — generally considered good internal consistency.
Frequently asked questions
What alpha value is "good enough"?
0.70 is a commonly cited minimum for research use, 0.80+ is often described as good, and above 0.95 can indicate item redundancy rather than better measurement. Context and stakes matter more than a fixed threshold.
Can alpha be negative?
Yes, when the average inter-item correlation is negative — a strong signal that the items are not measuring a common construct, or that some items need to be reverse-scored before analysis.
How is this different from calculating alpha directly from raw data?
This standardized version needs only the item count and average correlation. A raw-data (covariance-based) calculation additionally accounts for unequal item variances, and can differ slightly as a result.
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