Cronbach’s alpha calculator
Internal consistency reliability for a Likert-type questionnaire.
Calculator inputs
Results
Enter your values and press “Calculate” to see the result.
In short
- What it calculates
- Internal consistency reliability for a Likert-type questionnaire.
- Formula used
α = (k / (k − 1)) × (1 − Σs²ᵢ / s²ₜ)- Example
- Matrix of 5 respondents and 4 items:
Cronbach’s alpha calculator
Cronbach's alpha is the figure every thesis panel asks for when an instrument is validated: it measures whether the items on a scale point in the same direction.
Paste the matrix with one row per respondent and one column per item.
How it works
The sum of the individual item variances is compared with the variance of the total score. If the items measure the same construct, the total variance is much larger than the sum of the individual ones and alpha rises.
Formula
α = (k / (k − 1)) × (1 − Σs²ᵢ / s²ₜ)
k = number of items
s²ᵢ = variance of each item
s²ₜ = variance of total scores
≥ 0.9 excellent · ≥ 0.8 good · ≥ 0.7 acceptable · ≥ 0.6 questionable
Worked example
Matrix of 5 respondents and 4 items:
4 5 4 5 / 3 3 4 3 / 5 5 5 4 / 2 3 2 3 / 4 4 5 4
α = 0.934 → excellent reliability
Explanation
A high alpha does not mean the scale is good
It only indicates that items behave similarly to one another. If they all ask nearly the same thing in different words, alpha will be very high and the scale redundant. Values above 0.95 usually signal exactly that, and it is worth checking for surplus questions rather than celebrating.
It depends on the number of items
Adding questions raises the coefficient even when they improve nothing. A forty-item mediocre scale can exceed 0.90 while an excellent six-item one sits at 0.70. The value should always be read alongside the number of questions and the structure of the scale.
Reversed items must be recoded first
If some questions are worded in the opposite direction to catch automatic responding, they must be inverted before calculating. Forgetting sinks alpha and sometimes turns it negative, an impossible result that almost always betrays this error.
Unidimensionality
Alpha assumes the scale measures one thing. If it actually measures two or three distinct dimensions, the coefficient can look reasonable while the instrument is poorly conceived. A factor analysis answers that question; alpha does not.
Frequently asked questions
Which alpha value is acceptable?
From 0.7 upwards is considered acceptable for research; decisions about individuals require 0.8 or higher.
Should I reverse negative items first?
Yes. Reverse-worded items must be recoded before computing alpha, otherwise the result comes out artificially low.
Does it work for yes/no items?
For dichotomous items the equivalent formula is KR-20, available in another calculator on this site.
Is a very high alpha a sign of quality?
Not necessarily. Above 0.95 it usually indicates redundant items asking nearly the same thing in different words.
Why is my alpha negative?
Almost always because reverse-worded items have not been recoded before calculating.
Need to calculate something else?
These tools are often used alongside this calculator.
Standard deviation
Sample and population deviation, variance and coefficient of variation.
Pearson
The r coefficient, R², p value and an interpretation of the strength.
Sample size
How many responses you need for your survey to be representative.
t test
Compare two group means, paired samples, or one sample against a value.
Margin of error
How precise your survey is, given the sample you actually collected.
Chi-square
Test whether two categorical variables are related, with Cramér’s V.