Cronbach's Alpha Calculator

In short, it measures internal consistency: how reliably a set of questions that are meant to measure the same idea get answered together. It is a reliability check, not a hypothesis test, so it gives a number between 0 and 1 rather than a p-value. Think of a survey with several Likert-scale questions (from strongly disagree to strongly agree) about one concept, such as anxiety: if people who rate one question highly also rate the others highly, the questions correlate with each other and alpha goes up. Alpha is built from those question-to-question correlations. What it does not tell you: whether you are measuring the right thing (validity), and whether your questions measure exactly one idea rather than several (dimensionality). Both need separate checks, such as factor analysis.

Lee Cronbach named it coefficient alpha when he published the measure in 1951, so in older papers you will see it called that, or simply alpha. It is a measure of internal consistency reliability. A close relative is the Kuder-Richardson Formula 20 (KR-20): it is mathematically the same as alpha, but it is used when questions have only two possible answers, such as yes or no, or right or wrong.

The formula uses three things: the number of questions (k), how much each question's scores vary (each question's variance), and how much each person's total score varies (the variance of the totals).

In the formula, Σσ_i² is the sum of each question's variance, and σ_t² is the variance of the total scores.

To work it out by hand, for example in Excel: add up each person's scores to get their total, work out the variance of each question's column with VAR.S, add those variances together, then work out the variance of the total-score column and put the numbers into the formula. This calculator does all of that for you, and also shows each question's corrected item-total correlation and what alpha would be if that question were deleted.

Cronbach's alpha tells you how well your questions "hang together": do people who answer one question a certain way also answer the other questions the same way? The value usually falls between 0 and 1, and the closer it is to 1, the more consistently people answer across your questions. It can even come out negative, which usually means some questions were worded in reverse and were not flipped (reverse-coded) before calculating. When you read the number, keep two cautions in mind. First, a high alpha does not prove your scale measures what you think it measures; that is a question of validity, not reliability. Second, it does not prove your scale measures exactly one thing; use an exploratory factor analysis to check that. Also look at the "alpha if item deleted" column in your results: if alpha would go up without a question, that question is dragging the scale down.

As a rule of thumb, aim for 0.70 or higher. Here is how the common ranges are read:

• 0.90 and above: Excellent. But above 0.95, be careful: it often means some questions are near-duplicates, asking almost the same thing in slightly different ways.
• 0.80 to 0.89: Good. Strong reliability for most research.
• 0.70 to 0.79: Acceptable. Fine for comparing groups.
• 0.60 to 0.69: Questionable. Usually only okay for brand-new or exploratory scales, and worth investigating.
• Below 0.50: Unacceptable. The questions do not hang together and are not reliably measuring the same thing.

What counts as good enough also depends on your field and how the results are used: high-stakes clinical or diagnostic tests should aim for 0.90 or higher, while early exploratory research can justify lower values.

Each value is read against the usual ranges:

• 0.60 to 0.69: Questionable. Usually only okay for brand-new or exploratory scales.
• 0.70 to 0.79: Acceptable. Fine for most research and for comparing groups. It also means roughly 70% of the differences in total scores come from the thing you are measuring, with the rest from noise. With only 2 or 3 questions, a 0.7 is actually quite good.
• 0.80 to 0.89: Good. Strong reliability for most research.
• 0.90 and above: Excellent. The level expected when scores drive decisions about individual people, such as clinical diagnoses or admissions.
• Above 0.95: Be careful. It often means some questions are near-duplicates, asking almost the same thing twice.

One caution: if the scores are used for high-stakes decisions about individuals, such as clinical diagnoses or admissions, 0.7 is usually considered too low, and 0.9 or higher is the norm.

A low alpha (below 0.70, and especially below 0.60) means your questions are not being answered together: people who score high on one question do not necessarily score high on the others. The usual reasons: the questions measure different ideas, so the scale accidentally mixes two or more concepts; a negatively worded question was not flipped (reverse-coded) before calculating; the scale is very short, because alpha rises with the number of questions; or the group you tested is very similar, so their answers vary little and push alpha down. Start by checking the corrected item-total correlations and the alpha-if-item-deleted column in your results to find the questions dragging the score down.

A negative alpha is almost always a sign of a data problem rather than a real result. The most common cause is a reverse-worded question (for example, "I feel calm" on an anxiety scale) that was not flipped before calculating, so a high score on it means the opposite of a high score on the rest. Other causes are miscoded data, or questions that genuinely measure opposite things. To fix it: look at the correlations between questions, recode any reverse-worded ones (on a 1 to 5 scale, use 6 minus the score), and if a question still correlates negatively after that, it does not belong in the scale and should be dropped.

It answers a simple question: what would alpha be if I removed this question? If the number is higher than your overall alpha, that question is hurting the scale, because people answer it differently from the way they answer the rest. In that case, consider rewording or dropping it, but judge it against your theory as well, not just the number. This calculator lists alpha-if-item-deleted for every question, next to its corrected item-total correlation. A correlation below about 0.10 (or a negative one) points to the same problem.

Five things usually help. First, drop weak questions: check the corrected item-total correlations and the alpha-if-item-deleted column (this calculator shows both for every question), and remove one at a time any question whose correlation is below about 0.30 or whose removal would raise alpha, rerunning the analysis after each removal. Second, reverse-code any negatively worded questions before calculating; leaving them unflipped can drag alpha down or make it negative. Third, add more questions that genuinely measure the same idea, because alpha rises with the number of questions (but do not pad the scale with near-duplicates). Fourth, if the scale mixes several different ideas, split it into separate subscales and calculate alpha for each. Fifth, reword confusing or ambiguous questions, because people answering at random weakens the correlations.

For an exam, aim for 0.70 to 0.90. Below 0.70 the questions do not measure the same body of knowledge consistently, and the exam usually needs revision. Two exam-specific points: alpha rises as you add questions, so a short quiz can score lower even when its questions are fine; and an exam spread across many different topics often scores lower than one focused on a single skill, which is not necessarily a flaw. Also keep in mind that alpha shows whether students who do well on one question tend to do well on the others. It does not prove the exam tests what it is supposed to test.

In APA style, report the number of items and the value of alpha, the Greek letter α, to two decimal places with no zero before the decimal point (because alpha cannot exceed 1.0), together with a short phrase describing the reliability. For example: "The scale showed good internal consistency (12 items, α = .85)." If your scale has subscales, report each one separately with its own item count and alpha.

Four things to watch out for. Length: adding more questions pushes alpha up, even when the new questions relate only weakly to the rest, so a long scale can look reliable without being strong. Equal weight: alpha treats every question as contributing equally to the true score (the "tau-equivalence" assumption), which is rarely true in real data. Your sample: alpha depends on who you test; very similar (homogeneous) groups produce lower values because their answers vary less, so the same scale can score differently in different groups. What it cannot do: a high alpha never proves the scale measures the right thing, or that it measures exactly one thing. If you want a sturdier estimate that drops the equal-weight assumption, consider McDonald's omega, and use factor analysis to check how many underlying dimensions your questions actually have.

Alpha assumes every question contributes equally to the idea being measured (the tau-equivalence assumption), which is rarely true in real data, and because of that it often slightly underestimates reliability. McDonald's omega drops that assumption: it is calculated from a factor analysis, so each question can have its own strength of relationship to the underlying idea, and it copes better with scales that touch several related dimensions. In practice the two numbers are often close when your questions are fairly uniform, but omega is the more defensible estimate, and many journals now like to see both reported.