Cronbach’s alpha and McDonald’s omega calculator

Name: Cronbach’s alpha calculator
Author: Richard Injante

Reliability of a scale or questionnaire: alpha with a confidence interval, omega, and which items improve or hurt it.

Content reviewed by Richard Injante Published by SolucionesAhora.com Updated on 2026-10-20 How we verify

Calculator inputs

Enter your figures, or press “See example” to watch it work.
If your case is unusual, open “Advanced options”.
Read the result and, below it, what it means and how it was worked out.

Scale responses

Each row is a participant and each column an item of the scale (for example, a Likert question from 1 to 5). All items must point the same way: recode reversed ones first. You can put the item names on the first line. No missing data.

One row per person, one column per item

Advanced options

Confidence level (optional)

Level of the confidence interval for alpha. 95% is the standard.

See the result

Results

Cronbach’s alpha0.914

Alpha CI: lower0.245

Alpha CI: upper0.979

Rating of alphaExcellent

McDonald’s omega (total)0.925

Standardised alpha0.920

Mean inter-item correlation0.742

Number of items4

Number of respondents5

Item analysis
Item	Mean	SD	Corrected item-total correlation	Alpha if deleted	Factor loading
1	3.6	1.14	0.948	0.833	0.986
2	4	1	0.868	0.867	0.947
3	4	1.225	0.731	0.923	0.745
4	3.8	0.837	0.725	0.918	0.777

See the working step by step

Standardised alpha = 0.920; mean inter-item correlation = 0.742
4 items and 5 people

Free, no sign-up! What if you could do this without a calculator? A five-minute game with challenges, lives and points. It clicks even when you cannot be bothered.

In short

What it calculates: Reliability of a scale or questionnaire: alpha with a confidence interval, omega, and which items improve or hurt it.
Formula used: α = k/(k − 1) × (1 − Σ s²ᵢ / s²ₜ) k = items, s²ᵢ = variance of each item, s²ₜ = variance of the total
Example: Example 1. Five people and four items.

Cronbach’s alpha calculator

When a scale adds up several questions to measure one thing (satisfaction, anxiety, attitude…), you must check that those questions “pull in the same direction”. Cronbach’s alpha measures that internal consistency, and it is the first thing reviewers ask of a questionnaire.

Paste the responses (one row per person, one column per item). You get alpha with its confidence interval, McDonald’s omega (which does not require all items to weigh the same), the mean inter-item correlation and, for each item, its correlation with the rest of the scale and how much alpha would change if you dropped it. Everything runs in your browser.

How it works

Alpha compares the sum of the item variances with the variance of the total score: if the items measure the same thing, the total variance far exceeds the sum of the individual ones and alpha goes up. It depends on the number of items (more items, more alpha) and on how correlated they are.

Omega estimates reliability from a one-factor model, using each item’s loading; it does not assume all items weigh the same (tau-equivalence), so it is usually more realistic. Here it is obtained by iterated principal axis factoring. The confidence interval for alpha uses the F distribution (Feldt).

Formula

α = k/(k − 1) × (1 − Σ s²ᵢ / s²ₜ) k = items, s²ᵢ = variance of each item, s²ₜ = variance of the total
Alpha CI (Feldt): [1 − (1 − α) / F₍α/2₎ ; 1 − (1 − α) / F₍1−α/2₎] with F(n − 1, (n − 1)(k − 1))
Standardised alpha = k·r̄ / (1 + (k − 1)·r̄) r̄ = mean inter-item correlation
Omega = (Σλᵢ)² / ((Σλᵢ)² + Σ(1 − λᵢ²)) λᵢ = each item’s loading on the single factor
Alpha rating: ≥ 0.9 excellent · ≥ 0.8 good · ≥ 0.7 acceptable · ≥ 0.6 questionable · ≥ 0.5 poor

Worked example

Example 1. Five people and four items.
With the responses 4 5 4 5 / 3 3 4 3 / 5 5 5 4 / 2 3 2 3 / 4 4 5 4, alpha is 0.914 and omega 0.925; the mean inter-item correlation is 0.742. Good consistency, but with only five people the 95% confidence interval is huge: 0.245 to 0.979.

Example 2. An item that does not fit.
Six people and four items: 5 4 5 2 / 4 4 4 5 / 2 1 2 3 / 3 3 3 1 / 5 5 4 4 / 1 2 1 2. Alpha is 0.869 (CI 0.156 to 0.963) and omega 0.896. The fourth item correlates only 0.359 with the rest; dropping it raises alpha to 0.961. It is a sign that item may not measure the same thing.

Explanation

What Cronbach’s alpha measures

It measures the internal consistency of a scale: how far its items vary together. A high alpha means the items measure something in common; it does not prove they measure what you want to measure (that is validity).

How to interpret the value

- 0.9 or more: excellent (above 0.95, possible redundancy).
- 0.8 to 0.9: good.
- 0.7 to 0.8: acceptable for research.
- 0.6 to 0.7: questionable.
- Below 0.6: poor.
These thresholds are a convention. Individual decisions demand more (0.9) than comparing groups (0.7).

Alpha or omega

Alpha assumes all items weigh the same on the factor. If not (the usual case), it underestimates reliability. Omega makes no such assumption. Reporting both, with their intervals, is now the recommended practice.

The confidence interval matters

With few people, alpha is very imprecise: 0.91 with five people could really be 0.25. A sample of at least 100 gives reasonable intervals.

Improving the scale

The item table shows each item’s correlation with the rest (ideally ≥ 0.30) and alpha if deleted. An item with a low correlation, or whose removal raises alpha, is a candidate for review. But do not drop items just to raise alpha: you lose content.

Common mistakes

Forgetting to recode reversed items: alpha comes out artificially low, or negative.
Computing a single alpha for a scale with several dimensions.
Thinking a high alpha proves validity.
Using alpha with dichotomous items without knowing it equals KR-20.
Interpreting alpha without its interval, with few people.

Limits of this calculator

It assumes a one-dimensional scale; if there are several subscales, compute each separately.
Data must be complete (no missing values).
Omega is the total from a one-factor model (iterated principal axis), not a hierarchical or maximum-likelihood model.
Feldt’s interval assumes roughly normal scores.
It accepts up to 40 items and 2,000 people.

Notice

This is an estimate. For publication, check the figures with your statistics package and describe the method.

Frequently asked questions

What Cronbach’s alpha is acceptable?

From 0.7 for research and 0.8 or more for decisions about individuals. Above 0.95 may indicate redundancy.

What is the difference between alpha and omega?

Alpha assumes all items weigh the same; omega uses each item’s loading and is more realistic. It is worth reporting both.

How many people do I need?

The more the better: below 30, alpha is very imprecise. A minimum of 100 gives reasonable intervals.

Should I reverse negative items?

Yes. Reverse-worded items must be recoded before calculating, or the result comes out artificially low.

Can I drop an item to raise alpha?

Only if it makes theoretical sense. An item with a very low correlation with the rest can be reviewed, but do not drop content just to improve the number.

Does it work for yes/no items?

For dichotomous items, alpha equals KR-20, which has its own calculator.

Does alpha prove my scale is valid?

No. Alpha measures consistency; validity needs other evidence (content, factor structure, relation to other criteria).

Is my data sent to a server?

No. The calculation runs in your browser.

Sources and references

The formula behind this calculator is not ours. These are the sources it comes from, in APA 7 format, in case you want to go to the original or cite them in your own work.

Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297–334. https://doi.org/10.1007/BF02310555 https://doi.org/10.1007/BF02310555 The definition of coefficient alpha.
Feldt, L. S., Woodruff, D. J., & Salih, F. A. (1987). Statistical inference for coefficient alpha. Applied Psychological Measurement, 11(1), 93–103. https://doi.org/10.1177/014662168701100107 https://doi.org/10.1177/014662168701100107 The confidence interval for alpha using the F distribution.
McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. The omega coefficient from a factor model.
Dunn, T. J., Baguley, T., & Brunsden, V. (2014). From alpha to omega: A practical solution to the pervasive problem of internal consistency estimation. British Journal of Psychology, 105(3), 399–412. https://doi.org/10.1111/bjop.12046 https://doi.org/10.1111/bjop.12046 Why omega should be reported as well as alpha.

Need to calculate something else?

These tools are often used alongside this calculator.