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Composite Reliability and AVE Calculator (with Fornell-Larcker and HTMT)

How do you calculate composite reliability and AVE?

AVE = sum of squared loadings / number of items. CR = (sum of loadings)² / [(sum of loadings)² + sum of (1 - loading²)]. With loadings .858, .798 and .818, AVE = .681 and CR = .865. The usual thresholds are AVE of .50 or more and CR of .70 or more; discriminant validity is then checked with HTMT (below .85 or .90).

Every PLS-SEM or CFA thesis has the same table: CR, AVE, Fornell-Larcker and HTMT. Most free tools do one of the four. Paste your loadings, construct correlations and item correlation matrix here and get the whole table.

The example is the corporate reputation model from the PLS-SEM Primer; the calculator reproduces its published AVE and composite reliability values.

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Built by Muhammad Shahzeb Anwar, MSc Industrial and Organizational Psychology. Measurement validity is the part of a research design an I/O psychologist is trained to check first.

The calculator

Your measurement model

Runs in your browser. Nothing you type is stored or sent anywhere.

Example: the corporate reputation model from the PLS-SEM Primer (3rd ed.). Replace with your own outer loadings (PLS) or standardised loadings (CFA).
The latent variable correlations from your output. The example values are illustrative.
Full or lower-triangular, separated by spaces, commas or tabs (paste straight from Excel). Item names must match the loadings list. The example values are illustrative. Nothing you paste leaves this page.

The four checks and their thresholds

Indicator loadings: .708 or more (so the construct explains at least half of the item's variance). Items between .40 and .70 are usually kept unless deleting them raises CR or AVE above the threshold; items below .40 are usually removed (Hair et al.).

Composite reliability (rho c): .70 or more; .60 to .70 is acceptable in exploratory work; above .95 suggests the items repeat each other. AVE: .50 or more for convergent validity (Fornell and Larcker, 1981).

Discriminant validity: under the Fornell-Larcker criterion the square root of each construct's AVE must be larger than its correlations with every other construct (equivalently, AVE larger than the maximum shared variance, MSV). Under HTMT (Henseler, Ringle and Sarstedt, 2015), the mean correlation between items of different constructs, divided by the geometric mean of the average correlations within each construct, should be below .85, or .90 for conceptually similar constructs.

Why HTMT replaced Fornell-Larcker

Henseler and colleagues' simulations showed that the Fornell-Larcker criterion and cross-loadings detect a lack of discriminant validity in only a small share of cases when loadings differ only slightly. HTMT detected it far more reliably. Examiners still ask for the Fornell-Larcker table, so report both, but treat HTMT as the decision. For a formal test, report a bootstrap confidence interval for HTMT from your PLS or CFA software; this calculator gives the point value.

Worked example

COMP has loadings .858, .798 and .818. Squares: .736, .637, .669; their mean is AVE = .681. The sum of loadings is 2.474, squared 6.121; the error variances sum to 3 - 2.042 = 0.958; CR = 6.121 / (6.121 + 0.958) = .865. The square root of the AVE, .825, is what the Fornell-Larcker table puts on the diagonal. These match the published values in the PLS-SEM Primer's case study.

Before you rely on this

What this will not tell you

This uses standardised loadings for reflective constructs. It does not apply to formative constructs, does not compute rho A (which needs the weights), does not bootstrap HTMT, and computes HTMT with absolute correlations as SmartPLS does. Cronbach's alpha needs the item variances and cannot be derived from loadings. Nothing you paste leaves your browser.

Questions

Questions people actually ask

What is a good AVE value?

0.50 or more: the construct explains at least half of the variance of its items. Below .50, more of the item variance is error than construct.

What is the difference between composite reliability and Cronbach's alpha?

Cronbach's alpha assumes every item loads equally; composite reliability uses each item's own loading. When loadings differ, alpha is usually lower and CR higher, with the true reliability usually between the two.

Can AVE be below .50 if CR is above .70?

Yes. Fornell and Larcker noted that convergent validity can be argued from CR alone when AVE is a little under .50, but most examiners expect both thresholds to be met.

What HTMT value shows discriminant validity?

Below .85 is the conservative threshold, and below .90 is accepted for conceptually similar constructs (Henseler et al., 2015). A bootstrap confidence interval that stays below the threshold is the stronger evidence.

How do I get the item correlation matrix for HTMT?

From your software's indicator correlations (SmartPLS shows them in the results report) or from SPSS or Excel with CORREL on the raw item scores. Paste it with item names as the header row.

The papers behind the method

Sources

Formulas from Fornell and Larcker (1981) and Henseler, Ringle and Sarstedt (2015); thresholds as summarised by Hair et al. The worked example reproduces the PLS-SEM Primer's published values. Checked on 2 November 2026.

  1. Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39-50: https://doi.org/10.1177/002224378101800104
  2. Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). A new criterion for assessing discriminant validity in variance-based structural equation modeling. Journal of the Academy of Marketing Science, 43(1), 115-135: https://doi.org/10.1007/s11747-014-0403-8
  3. Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. PLS-SEM Primer, 3rd ed., Chapter 4 case study (published loadings, AVE and rho c): https://www.smartpls.com/primer-book-case-studies/primer_3e_chap4_case_new.pdf
Citation

Cite this tool

Free to use and free to quote. If a figure here is useful in something you are writing, a link back is all that is asked.

Muhammad Shahzeb Anwar, MSc Industrial and Organizational Psychology. Composite Reliability, AVE and HTMT Calculator. Shahzeb Speaks. https://www.shahzebspeaks.com/composite-reliability-ave-calculator/

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