# Pantropical Weibull height–diameter model

Height equation for Tropical forest trees (permanent plots), Pantropical, from Feldpausch et al. 2012. 42,656 trees, DBH from 10 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Feldpausch et al. 2012 (Eq. 5, p. 3387):

> H = a(1 − exp(−bD^c))

Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-pantropical/#equation

In this library's units, ready to compute (height in m):

```
Height = 50.874 * (1 - exp(-0.042 * D^0.784))
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: 50.874 * (1 - exp(-0.042 * D^0.784)), with D in cm; output in m.
Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-pantropical/#canonical

## What it covers

- Output: Height, m
- Taxon: Tropical forest trees (permanent plots) (mixed species); mixed
- Where: Permanent plots in Africa, Asia, Australia and South America. Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-pantropical/#where
- Biomes: tropical
- Stand: natural
- Trees measured: 42,656. Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-pantropical/#n_trees
- DBH range: from 10 cm. Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-pantropical/#dbh
- Method: nonlinear Weibull H:D fit. Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-pantropical/#method
- Verification: read in the original source
- Last checked: 2026-11-01. Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-pantropical/#checked_at

A missing fit statistic is one the source doesn't state, or that we haven't recorded; it is never estimated. Outside the stated DBH range or region, the equation is an extrapolation.

## Source

Feldpausch, T. R., Lloyd, J., Lewis, S. L., et al. (2012). Tree height integrated into pantropical forest biomass estimates. Biogeosciences, 9, 3381–3403.

- DOI: https://doi.org/10.5194/bg-9-3381-2012
- Access: open access
- Copy we read: https://bg.copernicus.org/articles/9/3381/2012/bg-9-3381-2012.pdf
- Every equation from this source: https://treeallometry.org/sources/feldpausch-2012/
- Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-pantropical/#source

## The facts, in the source's words

**Equation** (Eq. 5, p. 3387):

> H = a(1 − exp(−bD^c))

Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-pantropical/#equation

**Units** (Table 3 caption, p. 3393):

> Coefficients for Weibull-H region-, continent-specific and pantropical models (H = a(1−exp(−bD^c))) to estimate tree height (H, m) from diameter (D, cm) ≥ 10 cm in pantropical forests

Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-pantropical/#quote-published-units

**Trees measured** (Table 3 (columns a, b, c, RSE, AIC, n), p. 3393):

> Pantropical 50.874 0.0420 0.784 5.479 266 169 42656

Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-pantropical/#quote-fit-n-trees

**Our note:** Weibull height–diameter model; RSE 5.479 m (on the height scale, not log scale, so not stored in fit.rse). Fitted on concurrent H and D measurements in permanent plots, trees ≥ 10 cm D; the paper gives no maximum D for this fit. Table 3 footnote: models adapted from the pantropical H:D database of Feldpausch et al. (2011).

## Checks this equation passes

On every build, the library's form and the source's own form (in its units) must both give these values within 1%.

| Inputs | Expected | We get | From |
| --- | --- | --- | --- |
| D = 30 | 23.1 | 23.1 | Computed from the printed form: computed with python3 from the published form |
| D = 80 | 37.1 | 37.1 | Computed from the printed form: computed with python3 from the published form |

Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-pantropical/#checks

## How to cite

Cite the source for the equation: Feldpausch, T. R., Lloyd, J., Lewis, S. L., et al. (2012). Tree height integrated into pantropical forest biomass estimates. Biogeosciences, 9, 3381–3403. https://doi.org/10.5194/bg-9-3381-2012

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Pantropical Weibull height–diameter model", checked 2026-11-01, https://treeallometry.org/equations/feldpausch-2012-weibull-pantropical/. Data CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Quotes are the authors' words.

Data for this equation: https://treeallometry.org/data/equations/feldpausch-2012-weibull-pantropical.json
Report a problem: email info@restorationscope.com with the equation id (feldpausch-2012-weibull-pantropical) and where the right value appears.