# Tree height from diameter (Eq. 1a)

Height equation for Fagus sylvatica, Netherlands, from Bartelink 1997. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Bartelink 1997 (Equation [1a], p. 43 (rendered page-06).):

> ln(h) = 0.549 + 0.769*ln (dbh)

Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#equation

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

```
Height = exp(0.549 + 0.769 * ln(D))
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: exp(0.549 + 0.769 * ln(dbh)), with dbh in cm; output in m.
Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#canonical

## What it covers

- Output: Height, m
- Taxon: Fagus sylvatica (species); broadleaf
- Where: Forest area in the centre of the Netherlands. Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#where
- Biomes: not stated
- Stand: not stated
- R²: 0.934. Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#r2
- Method: log-log linear regression. Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#method
- Verification: read in the original source
- Last checked: 2026-11-05. Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#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

Bartelink, H. H. (1997). Allometric relationships for biomass and leaf area of beech (Fagus sylvatica L). Annales des Sciences Forestières, 54(1), 39–50.

- DOI: https://doi.org/10.1051/forest:19970104
- Peer review: A paper in a peer-reviewed journal.
- Access: open access
- Copy we read: https://hal.science/hal-00883130/document
- Every equation from this source: https://treeallometry.org/sources/bartelink-1997/
- Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#source

## The facts, in the source's words

**Equation** (Equation [1a], p. 43 (rendered page-06).):

> ln(h) = 0.549 + 0.769*ln (dbh)

Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#equation

**Equation** (Eq. 1a, p. 43):

> 0.549 + 0.769*ln (dbh)

Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#quote-expression

**Equation** (Eq. 1b, p. 43 (rendered page)):

> h = 1.732 * dbh⁰·⁷⁶⁹

Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#quote-expression-2

**Output** (Below Eq. 1b, p. 43):

> tree height (m)

Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#quote-output

**Units** (Table II, p. 43 (rendered page)):

> dbh (in cm)

Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#quote-published-units

**R²** (Eq. 1a, p. 43):

> 0.934 [1a]

Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#quote-fit-r2

**method** (Results, p. 43):

> tree height was best described after a log-log

Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#quote-fit-method

**Taxon** (Title, p. 39):

> beech (Fagus sylvatica L)

Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#quote-taxon

**Where** (Data collection, p. 40):

> centre of the Netherlands.

Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#quote-region

**Our note:** DBH is measured at 1.30 m. Eq. 1a is exponentiated using its printed coefficients. The paper gives no back-transformation correction and none is applied. Its Eq. 1b uses the rounded multiplier 1.732, producing a small rounding difference. R² is adjusted for degrees of freedom.

## 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 = 15 | 13.9 | 13.9 | Computed from the printed form: Computed by exponentiating Eq. 1a; diameter is within the plotted sample. |

Cite: https://treeallometry.org/equations/bartelink-1997-eq1a-height/#checks

## How to cite

Cite the source for the equation: Bartelink, H. H. (1997). Allometric relationships for biomass and leaf area of beech (Fagus sylvatica L). Annales des Sciences Forestières, 54(1), 39–50. https://doi.org/10.1051/forest:19970104

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Tree height from diameter (Eq. 1a)", checked 2026-11-05, https://treeallometry.org/equations/bartelink-1997-eq1a-height/. 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/bartelink-1997-eq1a-height.json
Report a problem: email info@restorationscope.com with the equation id (bartelink-1997-eq1a-height) and where the right value appears.