Tree Allometrics

Fagus sylvatica / Height

Tree height from diameter (Eq. 1a)

HeightFagus sylvaticaNetherlandsRead from the original paperPeer-reviewed source
Photo of Fagus sylvatica
© Rebecca Gimenez Husted · CC BY · iNaturalist
Equation

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

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

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

Height = exp(0.549 + 0.769 * ln(D))
D
Diameter at breast height (1.3 m), cm

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.

Source
0.549 + 0.769*ln (dbh)
Equation · Eq. 1a, p. 43
h = 1.732 * dbh⁰·⁷⁶⁹
Equation · Eq. 1b, p. 43 (rendered page)
tree height (m)
Output · Below Eq. 1b, p. 43
dbh (in cm)
Units · Table II, p. 43 (rendered page)
0.934 [1a]
R² · Eq. 1a, p. 43
tree height was best described after a log-log
method · Results, p. 43
beech (Fagus sylvatica L)
Taxon · Title, p. 39
centre of the Netherlands.
Where · Data collection, p. 40
R²
0.934
Method
log-log linear regression
Where
Forest area in the centre of the Netherlands
Last checked
2026-11-05
Calculate
13.9
Height (m)

Shaded: the DBH range the model was fitted on. Other inputs held at the values above.

Checks this equation passes

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

InputsExpectedWe getFrom
D = 1513.913.9Computed from the printed form
Computed by exponentiating Eq. 1a; diameter is within the plotted sample.

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