Tree Allometrics

Equations / Stem volume

Commercial stem volume from DBH, Husch log model (MV1)

Stem volume20 commercial tree species of a managed forest (DBH >= 50 cm)BrazilnaturalRead from the original paper
Many species, no single photo
Equation

As printed (Table 1, MV1 (Husch 1963; logarithmic))

ln(V) = β0 + β1 ln(d) + ε

In this library's units, ready to compute (m³)

Stem volume = exp(-6.5125) * D^1.88558 * 1.0527
D
Diameter at breast height (1.3 m), cm

Commercial stem volume over bark (Smalian) in m3. Coefficients and CF as printed; the CF multiplies the back-transformed estimate. R2 is on the log scale. Applies to commercial stems only (stump at 30 cm, buttresses removed, crown left in the forest) of trees with DBH >= 50 cm; do not use for whole-tree totals. The authors selected the equations with commercial stem length l as the best ones; these are the ones that use only canonical variables.

Source
MV1 −6.51250 * 1.88558 * 2.318 0.67 1011.70 1.621 1.0527
R² · Table 3 (β0, β1, RMSE, R2, AIC, MAD, CF)
Total 223 50.4–149.9 79.6 ± 19.8 0.27–0.89 0.56 ± 0.16
Smallest DBH · Table 2 (n, DBH range and mean, wood density range and mean)
Trees measured
223
DBH range
50.4–149.9 cm
R²
0.67
Correction factor
1.0527 (applied)
Method
Linear regression on ln(V) vs ln(d), back-transformed with correction factor
Where
Fazenda Antimari I and II, Porto Acre, Acre
Last checked
2026-11-02
Calculate
3.52
Stem volume (m³)
Fitted DBH range0246810121420406080100120DBH (cm)Stem volume (m³)Stem volume

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 = 603.523.52Computed from the printed form
computed from the published form
D = 1009.239.23Computed from the printed form
computed from the published form

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