# European general equation, Fagus sylvatica, aboveground, diameter only (Eq. 3)

Aboveground biomass equation for Fagus sylvatica, Europe (latitude min/mean/max 42.3 / 49.6 / 56 °N), from Forrester et al. 2017. DBH 1–84 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Forrester et al. 2017 (Eq. 3, revised manuscript l. 322):

> ln(Y) = lnβ0 + β1ln(d) + ε (3)

Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#equation

In this library's units, ready to compute (aboveground biomass in kg):

```
Aboveground biomass = 0.996924 * exp(-1.6594 + 2.3589 * ln(D))
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: 0.996924 * exp(-1.6594 + 2.3589 * ln(d)), with d in cm; output in kg.
Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#canonical

## What it covers

- Output: Aboveground biomass, kg
- Taxon: Fagus sylvatica (species), family Fagaceae; broadleaf
- Where: Europe (latitude min/mean/max 42.3 / 49.6 / 56 °N). Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#where
- Biomes: temperate
- Stand: mixed
- DBH range: 1–84 cm. Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#dbh
- R²: 0.981. Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#r2
- Correction factor: 0.996924 (applied). Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#cf
- Method: Mixed-effects regression of ln(Y) on ln(d) (source as random effect) on 330 pseudo-observations generated from published equations plus raw data; Snowdon ratio CF. Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#method
- Verification: read in the original source
- Last checked: 2026-11-01. Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#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

Forrester, D.I., Tachauer, I.H.H., Annighoefer, P., Barbeito, I., Pretzsch, H., Ruiz-Peinado, R., Stark, H., Vacchiano, G., Zlatanov, T., Chakraborty, T., Saha, S., Sileshi, G.W. (2017). Generalized biomass and leaf area allometric equations for European tree species incorporating stand structure, tree age and climate. Forest Ecology and Management, 396, 160–175.

- DOI: https://doi.org/10.1016/j.foreco.2017.04.011
- Access: paywalled
- Copy we read: https://data.mendeley.com/datasets/4jytx9s44j/1
- Every equation from this source: https://treeallometry.org/sources/forrester-2017/
- Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#source

## The facts, in the source's words

**Equation** (Eq. 3, revised manuscript l. 322):

> ln(Y) = lnβ0 + β1ln(d) + ε (3)

Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#equation

**Correction factor** (Methods, revised manuscript ll. 343–346):

> a correction factor (CF) was calculated from the mean of the pseudo-observations divided by the mean of the values predicted by the regional equation (Snowden, 1991)

Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#quote-fit-cf

**Equation** (Appendix A, worksheet Table A.5, row 306):

> Fagus sylvatica | Aboveground | 3 | -1.6594 | 2.3589 | CF 0.996923865219428 | N 330

Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#quote-expression

**Smallest DBH** (Appendix A, Table A.5, row 306, column AU):

> d range (cm) 1 / … / 84 (min / mean / max)

Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#quote-fit-dbh-min-cm

**Our note:** Y in kg per tree, d in cm at 1.3 m (manuscript l. 316). Printed intercept is ln(β0). CF (0.996924) multiplies the back-transformed prediction and is applied in both forms. N = 330 is the number of pseudo-observations plus raw observations, not trees. The same worksheet also gives versions with age, basal area, stand density and climate terms (Eqs. 4–21).

## 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 | 579 | 579 | Computed from the printed form: computed from the published form (with CF) at d = 30 cm |

Cite: https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/#checks

The calculator on the page shows carbon as biomass × 0.47 (IPCC 2006 Guidelines, Vol. 4, Ch. 4, Table 4.3) and CO₂e as carbon × 44/12.

## How to cite

Cite the source for the equation: Forrester, D.I., Tachauer, I.H.H., Annighoefer, P., Barbeito, I., Pretzsch, H., Ruiz-Peinado, R., Stark, H., Vacchiano, G., Zlatanov, T., Chakraborty, T., Saha, S., Sileshi, G.W. (2017). Generalized biomass and leaf area allometric equations for European tree species incorporating stand structure, tree age and climate. Forest Ecology and Management, 396, 160–175. https://doi.org/10.1016/j.foreco.2017.04.011

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "European general equation, Fagus sylvatica, aboveground, diameter only (Eq. 3)", checked 2026-11-01, https://treeallometry.org/equations/forrester-2017-fagus-sylvatica/. 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/forrester-2017-fagus-sylvatica.json
Report a problem: email info@restorationscope.com with the equation id (forrester-2017-fagus-sylvatica) and where the right value appears.