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Forest Biomass Allometric Equation Simulator

Estimate above- and below-ground biomass, carbon stock, annual CO₂ sequestration and carbon-credit value for a stand from DBH, tree height, forest type and density. Built on the Chave 2014 pantropical allometry — useful for screening REDD+ and J-Credit projects, or for IPCC NGGI back-of-envelope calculations.

Parameters
Forest type
Sets wood density ρ and MAI (annual increment)
Diameter at breast height (DBH)
cm
Trunk diameter at 1.3 m above the ground
Tree height H
m
Stand density
trees/ha
Number of trees per hectare (per representative tree)
Stand area
ha
Rotation age
year
Cumulative credit window (years to main harvest)
Results
—
Single-tree AGB (kg)
—
AGB per ha (t/ha)
—
Stand total biomass (t)
—
Stand carbon stock (t-C)
—
Annual CO₂ uptake (t-CO₂/y)
—
Annual credit value (USD)
—
Forest cross-section — biomass & CO₂ uptake

Trees are drawn proportional to DBH and height, with roots underground, animated CO₂ uptake arrows and an AGB gauge. Colour shows carbon density (light → deep green).

Allometric curve — AGB vs DBH
MAI by forest type (t/ha/y)
Theory & Key Formulas

$$AGB = 0.0673\,(\rho D^{2} H)^{0.976},\qquad BGB = 0.24\cdot AGB$$

Chave et al. (2014) pantropical allometry. ρ: wood density (g/cm³), D: DBH (cm), H: tree height (m). AGB is above-ground, BGB is below-ground (root) biomass per tree (kg).

$$C = 0.47 \cdot Biomass,\qquad CO_{2} = \dfrac{44}{12}\cdot C$$

Carbon stock C and CO₂ equivalent. The IPCC default carbon fraction of dry biomass is 47%, and the CO₂-to-C molecular weight ratio is 44/12.

$$\Delta CO_{2}/y = MAI \cdot A \cdot 0.47 \cdot \dfrac{44}{12}$$

Annual CO₂ sequestration. MAI: Mean Annual Increment by forest type (t/ha/y), A: stand area (ha). Defaults used here: tropical moist 8, tropical dry 4, temperate broadleaf 5, temperate conifer 6, boreal 3.

Forest Biomass Allometric Equations — Estimating Carbon Sequestration

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Forest "biomass" basically means the weight of all the trees, right? But you can't weigh every tree in a 100-hectare forest — so how do you actually get the carbon stock?
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Exactly the right question. The job of estimating without felling belongs to allometric equations. Once you have DBH (trunk diameter at 1.3 m above the ground), tree height H and wood density ρ for the species, Chave 2014 gives single-tree above-ground biomass as AGB = 0.0673·(ρD²H)^0.976 — accurate to roughly ±10% for tropical forests. Multiply by trees per hectare and the stand area, and you get the total.
🙋
So I just remember "diameter² × height × wood density, then to the 0.976". Are roots just ignored?
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No, roots get added back. Below-ground biomass BGB is taken as 0.24× the AGB by the IPCC Guidelines default, so the total tree mass is 1.24·AGB. For tropical moist forest at DBH 30 cm and H 20 m, AGB ≈ 601 kg, BGB ≈ 144 kg, total ≈ 745 kg per tree. At 800 trees/ha that gives ~596 t/ha, and over 100 ha around 59,600 t. Forests are far heavier than people intuit.
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And how does that mass become a "CO₂ uptake"? The units look different.
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Two steps. Dry biomass is about 47% carbon (the rest is hydrogen and oxygen). Then that carbon all came from atmospheric CO₂, so multiplying by the molecular-weight ratio 44/12 ≈ 3.667 gives the equivalent CO₂ mass. One tonne of wood is therefore 0.47 t-C or about 1.72 t-CO₂ that was pulled out of the atmosphere — that is the "carbon stock" of the forest.
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The annual CO₂ uptake and the credit value are also shown. Is that a separate calculation?
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Yes — "what is stored" and "what is added each year" are different things. Annual growth is called MAI (Mean Annual Increment) and runs 3-10 t/ha/y by forest type: about 8 in tropical moist, 3 in boreal. Multiply by area, carbon fraction 0.47 and 44/12 for the annual CO₂ uptake, and by $50/t-CO₂ for the credit value. A 100 ha tropical-moist stand yields ~1,379 t-CO₂/y and about $69,000/y — exactly the kind of screening number you want before a REDD+ or J-Credit feasibility study.
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REDD+ is new to me. How is it different from J-Credit?
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REDD+ is a UNFCCC scheme for developing countries — it issues credits for the emissions avoided by stopping deforestation and forest degradation. J-Credit is Japan's domestic system, run by the Ministry of the Environment and the Forestry Agency, that turns thinning and planting into credits companies can buy for offsets. J-Credit certifies on the order of a million t-CO₂/y and uses a formal MRV (Measurement, Reporting, Verification) framework comparable to Verra VCS and Gold Standard. The numbers from this tool are only first-cut estimates, but they are exactly what an early-stage screening needs.

Frequently Asked Questions

An allometric equation is an empirical fit that estimates total standing-tree biomass (kg) from easily measured tree dimensions — DBH (diameter at breast height), tree height and wood density. Because forests can be inventoried without felling, the Chave 2014 pantropical form AGB = 0.0673·(ρD²H)^0.976 is widely used as a global standard for tropical forests. For temperate forests Jenkins 2003 (USA) and for mangroves Komiyama 2008 are preferred — pick a form that matches the ecosystem and region.
Root mass is taken as 0.24× the above-ground biomass (root-to-shoot ratio = 0.24), the IPCC 2006 Guidelines default. In reality the ratio varies from 0.15 to 0.40 depending on forest type and stand age, and tends to be larger for boreal and dry-land forests. This tool uses Total biomass = AGB + 0.24·AGB = 1.24·AGB, producing the standard total used in carbon-credit accounting.
Dry biomass is about 47% carbon (IPCC 2006 default, with 50% for conifers and 47% for broadleaves as common figures), so Carbon (t-C) = Biomass × 0.47. The mass of CO₂ that was removed from the atmosphere to build that carbon is then CO₂ (t-CO₂) = C × 44/12 ≈ C × 3.667, using the CO₂-to-carbon molecular-weight ratio. This tool reports stand carbon stock and the MAI-based annual CO₂ sequestration separately.
Carbon-credit value = annual CO₂ sequestration × 50 USD/t-CO₂. The $50/t reference falls between 2024 voluntary forest-credit prices on Verra VCS / Gold Standard ($10-50/t-CO₂) and EU-ETS compliance prices (€60-90/t-CO₂). Actual project revenue varies strongly with project type, holding period, additionality demonstration and verification fees, so treat the value as an order-of-magnitude screening figure rather than a forecast.

Real-World Applications

REDD+ / J-Credit project screening: Before launching a REDD+ project in a tropical country or a Japanese J-Credit (Forestry Agency / MoE) project, you need a first read on existing carbon stock and annual uptake of the target stand. An allometric-style estimate like this gives a 1-minute answer on whether the project will exceed 1,000 t-CO₂/y or generate $50,000/y in credits — enough to decide whether to commission a full forest inventory (typically hundreds of thousands of dollars).

IPCC NGGI reporting and national forest inventories: Under the Paris Agreement, every country reports a National Greenhouse Gas Inventory (NGGI) including the LULUCF (Land Use, Land-Use Change and Forestry) sector. Japan's annual forest sink is about 44 million t-CO₂/y (FY2022) and is computed from allometries (Chave-type, Jenkins-type, region-specific) applied to forest inventory data. This tool is for individual-stand back-of-envelope work; full accounting needs FRA (Forest Resources Assessment) data and regionally calibrated equations.

Forest management plans and long-term economics: When a forest manager extends the rotation from 50 to 80 years, this tool lets you see how the combined harvest revenue and carbon-credit revenue change. Move the rotation slider from 60 yr to 80 yr and the cumulative credit grows by about 33%, but harvest revenue is deferred. Rotation-extension projects are eligible for J-Credit forest management, similar to Verra IFM (Improved Forest Management) under the international voluntary market.

Ground truth for remote-sensing AGB mapping: Wide-area AGB mapping with NASA GEDI (Global Ecosystem Dynamics Investigation), ESA Sentinel-2 and JAXA ALOS-2 PALSAR-2 is advancing rapidly. Calibrating these satellite estimates needs ground-based DBH / height measurements turned into "truth" via allometry, and this kind of quick estimate is a useful benchmark to check whether satellite outputs are in the right order of magnitude.

Common Misconceptions and Pitfalls

The biggest pitfall is applying a pantropical allometric equation to any forest. Chave 2014 was fit on more than 4,000 felled-tree records from tropical forests, and using it on temperate conifers or mangroves introduces 20-50% systematic error. This tool switches wood density ρ and MAI by forest type but keeps the Chave functional form. For production work, prefer ecosystem-specific equations: Jenkins 2003 for temperate broadleaves, Komiyama 2008 for mangroves, Lambert 2005 for boreal forests, and so on. If a region- or species-specific equation exists, use it first.

Next, assuming MAI is constant over the entire rotation. For simplicity this tool uses one MAI value per forest type (e.g. 8 t/ha/y for tropical moist). In reality annual growth follows an S-curve: low in the juvenile phase, peaking after canopy closure, declining in old growth. Yield tables and dynamic models such as CBM-CFS3 (Carbon Budget Model) capture age-dependent NPP (Net Primary Productivity); the steady MAI here is only an average. Young stands (under 10 years) in particular tend to grow slower than the tool predicts.

Finally, the carbon-credit value is not net profit. The "annual credit value (USD)" shown is gross revenue. Real project economics deduct certification fees (initial $50,000-$200,000 under Verra VCS or Gold Standard), MRV (Measurement, Reporting, Verification) costs ($20,000-$100,000/yr), leakage deductions (10-30%), a permanence buffer (10-20%), royalties and brokerage fees. Small projects of around 100 ha typically cannot absorb the fixed certification overhead — a practical floor is often quoted as 1,000+ ha and 5,000+ t-CO₂/y. Always run a detailed cost model with a project developer (PDD) before committing.

How to Use

  1. Enter individual tree diameter at breast height (DBH) in centimeters (e.g., 35 cm for a mature pine)
  2. Input tree height in meters (e.g., 28 m for a softwood plantation species)
  3. Specify stand density in trees per hectare (e.g., 400 trees/ha for a thinned loblolly pine stand)
  4. Enter total stand area in hectares (e.g., 50 ha for a managed forest compartment)
  5. The simulator applies species-specific allometric equations (e.g., Chojnacky equations for hardwoods, Jenkins equations for conifers) to calculate above-ground biomass (AGB) and applies standard carbon conversion factors (0.5 for AGB to carbon; 1.833 for carbon to CO₂)
  6. Review single-tree AGB, per-hectare density, total stand biomass, carbon stock, annual CO₂ sequestration rate, and voluntary carbon market value at USD 15/t-CO₂

Worked Example

A 40 ha mixed-oak forest stand with 350 trees/ha. Individual tree: DBH = 42 cm, height = 24 m. Single-tree AGB using USDA FIA allometric model: approximately 680 kg. Stand-level AGB: 238 t/ha × 40 ha = 9,520 t. Carbon stock: 9,520 t × 0.5 = 4,760 t-C. Annual CO₂ sequestration (assuming 2% annual growth increment on standing biomass): 190 t-CO₂/year. Annual credit value at voluntary market rate: 190 t-CO₂ × USD 15 = USD 2,850/year for offset projects.

Practical Notes

  1. DBH measurement protocol: use forestry caliper at 1.3 m height above ground; avoid measurements on sloped terrain without terrain correction
  2. Height estimates from field plots should be measured with clinometer or laser hypsometer; eye-estimated heights introduce 5–15% error in AGB calculations
  3. Stand density thresholds: plantations typically 400–1,200 trees/ha; natural forests 100–600 trees/ha; apply species-specific allometric equations—pine and oak require different coefficients
  4. Carbon credit value fluctuates: USD 10–20/t-CO₂ for verified emission reductions (VER) depending on project certification (VCS, Gold Standard) and registry liquidity
  5. Below-ground biomass (roots) typically 20–30% of AGB; simulator includes this in total carbon calculations for greenhouse gas inventory compliance