The CINK calculator quantifies the carbon-sink value of soil-applied biochar over a chosen time horizon. From the biochar mass, carbon content, and persistence class, it splits the carbon into its geologically persistent (GPC) and semi-persistent (SPC) pools and computes CINKH — the annual average carbon stored over H years — using the SPC decay function of the Global Biochar C-Sink Standard. It reports the GPC available for CO2 offsetting after production emissions are retired, the CINK value of the SPC pool alone, and of both pools combined.
The calculator also derives the Total Climate Effect (TCE) of each pool, expressing the time-integrated cooling delivered by the sink in line with the impulse–response framework used for methane offsetting. CINK units are used by Carbon Standards to calculate the value of C-sinks, while the TCE provides the climate value of temporary C-sinks.
GPC share is classified automatically: Ro > 3.8 % → 90 %; else H/C ≤ 0.4 → 75 %; H/C > 0.4 → 0 %.
When on, these values override the biochar classification.
How much CO2e emission should be offset with this biochar carbon sink?
Over how many years is the offset delivered? Whole years, 1 to beyond 1000.
| Result | Value | Unit |
|---|---|---|
| Carbon pools | ||
| Total biochar carbon | -- | tCO2e |
| Geological persistent carbon (GPC) | -- | tCO2e |
| Semi-persistent carbon (SPC) | -- | tCO2e |
| Production emissions retired (offset) | -- | tCO2e |
| Available GPC after offset | -- | tCO2e |
| Carbon sink — CINK over H years | ||
| CINKH of SPC | -- | tCO2e |
| CINKH of GPC + SPC | -- | tCO2e |
| Total Climate Effect — TCE over H years cooling (removals negative) | ||
| TCEH of SPC fraction | -- | tCO2e·yr |
| TCEH of GPC pool | -- | tCO2e·yr |
| TCEH of C-sink (cooling) | -- | tCO2e·yr |
| TCEH of production emissions (warming) | -- | tCO2e·yr |
| Net TCEH (sink + emissions) | -- | tCO2e·yr |
Cumulative climate effect at each year. The C-sink cools (below the axis, negative); the retired production emissions warm (above the axis, positive). Units: tCO2e·yr.
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Total carbon as CO2e (stoichiometric factor $44/12$):
$$\text{total}_{\mathrm{CO_2e}} = m_{\mathrm{biochar}} \cdot \frac{\text{carbon\%}}{100} \cdot \frac{44}{12}$$
The GPC share is classified from random reflectance $R_o$ and the molar H/C ratio:
$$\mathrm{GPC} = \text{total}_{\mathrm{CO_2e}}\cdot\frac{\text{GPC\%}}{100}, \qquad \mathrm{SPC} = \text{total}_{\mathrm{CO_2e}} - \mathrm{GPC}$$
Alternatively, GPC and SPC may be supplied directly (e.g. from a registry record), which overrides the classification above.
Using the closed-form analytic integral of the retention curve (not a numerical sum):
$\mathrm{CINK}_H$ is the annual average carbon retained — this integral divided by the horizon $H$:
$$\mathrm{CINK_{SPC}} = \mathrm{SPC}\cdot\frac{\Phi_{\mathrm{SPC}}(H)}{H}, \qquad \mathrm{CINK_{both}} = \mathrm{CINK_{SPC}} + \mathrm{GPC\ contribution}$$
GPC is the permanent (geological) pool, treated as constant for any horizon, so its $\mathrm{CINK}_H$ contribution equals its full mass (or the available GPC after offsetting — see §4).
When the draw-from-GPC toggle is on, production emissions are retired from the persistent pool:
$$\mathrm{available\ GPC} = \max\!\left(0,\ \mathrm{GPC} - \mathrm{offset}\right), \qquad \mathrm{shortfall} = \max\!\left(0,\ \mathrm{offset} - \mathrm{GPC}\right)$$
This available GPC is the mass used in $\mathrm{CINK_{both}}$ and $\mathrm{TCE_{GPC}}$. With the toggle off, the full GPC is used and no shortfall is reported.
TCE is a separate integral of the same SPC decay curve against the CO2 impulse-response function (IRF) — it is not a rescaling of $\mathrm{CINK}_H$. It measures the radiative-forcing-equivalent climate benefit over the horizon, in tonne-CO2e years. Following Schmidt & Hagemann (2026), removals (cooling) are reported as negative.
The IRF (Jeltsch-Thömmes & Joos 2019, five-term) is
The SPC-sink kernel $I(H)$ is the closed-form analytic integral of $f_{\mathrm{SPC}}(t)\,\mathrm{IRF}(t)$ (Schmidt & Hagemann 2026, Eq. 19), with $(A_1,k_1)=(0.1787,0.5337)$ and $(A_2,k_2)=(0.8237,0.00997)$:
$\bigl[\,I(20)\approx 11.151,\quad I(100)\approx 28.441,\quad I(200)\approx 34.801\ \text{yr}\,\bigr]$
The persistent GPC pool does not decay over $H\le 1000$, so it uses the constant-pulse IRF integral:
$$\mathrm{TCE_{SPC}} = -\,\mathrm{SPC}\cdot I(H), \qquad \mathrm{TCE_{GPC}} = -\,\mathrm{GPC}\cdot\mathrm{irf_{int}}(H), \qquad \mathrm{TCE_{total}} = \mathrm{TCE_{SPC}} + \mathrm{TCE_{GPC}}$$
The GPC mass used mirrors the same available-vs-full GPC toggle that feeds $\mathrm{CINK_{both}}$ (§4).
The retired production emissions are a CO2 pulse whose climate effect is the mirror image — a warming (positive) — over the same horizon, using the same constant-pulse integral:
$$\mathrm{TCE_{emission}} = +\,\mathrm{offset}\cdot\mathrm{irf_{int}}(H), \qquad \mathrm{TCE_{net}} = \mathrm{TCE_{total}} + \mathrm{TCE_{emission}}$$
The TCE diagram plots the cumulative effect at each year $t\le H$: the sink cooling below the axis ($-\,[\,\mathrm{SPC}\cdot I(t) + \mathrm{GPC}\cdot\mathrm{irf_{int}}(t)\,]$) and the emission warming above it ($+\,\mathrm{offset}\cdot\mathrm{irf_{int}}(t)$). A net cooling results when the sink outweighs the emissions.
POST https://dev.ithaka-institut.org/api/cink-calc| Key | Type | Description |
|---|---|---|
mass_biochar | Float | Biochar dry mass (t). |
carbon_pct | Float | Organic carbon, % of dry mass. |
hc_ratio | Float | Molar H/C ratio (optional if Ro > 3.8). |
ro_reflectance | Float | Random reflectance Ro, % (optional). |
gpc_override | Float | Direct GPC (tCO2e); supply with spc_override. |
spc_override | Float | Direct SPC (tCO2e). |
co2_offset | Float | Production emissions to retire (tCO2e). |
horizon | Integer | Horizon H in whole years (≥ 1, may exceed 1000; default 100). |
offset_from_gpc | Boolean | Subtract the offset from GPC. |
{
"mass_biochar": 100.0,
"carbon_pct": 80.0,
"ro_reflectance": 4.0,
"horizon": 100.0,
"offset_from_gpc": true
}{
"gpc_override": 264.0,
"spc_override": 29.33,
"horizon": 100.0
}