Halyard
Halyard

How every number is calculated.

The mathematics behind a FuelEU Maritime and EU ETS position, in the order the engine applies it. The AI transcribes numbers from documents and never calculates one; everything below is the engine.

1. What counts: the scope of a voyage

Both regulations apply to energy used, and emissions released, on voyages that touch the EU or the EEA. Each voyage, and each period at berth, gets a share between 0 and 100%. Everything downstream is multiplied by that share.

Both ports in the EU or EEA
100%
One port in the EU or EEA
50%
At berth in an EU or EEA port
100%
Neither port in the EU or EEA
0%

A voyage is read from the noon reports between two port calls. A call at a listed neighbouring container transhipment port does not count as a port of call for a containership; the leg chains to the nearest real call on each side.

2. Energy

Every fuel row in a noon report (fuel, consumer, tonnes) becomes energy through the fuel's lower calorific value, weighted by the voyage's scope share.

E [MJ] = Σ  mᵢ [t] × LCVᵢ [MJ/t] × sᵢ        s = scope share

A vessel's energy for the year is the sum over all its fuel rows. The fleet's is the sum over vessels. Nothing is ever summed by hand.

3. Emissions, well to wake

Emissions have two parts. Well-to-tank covers producing and delivering the fuel and is given per megajoule. Tank-to-wake covers burning it and is given per tonne of fuel for each gas. The gases are weighted to CO₂-equivalent with a global warming potential, and the two regulations use different sets.

WtT [gCO₂e] = E [MJ] × f(WtT) [gCO₂e/MJ]

TtW [gCO₂e] = m × ( CO₂ + GWP_CH₄ × CH₄ + GWP_N₂O × N₂O )     per unit of fuel, slip included

I = ( WtT + TtW ) ÷ E
Global warming potentialFuelEU MaritimeEU ETS (MRV)
CH₄, methane× 25× 28
N₂O, nitrous oxide× 298× 265

FuelEU uses 25 for methane and 298 for nitrous oxide (Regulation (EU) 2023/1805, Annex I, by way of the Renewable Energy Directive); the EU ETS uses 28 and 265 (Delegated Regulation (EU) 2020/1044). The engine computes each regime with its own set, never one set for both.

Two rules stand out. For biofuels and renewable fuels that meet the sustainability criteria, tank-to-wake CO₂ counts as zero; the well-to-tank part still counts. For LNG, unburnt methane that slips through the engine is added as extra CH₄, and the slip depends on the engine type: a medium-speed Otto engine slips far more than a slow-speed diesel-cycle one.

4. Fuel factors

The factors the demo fleet runs on, from the Annex II defaults. Intensity is what the formulas above give for each fuel on its own under the FuelEU set; the ETS factor is tank-to-wake CO₂e per tonne under the ETS set, slip included.

FuelLCV, MJ/tWtT, g/MJIntensity, g/MJETS, tCO₂e/tAgainst 89.34
HFO40,50013.591.73.163above
VLSFO41,00013.291.43.200above
MGO42,70014.490.83.255above
LNG, Otto medium speed (3.1% slip)49,10018.589.23.561below
FAME (UCO), B30 share37,20014.916.40.049below

Fossil oils all sit just above the line. The same LNG is a deficit or a surplus depending on the engine. Certified biofuels are deep surpluses, which is what makes a blend work.

5. FuelEU Maritime: intensity, balance, penalty

FuelEU measures how clean the energy is, not how much of it there was. The intensity is compared with a limit set as a reduction from a 2020 fleet baseline of 91.16 gCO₂e/MJ. For 2025 to 2029 the limit is 91.16 × 0.98 = 89.34; the engine keeps it unrounded (89.3368).

B [gCO₂e]        = ( L − I ) × E                  positive = surplus, negative = deficit

D [t VLSFO-eq]   = | B | ÷ ( I × 41,000 )

P [€]            = D × 2,400 × ( 1 + (n − 1) ÷ 10 )     n = consecutive deficit years
FromLimit, gCO₂e/MJReduction from baseline
2025current period89.342%
203085.696%
203577.9414.5%
204062.9031%
204534.6462%
205018.2380%

The 41,000 MJ per tonne is the energy content of a reference tonne of very-low-sulphur fuel oil; expressing a deficit in those tonnes is what the regulation prescribes. The penalty is €2,400 per such tonne, and the multiplier grows by a tenth for every consecutive year a ship stays in deficit. It resets after a year with no EU voyages.

6. EU ETS: allowances

The ETS measures quantity. For every tonne of in-scope tank-to-wake CO₂-equivalent, one allowance must be surrendered. From 2026 methane and nitrous oxide are included and the phase-in is complete.

ETS [tCO₂e] = Σ  mᵢ [t] × f(ETS)ᵢ [tCO₂e/t] × sᵢ

cost [€]    = ETS × phase-in × EUA price
2024 emissions
40%
2025 emissions
70%
2026 emissions onward
100%

The demo fleet on this site is priced at €69.00 per allowance, a fixed input so every figure on the site moves together. Client dashboards use the current auction price.

7. Blends

A blend is never a stored fuel. It is computed from its components by energy share, so B30 is thirty percent FAME and seventy percent gas oil, weighted by the energy each contributes.

I(blend) = Σ shareᵢ × Iᵢ        shares by energy, Σ shareᵢ = 1
B30 intensity, FuelEU set
68.4 gCO₂e/MJ
B30 calorific value
40,886 MJ/t
Compliance balance earned per tonne of B30 burned
0.854 tCO₂e
Cost of abatement at a €150 per t premium
€176 per tCO₂e

8. Ways out of a deficit

A ship in deficit has five legal options, and only a calculation says which is cheapest. Halyard prices all five at the current inputs and ranks them.

Pool within the fleet

Combine the ship's balance with a surplus ship's. A pool is compliant only if its total balance stays at or above zero, Σ Bᵢ ≥ 0; it is recorded by 30 April and approved by the verifier. The cost is the surplus ship's forgone sale value.

Buy surplus externally

Pool with another owner's surplus ship. Priced at the market index, €108.60 per tCO₂e in the demo (offer-based), plus 8% fees and spread: €117.29 per tCO₂e.

Borrow from next year

Take an advance of up to 2% of the limit times the ship's energy, Borrow ≤ 0.02 × L × E. Repaid at 110% the next year, not usable two years running, and not combinable with pooling in the same year.

Blend on remaining voyages

Replace part of the year's fuel with a blend until the balance closes. The cost is the bunker premium, €150 per t of B30 in the demo; it also lowers the ETS bill.

Pay the penalty

The do-nothing baseline: the penalty above, with the consecutive-year multiplier, paid with the Document of Compliance by 30 June.

9. The five deadlines

For the 2026 reporting year every deadline falls in 2027. The 30 September 2026 surrender covers 70% of 2025 emissions; 2026 emissions are covered at 100%.

31 January 2027
Emissions and FuelEU data to the verifier
31 March 2027
FuelEU balance verified; verified emissions report submitted
30 April 2027
Pool, bank and borrow elections close
30 June 2027
FuelEU Document of Compliance; penalties paid
30 September 2027
EUA surrender for 2026 emissions

10. Worked example: one noon report

MV Atlas Trader, 9 March 2026, Rotterdam to Hamburg, EU to EU (100% in scope). HFO 26.0 t main engine, MGO 1.8 t auxiliary; 312 nm; remaining on board 842.0 to 816.0 t, which ties out. Every line is engine output for the demo fleet.

E = Σ m · LCV · s
1,129,860 MJ
WtT
15.3 tCO₂e
TtW, FuelEU set
88.3 tCO₂e
WtT + TtW
103.6 tCO₂e
I = (WtT + TtW) ÷ E
91.68 gCO₂e/MJ against 89.34
B = (L − I) · E, for the day
−2.64 tCO₂e
Penalty equivalent
€1,689
ETS = Σ m · f · s
88.1 tCO₂e, €6,079 in allowances

11. Worked example: one year

MV Atlas Trader, bulk carrier, handysize, over 2026: HFO 4,800 t and MGO 400 t, 60% of it in EU scope. Every line is engine output for the demo fleet.

Energy in scope
126,888,000 MJ
GHG intensity, FuelEU set
91.7 gCO₂e/MJ
Limit, 2026
89.34 gCO₂e/MJ
Compliance balance Deficit
−295.5 tCO₂e
Penalty if nobody acts, first year
€188,678
EU ETS allowances at €69.00
9,891 tCO₂e, €682,476

The five ways out, priced by the engine at the demo inputs, cheapest first:

1. Pool within the fleet€29,767281.2 t from MV Celtic Dawn (its forgone sale value) plus 14.2 t bought
2. Buy surplus externally€34,654€108.60 per t CO₂e plus 8 % fees and spread
3. Borrow from next year€35,146Cap 226.7 t, repaid at 110%, 68.7 t bought
4. Blend B30 on remaining voyages€51,896About 346 t of B30 at €150 per t premium, €176 per t CO₂e abated
5. Pay the penalty€188,67878.6 t VLSFO-eq at €2,400

Surplus from inside the fleet is priced at what its owner could have sold it for, €99.91 per tCO₂e after fees; bought surplus costs €117.29; B30 abates at €176. Across the demo fleet, €207,800 of penalties if nobody acts becomes €5,103 once the fleet's own surplus is pooled (−43.5 tCO₂e left to cover). The market sets the prices and a broker executes the trade; Halyard computes the position and ranks the options. At different prices the ranking changes, which is why it is computed rather than assumed.

12. Where the AI stops

The AI transcribes numbers from documents and never calculates one. It reads a noon report (PDF, scan, spreadsheet or pasted text) into fields; every transcribed value is tied out against the day before and the bunker records, and a person on our team checks every exception before it reaches the ledger. From there on, every figure on this page is a deterministic calculation: same inputs, same answer.

13. Sources and limits

  • Regulation (EU) 2023/1805 (FuelEU Maritime): intensity limits, Annex I method, Annex II default factors, borrowing (Art. 20), pooling (Art. 21), penalty (Art. 23).
  • Directive 2003/87/EC as amended for maritime transport, with the MRV monitoring rules and Delegated Regulation (EU) 2020/1044 for the ETS global warming potentials.
  • Directive (EU) 2018/2001 (RED II) Annex V, the source of FuelEU's global warming potentials via 2023/1805 Annex I.
  • OceanScore OPX index, September 2026, for the demo surplus price of €108.60 per tCO₂e. It is offer-based: what sellers ask, not what trades settle at.
  • Argus publishes a weekly FuelEU pooling price, the second reference we read beside the offer-based index. The demo uses the index figure only.
  • EEX primary auction results for the EUA price on client dashboards.

The fuel factors and prices on this page are the demo set the public site runs on; client dashboards run on the certified factor tables, the fuel certificates where they exist, and current prices. The savings estimate on the home page simplifies this page; a real position is computed report by report.