Articles

How do you calculate CBAM direct emissions with a mass balance?

For an electric arc furnace the carbon arrives in a dozen materials and leaves in three. The mass balance counts it at the door, not at the stack.

Julian R. Sterling · from The CBAM Compliance Handbook

Under the mass balance method, direct emissions are the carbon contained in every input less the carbon contained in every output, multiplied by 3.664, the ratio of the molecular weight of CO2 to that of carbon. Fuels burned completely, such as natural gas, go on the standard method alongside. For an illustrative electric arc furnace making 500,000 tonnes of crude steel, 12,201 tonnes of net carbon give 44,706 tCO2, gas adds 22,440, and the attributed direct emissions are 67,146 tCO2. With pig iron and ferro-manganese carried in as precursors, the specific embedded emissions are 0.3933 tCO2e a tonne.

Worked in full in The CBAM Compliance Handbook by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →

The assumptions

The monitoring rules of the CBAM definitive period, which follow those of the EU ETS, allow two calculation-based methods alongside continuous measurement. The standard method takes activity data times an emission factor times an oxidation factor, fuel by fuel. The mass balance takes every carbon-bearing material across the installation boundary, with inputs positive and outputs negative, as set out in Annex III to Implementing Regulation (EU) 2023/1773 for the transitional period: activity data times carbon content times 3.664, summed over the source streams. The plant below is fictional; tonnages and carbon contents are illustrative orders of magnitude, and the carbon contents of a real installation come from its own sampling and analysis plan.

Carbon across the boundary, one year

Material	Tonnes	Carbon content	Tonnes of carbon
Scrap	470,000	0.20%	940
Pig iron	60,000	4.20%	2,520
Charge coal	6,000	85.00%	5,100
Injection carbon	4,500	88.00%	3,960
Graphite electrodes	900	99.00%	891
Carbon in			13,411
Crude steel (output)	500,000	0.15%	-750
Slag (output)	60,000	0.50%	-300
Dust (output)	8,000	2.00%	-160
Net carbon			12,201

Step 1: the mass balance

The charge coal, injection carbon and electrodes bring 9,951 of the 13,411 tonnes of carbon in. The pig iron brings 2,520, which is emitted here, in the furnace, as the iron is decarburised into steel.

Step 2: fuels on the standard method

Step 3: add the precursors and divide

Crude steel is a CBAM good with relevant precursors: pig iron and ferro-alloys among them. Scrap is not one, and brings no embedded emissions of its own. Each precursor consumed is carried in at its own specific embedded emissions, which the supplier of the pig iron or alloy must provide; the values below are illustrative.

Specific embedded emissions of the crude steel

Component	tCO2e	Per tonne	Share
Direct, attributed (mass balance and gas)	67,146	0.1343	34.1%
Pig iron, 60,000 t at 2.10	126,000	0.2520	64.1%
Ferro-manganese, 2,500 t at 1.40	3,500	0.0070	1.8%
Total over 500,000 t of crude steel	196,646	0.3933	100%

An importer of 40,000 tonnes of this steel, or of products made from it, declares 15,732 tCO2e on it. At an illustrative 80.00 a certificate, the full exposure once free allocation has gone is 1,258,536, or 31.46 a tonne; how much of that is payable year by year is worked in how much CBAM will cost per tonne of steel from 2026 to 2034. Products further down the chain carry this figure in as their own precursor, the step worked in CBAM embedded emissions for a steel product.

What if the charge changes?

The pig iron, at 11.3 per cent of the metallic charge, is 64.1 per cent of the answer. Replace scrap with pig iron tonne for tonne, holding everything else, and both its carbon in the mass balance and its precursor emissions rise.

Specific embedded emissions by pig iron share of the metallic charge

Pig iron, t	Share of charge	Mass balance, tCO2	SEE, tCO2e/t	Declared on 40,000 t
0	0.0%	35,912	0.1237	4,948
60,000	11.3%	44,706	0.3933	15,732
130,000	24.5%	54,966	0.7078	28,312
200,000	37.7%	65,225	1.0223	40,893

For a buyer comparing two arc furnace suppliers, the first question is not the furnace but the charge: an all-scrap melt at 0.1237 and one with a quarter pig iron at 0.7078 are both "EAF steel".

The common mistakes

• Leaving out the outputs. Multiplying all 13,411 tonnes of carbon in by 3.664 gives 49,140 tCO2, 4,434 too many, because the carbon that stays in the steel, the slag and the dust is never emitted. The product's SEE comes out at 0.4022, 2.3 per cent high.
• Omitting the precursors. Declaring the furnace's own 0.1343 understates the steel by 65.9 per cent. The pig iron's emissions happened at the blast furnace, but they belong to this product.
• Dividing by metal charged instead of steel produced. The activity level is the 500,000 tonnes of crude steel, not the 530,000 of scrap and pig iron; dividing by the input gives 0.3710.
• Adding the electricity. For iron and steel only direct emissions count. The furnace's 0.40 MWh a tonne at a 0.60 grid factor is 120,000 tCO2, 0.24 a tonne, and none of it belongs in the declared figure.

Takeaway

• Mass balance: (carbon in − carbon out) × 3.664; fuels burned completely on the standard method.
• Here 44,706 + 22,440 = 67,146 tCO2 direct, and 0.3933 tCO2e a tonne with precursors.
• Scrap brings no embedded emissions; pig iron brings most of them.

The supplier data request, the default-or-actual log and the obligation line by line are among the working documents in the free files for this book.

Questions readers ask

When is the mass balance method used instead of the standard method?

The standard method multiplies each fuel or material by an emission factor; it suits a fuel burned completely, such as natural gas. The mass balance tracks carbon in and out and suits processes where carbon enters in many materials and part of it leaves in products and wastes, as in steelmaking. Here gas is on the standard method, 22,440 tCO2, and the carbon materials on the mass balance, 44,706.

Does scrap carry embedded emissions under CBAM?

Scrap is not a relevant precursor, so it brings no embedded emissions of its own into crude steel. Its small carbon content still enters the mass balance, 940 tonnes of carbon on 470,000 tonnes here. Pig iron, by contrast, is a precursor: 60,000 tonnes at an illustrative 2.10 add 126,000 tCO2e, more than the furnace's own direct emissions.

Is the electricity of an electric arc furnace counted for CBAM?

Not for iron and steel in the definitive period, where only direct emissions count towards the embedded emissions. At an illustrative 0.40 MWh a tonne and a grid factor of 0.60, the furnace here uses electricity responsible for 120,000 tCO2, 0.24 a tonne, none of which enters the 0.3933 declared.

Also on this site

• How do you calculate CBAM embedded emissions for a steel product?Process emissions plus precursor consumed times its SEE, over output. 2,400 plus 21,500 t of wire rod at 1.90, over 20,000 t, gives 2.1625 tCO2e a tonne.
• How much will CBAM cost per tonne of steel from 2026 to 2034?With a 1.37 benchmark, 2.0 tCO2 a tonne and 80 euro certificates, CBAM costs 53.14 euros a tonne of steel in 2026, 103.56 in 2030 and 160.00 in 2034.
• How do you calculate CBAM embedded emissions for aluminium?Direct emissions only: extrusion process plus billet consumed times its SEE, over output. An illustrative profile gives 2.1925 tCO2e a tonne, coal or hydro.
• How do you calculate CBAM embedded emissions for ammonium nitrate?Own emissions, direct and indirect, plus ammonia and nitric acid consumed times their SEE, with N2O at a GWP of 265. An illustrative plant gives 1.55 tCO2e a tonne.
• How do you calculate CBAM embedded emissions for hydrogen?Gas feed and fuel times 56.1 tCO2 per TJ, less the exported steam, over tonnes of hydrogen. An illustrative reformer gives 8.9012 tCO2 a tonne, or 0.71 a kg.
• Is it worth staying under the CBAM 50 tonne threshold?Crossing 50 tonnes by 5 brings all 55 into CBAM. In 2026 the certificates cost 210 euros; the fixed compliance cost, 15,000 illustrative, is what makes the cliff.

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