Free tool
Bunker quantity calculator
Gauged volume and observed temperature in — metric tonnes in air out, with every step of the arithmetic shown. The volume correction factor is computed from the ASTM D1250-04 / API MPMS Ch. 11.1 relation using the Table 54B fuel-oil coefficients, not looked up from a copied table. Enter the bunker delivery note figure as well and it tells you how large the gap is, and whether it is larger than your own measurement uncertainty. Runs entirely in your browser; nothing you enter is sent anywhere.
1 · The delivery
Table 54B fuel-oil group: 838.5 – 1073.5 kg/m³. Covers HFO, VLSFO, LSMGO and MGO.
Enter volumes already corrected for trim and list from the vessel's own calibration tables. This tool does not model the tank geometry — it starts where your sounding tables end.
2 · The comparison optional
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- Volume correction factor: ASTM D1250-04 / API MPMS Chapter 11.1, the relation also published as ISO 91 — CTL = exp[−α₁₅·ΔT·(1 + 0.8·α₁₅·(ΔT + δ))], with ΔT = T − 15 °C and δ = 0.01374979547. The factor is computed from the formula on every run, not read from a transcribed table.
- Thermal expansion coefficient: α₁₅ = K₀/ρ₁₅² + K₁/ρ₁₅ + K₂ using the Table 54B fuel-oil constants K₀ = 186.9696, K₁ = 0.4862, K₂ = 0, valid for density at 15 °C between 838.5 and 1073.5 kg/m³. Cross-checked: ρ₁₅ = 991.0 kg/m³ gives α₁₅ = 6.81 × 10⁻⁴ and CTL = 0.9760 at 50 °C, matching the published 54B table entry.
- Weight in air: metric tonnes = V₁₅ × (ρ₁₅ − 1.1) ÷ 1000, where 1.1 kg/m³ is the standard air-buoyancy correction applied to convert density in vacuum to weight in air — the same convention the bunker delivery note uses.
- Deliberately out of scope: trim and list corrections (they come from the vessel's calibration tables), the gasoline, jet and transition density groups (different constants, no bunker application), water content and sediment, and any judgement on whether a shortfall is a claim. The joint survey record prevails over this calculation.
The survey behind the arithmetic
The calculation is the last step of a procedure that decides whether the numbers going into it mean anything. What to gauge before the hose is connected, how to read foam in a sounding pipe, what the MARPOL sample is for and how a quantity dispute is actually argued — the bunker survey guide walks the whole sequence from the barge deck.
Questions
How is bunker quantity calculated from a sounding?
The sounding or ullage gives an observed volume through the tank calibration tables, already corrected for the vessel's trim and list. That volume is corrected to 15 °C with the volume correction factor for the fuel's density at 15 °C, and the corrected volume is multiplied by the density less the air-buoyancy correction of 1.1 kg/m³ to give metric tonnes weight in air. This tool does the last two steps; the trim and list correction comes from your own tables.
Why does the calculator ask for the temperature twice?
Because the tank is not at the same temperature before and after the delivery — heated fuel comes aboard and the receiving tank warms. Correcting each sounding at its own observed temperature and then taking the difference is the correct order. Taking the difference in observed volume first and then correcting it at one temperature is a common shortcut that shifts the result, and the shift goes against the vessel when the warmer figure is the larger one.
Which density do I enter — the BDN figure or the lab result?
Enter density at 15 °C in vacuum, which is what the bunker delivery note states and what ISO 3675 / ISO 12185 report. The tool applies the 1.1 kg/m³ air-buoyancy correction itself to give weight in air, so do not subtract it beforehand. If your lab result differs from the BDN figure, run the calculation both ways — the difference panel is there for exactly that comparison.
Does this prove I was short-delivered?
No. It gives you the arithmetic and the size of the gap, which is what a letter of protest has to rest on. A quantity claim is settled on the survey record as a whole: joint gauging, the sounding log, sealed samples, the temperature readings taken at the time, and the barge figures. The calculator tells you whether the gap is bigger than the measurement uncertainty — the sensitivity panel shows what one degree and one density unit are actually worth in tonnes.
What about the cappuccino effect?
Air entrained into the fuel makes a sounding read more volume than the liquid actually present, so every step downstream inherits the error. The calculator cannot detect it — nothing computed from the sounding can. What it does show is the price of it: the panel converts an assumed entrained-air fraction into tonnes and money, so you can see why re-gauging after the foam collapses is worth the delay.
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