Volume correction factor and density at 15 °C explained

A volume correction factor (VCF) converts a volume measured at tank temperature into the volume the liquid would occupy at a reference temperature, usually 15 °C. Multiply that volume by the density at 15 °C and you have the mass. The volume changes with temperature; the mass does not.

Why volume moves with temperature and weight does not

A liquid expands as it warms: the same tonnes take up more cubic metres. A cargo loaded warm and measured cooler shows a smaller volume, yet its mass is unchanged. In trade, "weight" is a mass quantity, in kilograms or tonnes: NIST's guide to the SI notes that in commercial use weight is usually a synonym for mass. Whether it is stated in vacuo or in air is a separate convention, covered below.

That is why trade rules settle quantities as weights. The NIOP Trading Rules (effective 17 April 2025) have weights expressed in pounds and metric tons to three decimals, converted at 2,204.6 lb per tonne. FOSFA's Code of Practice for Member Superintendents (revised November 2022) has weights established in accordance with the relevant FOSFA contract. A volume only means something with its temperature attached.

What a volume correction factor does

VCF = volume at 15 °C ÷ volume at the observed temperature, so volume at 15 °C = observed volume × VCF. Above 15 °C the factor is below 1; below 15 °C it is above 1. OIML's recommendation R 63 (1994) sets 15 °C as the reference temperature for official quantities of petroleum, allowing 20 °C or 60 °F where national rules require.

How far it moves per degree depends on how strongly the liquid expands. For petroleum, the procedures sit in the joint API and ASTM Adjunct, API MPMS Chapter 11.1, which ASTM D1250-25 describes. The metric procedures cover base temperatures of 15 °C and 20 °C; they first compute the density at 60 °F with the customary-unit procedure and correct from there. At one atmosphere the pressure correction drops out. The algorithms themselves sit in supplementary adjuncts; this article uses none of those tables.

Density, relative density and density in air

Three terms that are easily confused:

• Density is mass divided by volume, in kg/m³ (NIST SP 811). It changes with temperature, so a density always carries one: 920.0 kg/m³ at 15 °C.
• Relative density is the ratio of a density to a reference density, usually that of water; IUPAC notes that older literature calls it specific gravity. It has no unit and needs both temperatures, liquid and water, to mean anything.
• Density in air, or apparent density, is the mass per volume as a balance in air would show it. FOSFA's code uses the term litre weight in air: the conventional mass per volume of a liquid oil, used to convert volume to mass, with reference to ISO 6883.

The difference comes from air buoyancy. OIML D 28 (2004) sets the conventions for weighing in air: air of 1.2 kg/m³, reference weights of 8,000 kg/m³ and a reference temperature of 20 °C. Its relation between mass and conventional mass, m × (1 − 1.2/ρ) ÷ (1 − 1.2/8,000), gives a liquid of 920.0 kg/m³ an apparent density of 918.938 kg/m³ in air: 1.062 kg/m³, or about 0.12%, less. A weight certificate should therefore say whether it gives weight in vacuo or in air.

Two routes from volume to weight

Route 1, the petroleum tables: observed volume × VCF = volume at 15 °C, and volume at 15 °C × density at 15 °C = mass. With a density in vacuo, the result is a mass in vacuo.

Route 2, the NIOP rules for vegetable oils: a laboratory determines the litre weight in air at the average tank temperature at the time of gauging, using AOCS Official Method Cc 10c-95, and the weight is the observed volume times that figure. No VCF is needed, because the density already belongs to the tank temperature. The result is a weight in air.

The two agree only if volume and density refer to the same temperature and to the same basis, in vacuo or in air. The errors to avoid are mixing them: a density at 15 °C applied to an uncorrected volume, or a weight in air compared with a mass in vacuo. NIOP averages at least three levels in each tank, and FOSFA's heating guidelines do not regard a tank as evenly heated when top and bottom differ by more than 5 °C.

Worked example: from tank volume to weight with the EU factor

This continues the ullage report and sounding tables example: 1,905.958 m³ observed at an average of 36.5 °C. The density at 15 °C, 920.0 kg/m³ in vacuo, is our own choice, from no table. For vegetable oil in the EU the density is corrected to tank temperature with 0.00068 kg/l per °C: ρT = ρ15 − (T − 15) × 0.00068. A real calculation uses the table, standard or method the contract prescribes.

Step	Calculation	Result
Temperature above 15 °C	36.5 − 15	21.5 °C
Density at tank temperature	0.9200 − 21.5 × 0.00068 = 0.90538	0.9054 kg/l
Mass (in vacuo)	1,905.958 × 0.9054	1,725.654 t
Litre weight in air, OIML D 28 conventions	(0.9054 − 0.0012) ÷ (1 − 0.0012/8)	0.9043 kg/l
Weight in air	1,905.958 × 0.9043	1,723.558 t

Rounding rule: densities to four decimals, weights to three, always half up. The same result can be written as a volume correction factor: 0.9054 ÷ 0.9200 = 0.98413 (a VCF applied to the volume, with the 15 °C density, gives the same mass). The two ways of writing it agree only if the same temperature and the same basis, in vacuo or in air, are used throughout.

Three checks, by our calculation:

• Skipping the correction. 1,905.958 × 0.9200 = 1,753.481 t, which overstates the mass by 27.827 t, or 1.61%.
• Air versus vacuum. The weight in air is 2.096 t, or 0.121%, below the mass in vacuo. That is air buoyancy, not a loss; the certificate has to say which it gives.
• Sensitivity. An average temperature 1 °C too high gives 1,724.320 t, 1.334 t less. A density 1 kg/m³ too high adds 1,905.958 m³ × 0.001 t/m³ = 1.906 t.

Ship's and shore figures worked out this way still differ; the vessel experience factor helps judge whether a difference is normal. For the densities of palm oil and its fractions, see palm oil density.

Agree the method before the figures

Based on the working practice of our sector specialist: 25 years in the port, 20 of them as a cargo surveyor. Density is worked at 15 °C, and for vegetable oil in the EU the correction factor is 0.00068 per °C. Many loading ports work from a density list (density per temperature) instead of a formula, so the list has to be possible to enter by hand. The palm oil figures are in palm oil density.

Two surveyors who use different tables, reference temperatures or air conventions can both calculate correctly and still disagree by tonnes. Settle beforehand which method the contract names and whether weights are in air or in vacuo, and put both on the certificate. That is part of what an independent cargo surveyor does.

FOSS

FOSS is software for inspection companies and the port, with a sector specialist at the table. Readings are entered once, offline on board if need be, and nine report types come from that input.