Type a line (850 m3 at 45 °C density 991.0 kg/m3) or fill in the fields: the line and the fields stay in step.
Enter the observed volume of the fuel received, in m3 or litres, from the tank sounding or the meter, the tank or meter temperature and the density at 15 °C from the bunker delivery note (BDN), and the calculator gives the volume correction factor (VCF) by the 1980 ASTM D1250 Table 54B equation for fuel oils, the volume at 15 °C and the mass in vacuum and in air. With the ordered quantity it gives the difference in tonnes and per cent; with a mass instead of a volume it gives the volume to take at the tank temperature. It shows the working with your numbers, draws the two volumes to one scale, and gives a line you can copy or add to a request.
The calculator covers the fuel oil band of the table, density at 15 °C from 839.0 to 1075.0 kg/m3: lighter products such as jet fuel, kerosene and gasoline use other constants, which it does not cover, and it says so instead of giving a figure. It is a reference check and does not replace the tank calibration tables, the meter calibration data, the bunker delivery note or the survey report.
Table 54B (1980) for fuel oils: alpha15 = 186.9696 / rho15^2 + 0.4862 / rho15, and VCF = exp(-alpha15 x dt x (1 + 0.8 x alpha15 x dt)) with dt = t - 15 °C. At 991.0 kg/m3: alpha15 = 0.00068100 per °C; at 45 °C, dt = 30 and VCF = 0.97945, or 0.9795 to four decimals.
V15 = observed volume x VCF. 850 m3 at 45 °C: 850 x 0.9795 = 832.575 m3. The fuel shrinks as it cools to 15 °C, so V15 is below the observed volume when the fuel is warmer than 15 °C, and above it when colder.
Mass in vacuum = V15 x rho15 = 832.575 x 991.0 / 1000 = 825.082 t. Mass in air = V15 x (rho15 - 1.1) = 832.575 x 989.9 / 1000 = 824.166 t: the weight-in-air correction takes the density in air as 1.1 kg/m3 (0.0011 kg/l) below the density in vacuum.
| Quantity | Relation | Note |
|---|---|---|
| Thermal expansion coefficient | alpha15 = K0 / rho15^2 + K1 / rho15 | K0 = 186.9696, K1 = 0.4862; fuel oils, density at 15 °C from 839.0 to 1075.0 kg/m3 |
| Volume correction factor (VCF) | VCF = exp(-alpha15 dt (1 + 0.8 alpha15 dt)) | dt = t - 15 °C; rounded to four decimals |
| Volume at 15 °C | V15 = V x VCF | m3 at 15 °C |
| Mass in vacuum | V15 x rho15 | t = m3 x kg/m3 / 1000 |
| Mass in air | V15 x (rho15 - 1.1) | weight-in-air correction: 1.1 kg/m3 = 0.0011 kg/l |
| Reverse | V = m / (rho15 - 1.1) / VCF | for a mass in air; m / rho15 / VCF in vacuum |
| Units | 1 m3 = 1000 l; 1 kg/l = 1000 kg/m3 | t = (°F - 32) / 1.8 for °C |
The calculator works the 1980 Table 54B equation from the density and the temperature as entered and rounds the VCF to four decimals, as the printed tables give it; V15 and the masses are worked from that factor and shown to three decimals. The 1980 procedure also rounds the inputs and the intermediate values (the density to 0.5 kg/m3), which the calculator does not, so the last digit can differ from a printed table. It is a reference check, not a replacement for the bunker delivery note or the survey report.
The equation and the constants of Table 54B (1980) for generalized products, fuel oil band 839.0 to 1075.0 kg/m3, K0 = 186.9696 and K1 = 0.4862, are given in the ASTM D1250-80 / API MPMS Chapter 11.1 (1980) metric tables and reproduced in flow computer documentation and in the Table 54B formula sheets used in cargo and bunker surveys; the upper edge, 1075.0 kg/m3, is the upper density limit of the 1980 Tables 53B and 54B. The calculator reproduces published 1980 Table 54B values (for example 840 kg/m3 at 40 °C: 0.9788 and at -10 °C: 1.0210, from a national weights and measures table; 903.5 kg/m3 at 30.5 °C: 0.988067 unrounded, from a formula sheet). The 2004 revision (API MPMS Chapter 11.1-2004, ASTM D1250-04) does not round the inputs or the intermediate values, rounds the factor to five decimals and adds a small temperature-scale term, so its four-decimal factor can differ from the 1980 table in the fourth decimal. The correction of 1.1 kg/m3 (0.0011 kg/l) between the density in vacuum and in air is the weight-in-air correction used in cargo and bunker calculations.
In four steps. The thermal expansion coefficient from the density at 15 °C: alpha15 = 186.9696 / rho15^2 + 0.4862 / rho15. The volume correction factor: VCF = exp(-alpha15 x dt x (1 + 0.8 x alpha15 x dt)), with dt = t - 15 °C. The standard volume: V15 = observed volume x VCF. The mass: V15 x rho15 in vacuum, V15 x (rho15 - 1.1) in air. For 850 m3 at 45 °C with 991.0 kg/m3: alpha15 = 0.00068100 per °C, VCF = 0.9795, V15 = 832.575 m3, 825.082 t in vacuum and 824.166 t in air.
Taken as a true density, in vacuum, the density at 15 °C gives the mass in vacuum: V15 x rho15. Weighed in air, the fuel is lighter by the air it displaces: the weight-in-air correction takes 1.1 kg/m3 (0.0011 kg/l) off the density, so the mass in air is V15 x (rho15 - 1.1). For 832.575 m3 that is 0.916 t less. The calculator shows both.
The 1980 tables form: the equation above with K0 = 186.9696 and K1 = 0.4862 for the fuel oil band, the factor rounded to four decimals. The 2004 revision (API MPMS Chapter 11.1-2004, ASTM D1250-04) works without rounding the inputs or the intermediate values, adds a small temperature-scale term and rounds the factor to five decimals; for refined products its four-decimal factor can differ from the 1980 table in the fourth decimal. Where a figure has to match a document, use the edition the document names.
It works the equation from the density and the temperature as entered, rounds the VCF to four decimals as the printed 1980 tables give it, and works V15 and the masses from that factor, shown to three decimals. The 1980 procedure also rounds the inputs and the intermediate values, the density to 0.5 kg/m3, which the calculator does not do, so the last digit can differ from a printed table. It is a reference check, not a replacement for the bunker delivery note or the survey report.
Densities at 15 °C from 839.0 to 1075.0 kg/m3, the fuel oil band of Table 54B (1980), in kg/m3 or kg/l (0.9910 is read as 991.0 kg/m3); lighter products such as jet fuel, kerosene and gasoline use other constants, which the calculator does not cover. Temperatures from -10 to 100 °C, in °C or °F. Volumes in m3 or litres, masses in tonnes or kg.
Enter a mass instead of a volume, such as need 500 t at 40 °C density 975. The calculator works the VCF, 0.9825, then V15 = 500 x 1000 / (975 - 1.1) = 513.400 m3 for 500 t in air, and the volume at 40 °C, 513.400 / 0.9825 = 522.544 m3; for 500 t in vacuum, 512.821 m3 at 15 °C and 521.955 m3 at 40 °C.
The calculator gives the quantity of fuel received. When parts for the fuel system are needed, for the separators, filters, pumps or meters, send the line from the calculator with the engine details and a photograph of the nameplate, and Vessel Core checks the details before an offer goes back.
