Type a line (box 2000 x 1500 x 1000 mm level 600, horizontal 1200 x 3000 mm level 400, vertical cylinder D 1500 H 2000 mm level 800 density 999.1) or fill in the fields: the line and the fields stay in step.
Pick the shape of the tank — a box, a vertical cylinder, a horizontal cylinder with flat ends or with 2:1 ellipsoidal heads — and enter the inside dimensions and the level from the bottom in mm, cm, m or inches. The calculator gives the total volume, the volume at the level in m3, litres and per cent of full, the ullage, and with a density the mass in kg and tonnes. It shows the working with your numbers, draws the tank to scale with the liquid up to the level, and for a horizontal tank gives a sounding table you can copy.
This is the geometry of an ideal shape. Frames, pipes, heating coils, a sloping bottom, trim and heel are not taken into account; the calibrated sounding tables of the ship govern. The densities on the page are examples to pick from only, each with its temperature or status; no tank rules or class requirements are given here.
The section does not change with height, so the volume is in proportion to the level: V = L x W x h for a box and V = 3.1416 x D x D / 4 x h for a vertical cylinder. A box of 2000 x 1500 x 1000 mm at a level of 600 mm holds 1.8 m3 of 3 m3.
The liquid in the section is a circular segment: A = r^2 acos((r-h)/r) - (r-h) sqrt(2rh - h^2), and the volume is A x L. For D 1200 x L 3000 mm at a level of 400 mm that is 0.3300 m2 x 3 m = 0.990 m3 of 3.393 m3.
The inside depth of a 2:1 ellipsoidal head is a quarter of the diameter; both heads at a level h add 3.1416 x a x h x h x (1 - h / (3r)), with a = D / 4. The mass is the volume times the density: 1.8 m3 x 890 kg/m3 = 1602 kg.
| Level, % of diameter | Volume, % of full | D 1000 mm, l per metre of length | D 2000 mm, l per metre of length |
|---|---|---|---|
| 0 | 0.0 | 0.0 | 0.0 |
| 10 | 5.2 | 40.9 | 163.5 |
| 20 | 14.2 | 111.8 | 447.3 |
| 30 | 25.2 | 198.2 | 792.7 |
| 40 | 37.4 | 293.4 | 1173.5 |
| 50 | 50.0 | 392.7 | 1570.8 |
| 60 | 62.6 | 492.0 | 1968.1 |
| 70 | 74.8 | 587.2 | 2348.9 |
| 80 | 85.8 | 673.6 | 2694.3 |
| 90 | 94.8 | 744.5 | 2978.1 |
| 100 | 100.0 | 785.4 | 3141.6 |
The per cent columns are the same for any horizontal cylinder with flat ends; multiply the litres per metre by the length of the tank in metres. With 2:1 heads the shares differ: the calculator above works them out. Units: 1 in = 25.4 mm, 1 m3 = 1000 l and 1 kg/l = 1000 kg/m3, all exact by definition.
The area of a circular segment and the volumes of a box and a cylinder are plain geometry. The partial volume of 2:1 ellipsoidal heads follows two published engineering methods for the volume of horizontal vessels, which give the same formula; the calculator is also checked against a numerical integration. Example densities: fresh water at 15 °C from water density tables (999.10 kg/m3); sea water at the typical 1025 kg/m3 that oceanography references give, with a spread of about 1020 to 1029 kg/m3; DMA, the upper limit in table 1 of ISO 8217, editions 2010 and 2017.
About 0.990 m3, or 990 litres, of 3.393 m3 full: 29.2 %. With r = 0.6 m and h = 0.4 m, the segment area is 0.36 x acos(0.2 / 0.6) - 0.2 x sqrt(2 x 0.6 x 0.4 - 0.4 x 0.4) = 0.3300 m2, and 0.3300 m2 x 3 m = 0.990 m3.
Because the section is a circle: narrow at the bottom and the top, widest in the middle. At 10 % of the diameter a flat-ended horizontal tank holds 5.2 % of its volume, at 20 % it holds 14.2 %, at 50 % exactly half. A box or a vertical cylinder fills in proportion to the level.
No. A real tank has frames, stiffeners, pipes and heating coils inside, often a sloping or stepped bottom, and the ship may trim or heel. The calibrated sounding tables of the tank govern; this page gives the geometry of an ideal shape, for a check or for a tank that has no table.
The density of the liquid in the tank, in kg/m3 or kg/l. For fuel, the bunker delivery note gives the density at 15 °C. The examples on the page are fresh water at 15 °C (999.1 kg/m3), sea water at a typical 1025 kg/m3 (real values about 1020 to 1029) and the ISO 8217 upper limit for DMA, 890 kg/m3 at 15 °C, which is a limit and not the density of a delivery. The calculator does not correct a density for temperature.
The inside depth of each 2:1 ellipsoidal head is a quarter of the diameter. Both heads full hold 2/3 x 3.1416 x r x r x r; at a level h they hold 3.1416 x a x h x h x (1 - h / (3r)), with a = D / 4. Enter the length of the cylindrical part, between the tangent lines. Torispherical, hemispherical and conical heads are not worked out here.
The calculator works out the geometry of an ideal tank from the dimensions you enter. When a part is needed — a level gauge, a valve, a filter, a pump — attach a photograph of the plate or the drawing, and Vessel Core checks the details before an offer goes back.
