Tank Volume and Fill Percentage: Two Examples
A tank volume calculation needs a defined shape and an internal liquid height. Rectangular and vertical cylindrical tanks have a constant horizontal area, making the ideal volume proportional to height; many real tanks do not behave that simply.
Published:
Concepts
Rectangular internal geometry
For internal length L, width B and height H, horizontal area is L × B. Multiply by H for total geometric capacity and by liquid height h for contained liquid. Use internal usable dimensions, not external steel dimensions.
Vertical cylindrical geometry
A vertical cylinder uses πD²/4 as its constant area. Its diameter is internal, and height is measured vertically from the chosen internal datum. The same formula does not give the liquid volume of a horizontal cylinder.
Remaining volume and fill percentage
Remaining geometric volume is total minus liquid volume; Fill % is liquid volume divided by total volume times 100. For these constant-area shapes, the fill fraction also equals h/H. Geometric remaining space is not necessarily the permitted operating fill allowance.
Real tank capacity
Internal structures, unusable or dead volume, sumps, irregular bottoms, trim and list may alter the volume associated with a sounding. A vessel's capacity or sounding calibration table may therefore take precedence over a simple ideal-shape calculation.
Basic formulas
Rectangular: A = L × B Vertical cylinder: A = π/4 × D² Vtotal = A × H; Vliquid = A × h Vremaining = A × (H − h) Fill [%] = Vliquid / Vtotal × 100 0 ≤ h ≤ H; V [L] = V [m³] × 1,000
- L: internal length; B: width; H: total height; h: liquid height; D: internal diameter. All are in m; L, B, H and D are positive, and 0 ≤ h ≤ H.
- A: horizontal area in m²; Vtotal: total, Vliquid: liquid and Vremaining: remaining geometric volume, all in m³.
- Fill: volume ratio in percent; multiply m³ by 1,000 to obtain L.
Worked example
First use a 4 m × 3 m × 2 m rectangular tank at h = 1.2 m. Then use a vertical cylinder of diameter 2 m and height 3 m at h = 1.5 m. Both examples assume level liquid and an unobstructed ideal shape.
Rectangular: L = 4 m; B = 3 m; H = 2 m; h = 1.2 m Vtotal = 24.000 m³; Vliquid = 14.400 m³; Vremaining = 9.600 m³; Fill = 60.0% Vliquid = 14400 L Vertical cylinder: D = 2 m; H = 3 m; h = 1.5 m Vtotal = 9.425 m³; Vliquid = 4.712 m³; Vremaining = 4.712 m³; Fill = 50.0% Vliquid = 4712.389 L
The rectangular tank contains 14.4 m³, or 14,400 L, at 60% geometric fill; 9.6 m³ remains. The cylinder has approximately 9.425 m³ total and 4.712 m³ liquid at 50% fill.
These quantities are not an authorized loading limit. Leave required operating margins and follow approved tank-capacity data and service procedures.
How to use this in practice
Use geometric capacity for early layout comparison, an independent arithmetic check or an estimate for a clearly defined simple tank. Record whether dimensions are internal and which height datum is used.
For an actual ship tank, consult the approved capacity/calibration table and required corrections. Compare a sounding to its table rather than assuming that half the height always means half the capacity in an irregular tank.
Common mistakes
- Entering external dimensions counts wall material as usable capacity.
- Applying the vertical-cylinder formula to a partly filled horizontal tank gives an incorrect volume-height relationship.
- Calling the geometric remainder safe loading capacity ignores operating limits, expansion margins and calibration.
Related calculators
Related guides
Frequently asked questions FAQ
Can this calculate a horizontal cylindrical tank?
Not with these formulas. Partial filling of a horizontal cylinder requires circular-segment geometry and an appropriate dedicated method.
Does 60% height always mean 60% volume?
Only for a constant-area tank under the stated assumptions. Irregular geometry and internal structures can change that relationship.
What should I use for an actual ship tank?
Use the vessel's approved capacity or sounding calibration information and required corrections. The ideal-shape result is a reference check, not a replacement.
References
Engineering Disclaimer
Calculations and examples are references based on general formulas and stated assumptions. Before design, construction, manufacturing, inspection or approval, check applicable standards, project requirements and approved manufacturer or vessel data, and follow the required review procedures. These results do not imply certification or design approval by any authority.
Calculation disclaimer