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Tank content calculator

Read liquid depth correctly in a rectangular or horizontal cylindrical tank. The curved-tank fill fraction is not generally equal to depth divided by diameter.

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The method

Rectangle: V = Lwd. Horizontal cylinder: V = L[r² acos((r−d)/r) − (r−d)√(2rd−d²)].

Before using the result

  • Level tank with constant internal cross-section and no deadwood or end-cap allowance.

Worked examples

These original training examples illustrate the method for USCG Chief Engineer Unlimited (UCEU). Use the matching “Load example” button above to explore a variation; example values are not equipment settings or prescribed criteria.

1. Worked example

Read liquid depth correctly in a rectangular or horizontal cylindrical tank. The curved-tank fill fraction is not generally equal to depth divided by diameter.

Tank shape
Rectangular
Tank length
4 m
Internal width
2 m
Internal height
2 m
Liquid depth
1 m
  1. Shape: Rectangular; internal length = 4 m; depth = 1 m.
  2. Calculated contents = 8 m³; fill = 8 / 16 × 100%.
  • Contents: 8 m³
  • Capacity: 16 m³
  • Fill: 50 %

2. Comparison example

Compare a different supplied condition using the same method. For Marine Exam, the important check is that the input meaning, units and method assumptions still match the problem.

Tank shape
Rectangular
Tank length
4 m
Internal width
2 m
Internal height
2 m
Liquid depth
0.5 m
  1. Shape: Rectangular; internal length = 4 m; depth = 0.5 m.
  2. Calculated contents = 4 m³; fill = 4 / 16 × 100%.
  • Contents: 4 m³
  • Capacity: 16 m³
  • Fill: 25 %

Check your understanding

1. Which relationship is used?

Rectangle: V = Lwd. Horizontal cylinder: V = L[r² acos((r−d)/r) − (r−d)√(2rd−d²)].

2. Which assumption should you check first?

Level tank with constant internal cross-section and no deadwood or end-cap allowance.

3. How should you verify a different unit system?

Convert every input to the displayed calculation units first. Equivalent physical inputs must give equivalent results; a unit label alone does not convert a number.

Continue with the matching exam topic

This tool connects to USCG Chief Engineer Unlimited (UCEU) free practice. Work through a question independently, then use the calculation steps to identify where your method differs. The tool stays free whether or not you choose paid preparation.

Tank content calculator — free with working | Marine Exam