Marine Exam · Free practical tool

Displacement and buoyancy calculator

Relate submerged volume to displaced mass and upward force using the appropriate water density. Do not turn displacement arithmetic into a vessel-stability assessment.

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The method

Displaced mass = ρV; buoyant force = ρVg.

Before using the result

  • Hydrostatic displacement only. This does not assess stability, loading limits, freeboard or seaworthiness.

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

Relate submerged volume to displaced mass and upward force using the appropriate water density. Do not turn displacement arithmetic into a vessel-stability assessment.

Displaced volume
10 m³
Water density
1,025 kg/m³
  1. Mass = 1025 × 10 = 10250 kg.
  2. Force = 10250 × 9.80665 N.
  • Displaced mass: 10,250 kg
  • Buoyant force: 100,518.2 N

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.

Displaced volume
15 m³
Water density
1,025 kg/m³
  1. Mass = 1025 × 15 = 15375 kg.
  2. Force = 15375 × 9.80665 N.
  • Displaced mass: 15,375 kg
  • Buoyant force: 150,777.2 N

Check your understanding

1. Which relationship is used?

Displaced mass = ρV; buoyant force = ρVg.

2. Which assumption should you check first?

Hydrostatic displacement only. This does not assess stability, loading limits, freeboard or seaworthiness.

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.