Ship's Hydrostatics and Stability Calculator

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Ship's hydrostatics and stability is a fundamental aspect of marine engineering and naval architecture. It involves the analysis of the ship's buoyancy, balance, and the ability to resist capsizing. This area is crucial for the safe and efficient design and operation of ships. It encompasses various calculations, including the ship's displacement, center of buoyancy, metacentric height, and righting levers. This tutorial will provide an overview of the calculations and formulas related to ship's hydrostatics and stability, and their importance in marine engineering.

Calculator restrictions: the formulas used in this calculator for Metacentric Height (GM) and Righting Lever (GZ) are simplified and do not consider the ship's geometry, loading conditions, and the distribution of weight.

Ship's Hydrostatics and Stability Calculator
Ship's Hydrostatics and Stability Calculator Results (detailed calculations and formula below)
Metacentric Height (gm) = metres
Righting Lever (gz) = metres
Metacentric Height Formula and Calculations
Metacentric Height (gm) = breadth (w)/2 - draft (d)/3
gm = w/2 - d/3
gm = /2 - /3
gm = -
gm =
Righting Lever Formula and Calculations
Righting Lever (gz) = Metacentric Height (gm) × sinAngle of the heel (a) × π/180
gz = gm × sina × π/180
gz = × sin × π/180
gz = × sin ×
gz = × sin
gz = ×
gz =
Ship's Hydrostatics and Stability Calculator Input Values
Length of the Ship (l) metres
Breadth of the Ship (w) metres
Draft of the Ship (d) metres
Displacement of the Ship (k) tonnes
Angle of the heel (a) degrees

Example Formula

Ship's Hydrostatics and Stability Calculator - Learn about ship's hydrostatics and stability, the associated calculations, formulas, and their applications in marine engineering

One of the essential calculations in ship's hydrostatics and stability is the Righting Lever (GZ), which measures the ship's ability to resist heeling or capsizing. The formula for calculating the Righting Lever is:

GZ = GM × sin(θ)


  1. GZ: Righting Lever (in meters)
  2. GM: Metacentric Height (in meters)
  3. sin(θ): Sine of the angle of heel

Impact on Society

The development and refinement of hydrostatics and stability calculations have been a collective effort of marine engineers and naval architects over many years. These formulas and calculations have played a critical role in ensuring the safety and efficiency of maritime transportation. They are essential for designing ships that can safely carry heavy loads across the oceans, contributing significantly to global trade and the economy. Besides marine engineering, the concepts of hydrostatics and stability are also relevant in offshore engineering, particularly in the design and construction of oil rigs and other offshore structures.

Real Life Application in Industry

In the maritime industry, ship's hydrostatics and stability calculations are utilized extensively in the design phase of a ship. For instance, when a shipping company needs to build a new cargo vessel, naval architects perform these calculations to ensure that the ship can safely carry the intended cargo without capsizing. Furthermore, these calculations are vital during the ship's operation, especially when loading cargo to ensure that the load is distributed properly to maintain stability.

Key Individuals in the Discipline

One of the prominent figures in the development of naval architecture and ship stability is William Froude (1810-1879). He is known for establishing the fundamentals of ship resistance and propulsion. His work laid the foundation for modern hydrodynamic theory, which is crucial for understanding ship's hydrostatics and stability.

Interesting Facts

  • The loss of the SS Eastland in 1915, which capsized in the Chicago River, leading to over 800 fatalities, was a key event that led to significant improvements in the understanding of ship stability.
  • Modern-day cruise ships are designed with very high stability standards to ensure the safety of thousands of passengers and crew members onboard.
  • Ship's hydrostatics and stability are not only applicable to seagoing vessels but also to submarines. It is critical in controlling the buoyancy and balance of submarines.


Ship's hydrostatics and stability are essential components in marine engineering and naval architecture, ensuring the safe and efficient design and operation of ships. The ability to perform precise calculations related to the buoyancy and balance of a ship is vital in preventing catastrophes at sea. As maritime transportation continues to play a critical role in global trade and economy, the importance of understanding and applying principles of ship's hydrostatics and stability remains paramount for engineers and naval architects.