Center of Gravity Calculator
Calculate the total weight and center of gravity of a boat, vessel, vehicle, or other system from multiple weights and their positions. Find longitudinal center of gravity (LCG), vertical center of gravity (VCG), and total moments.
Center of Gravity Results
What is the center of gravity?
The center of gravity is the point at which the entire weight of a boat or other object can be considered to act. For a vessel, its position has an important influence on trim, stability, and overall handling.
When a boat contains many individual weights, the overall center of gravity can be calculated by combining each item's weight and its position relative to a common reference point.
How is center of gravity calculated?
The center of gravity is calculated using the sum of the moments of all individual weights divided by the total weight.
$$LCG = \frac{\sum(W_i \times X_i)} {\sum W_i}$$
$$VCG = \frac{\sum(W_i \times Z_i)} {\sum W_i}$$
- Wi: Weight of an individual item.
- Xi: Longitudinal position of that item.
- Zi: Vertical position of that item.
- LCG: Longitudinal center of gravity.
- VCG: Vertical center of gravity.
What is LCG?
LCG stands for Longitudinal Center of Gravity. It describes the forward or aft position of the vessel's total center of gravity relative to the selected longitudinal reference point.
Moving a heavy item toward the bow generally moves the vessel's LCG forward. Moving the same item toward the stern moves the LCG aft.
What is VCG?
VCG stands for Vertical Center of Gravity. It describes how high the vessel's center of gravity is above the selected vertical datum.
Heavy equipment installed high in the boat can raise the VCG, while placing weight low in the hull can lower it. VCG is therefore particularly important when assessing vessel stability.
What is a weight moment?
A moment is the product of a weight and its distance from the reference point.
$$Moment = Weight \times Distance$$
$$M_x = W \times X$$
$$M_z = W \times Z$$
The calculator sums all individual moments before dividing by the total weight. This produces the location where the equivalent combined weight would act.
Why is center of gravity important on a boat?
The location of the center of gravity influences longitudinal trim and the vessel's stability characteristics. Loading cargo, fuel, water, batteries, passengers, engines, and equipment in different locations can therefore change how the vessel behaves.
How does adding weight affect the center of gravity?
Adding a weight close to the existing center of gravity has a small effect on its position. Adding the same weight far away has a much larger effect because the additional moment is larger.
$$New\ CG = \frac{ W_1 X_1 + W_2 X_2 }{ W_1 + W_2 }$$
What happens when fuel or water is consumed?
Fuel and water tanks are especially important because their weight changes during operation. As tank contents are consumed or transferred, both total displacement and the vessel's center of gravity can change.
For detailed stability work, tank geometry and free-surface effects may also need to be considered rather than treating every tank as a simple fixed weight.
Can this calculator determine boat stability?
No. Center of gravity is only one part of a vessel stability analysis. Stability also depends on the center of buoyancy, metacentric height, hull geometry, displacement, free-surface effects, loading condition, and other factors.
What is the difference between CG and displacement?
Displacement represents the total weight of the vessel and its contents in a floating condition. Center of gravity describes where that total weight acts. The two values are related but represent different properties.