How the Center of Gravity Calculator Works
The Center of Gravity Calculator finds the balance point of a system of objects. Each object contributes based on both its position and its mass.
The more massive an object is, the more strongly it pulls the center of gravity toward its position.
Center of Gravity Formula
For objects treated as point masses in 2D:
where mᵢ is the mass of object i, and xᵢ, yᵢ are its coordinates.
How to Use the Calculator
- Enter the x-coordinate, y-coordinate, and mass of each object.
- Click Add Object to include more point masses.
- Click Calculate Center of Gravity.
- Review the CG coordinates and the plotted graph.
Example Calculation
Suppose three point masses are located at:
Object 1: x = 0, y = 0, mass = 2 kg Object 2: x = 4, y = 0, mass = 3 kg Object 3: x = 2, y = 3, mass = 5 kg
The total mass is:
The center of gravity is calculated using the weighted average of coordinates.
Center of Gravity vs Center of Mass
| Term | Meaning |
|---|---|
| Center of mass | Average location of mass distribution. |
| Center of gravity | Point where the resultant gravitational force acts. |
| Uniform gravity | The two points are effectively the same. |
Applications
- Vehicle design: rollover stability and handling.
- Aircraft: safe loading and flight stability.
- Robotics: balance and movement control.
- Structures: stability and tipping analysis.
- Cargo loading: safe transport by truck, ship, or aircraft.
Frequently Asked Questions
Can the center of gravity be outside the object?
Yes. For hollow, curved, or irregular systems, the center of gravity can lie outside the physical material.
Why does mass matter?
A heavier object has more influence on the final center of gravity location than a lighter object.
Can I use negative coordinates?
Yes. Coordinates can be positive, negative, or zero as long as they use the same coordinate system.
Can mass be zero?
No. A zero-mass object does not affect the center of gravity and should not be included.