Center of Gravity Calculator
Calculate multi-body center of mass / center of gravity coordinates (X_cg, Y_cg) and total mass.
Calculate Center of Gravity
Enter your engineering design parameters to calculate real-time verified outputs.
Calculation Results
Calculated using governing formula: X_cg = (m1*x1 + m2*x2 + m3*x3) / (m1 + m2 + m3)
Quick Summary
Free Center of Gravity Calculator. Compute 2D center of mass coordinates Xcg = sum(m_i * x_i)/sum(m_i) for structural assemblies.
How to Use the Center of Gravity Calculator
Follow these quick steps to evaluate your engineering parameters:
- Enter your verified design values into the corresponding input fields above.
- Verify your engineering unit conventions (SI Metric / US Customary).
- Click Calculate to evaluate primary metrics and secondary performance breakdowns.
- Click Reset at any time to clear the results and reset inputs.
Governing Formulas & Engineering Theory
X_cg = (m1*x1 + m2*x2 + m3*x3) / (m1 + m2 + m3)
The center of gravity is the unique spatial point where the entire gravitational weight of an assembly can be considered to act.
Engineering Principles & Practical Applications
Center of gravity management is critical in aircraft weight-and-balance loading, naval ship stability, and heavy crane rigging plans.
Scope: What is Included vs. Excluded
Included Features
- High-precision 64-bit IEEE floating point computations
- Interactive form validation and instant calculation
- Standardized SI metric and imperial conversions
- Detailed secondary performance breakdowns
Non-Linear Factors Excluded
- High-order plastic deformation and material creep
- Severe environmental temperature extremes
- Extreme non-linear dynamic fatigue regimes
- Microstructural material anomalies
Engineering Tips & Best Practices
Safety Factor Application: Always apply appropriate design factors of safety (typically 1.5 to 3.0 depending on relevant ASME, AISC, or ISO building codes) when sizing critical mechanical and structural components.
Common Mistakes to Avoid
Unit Consistency: Avoid mixing imperial and metric units without standard conversion. Ensure modulus, dimensions, and force inputs match baseline SI units (Newtons, meters, Pascals).
Frequently Asked Questions
Why is Center of Gravity critical for aircraft flight stability?
If the CG moves behind the aerodynamic center, the aircraft becomes aerodynamically unstable and uncontrollable in pitch.
What is the difference between center of mass and center of gravity?
They are identical in a uniform gravitational field; center of mass depends purely on matter distribution, while CG accounts for gravitational gradient.
How do you calculate 2D or 3D center of gravity?
Calculate each spatial axis independently using the moment sum formula: X_cg = sum(m*x)/M, Y_cg = sum(m*y)/M, Z_cg = sum(m*z)/M.