Center of Mass Calculator to Find the Balance Po...
Calculate the center of mass of any system of particles or objects in 1D, 2D, or 3D. Essential for mechanics, engineering, and understanding orbital dynamics.
What is Center of Mass?
The center of mass (CoM) is the unique point where a system's total mass can be considered to act. For a uniform object like a sphere, it's the geometric center. For complex systems, it's the mass-weighted average position of all particles. It is the point that moves under the influence of external forces.
⚖️ Center of Mass Calculator
Use our free calculator for instant, accurate results.
📐 Formula
x_cm = Σ(mᵢ × xᵢ) / Σmᵢ
Applied to each coordinate axis separately (x, y, z). mᵢ = mass of particle i, xᵢ = position along axis.
📝 Worked Example
Two masses on a rod: m₁=3kg at x=0, m₂=1kg at x=4m:
x_cm = (3×0 + 1×4) / (3+1) = 4/4 = 1 m from m₁
The heavier mass pulls the CoM closer to itself.
📝 How to Use the Calculator
❓ FAQ
Is center of mass the same as centroid?
Only for uniform density objects. Centroid is geometric; center of mass is mass-weighted and they differ when density varies.
Why does center of mass matter in space?
Orbital mechanics treats planets as point masses at their center of mass. Binary star systems orbit their mutual center of mass (barycenter).
Veer Kumavat
Founder & AuthorVeer is a 14-year-old student from Nashik, Maharashtra, who built SciFi Calculators to help students worldwide master STEM subjects. He is passionate about making complex science and math problems accessible through intuitive digital tools.