Calculator · Engineering Mechanics
Center of Mass Calculator
Locate G from either discrete point masses or a composite body. Geometry, mass and area density remain explicit so the centre of mass is never confused with the geometric centroid.
Model
Each mass acts at one x-y coordinate.
Mass layout
Centre of mass G
Total mass 10 kg
Selected mass
| Name | m1 |
|---|---|
| Mass | 2 kg |
| Position | (0, 0) m |
Point masses
m1
Discrete point mass
m2
Discrete point mass
m3
Discrete point mass
Results
| Total mass | 10 kg |
|---|---|
| Centre of mass G | (0.22, 0.15) m |
| Geometric centroid C | Not applicable to point masses |
| Mass moment about G | Not included for this model |
Diagnostics
Technical reference
r_G = Σmi·ri / Σmi
(x_G, y_G) = (Σmi·xi / Σmi, Σmi·yi / Σmi)
- mi
- signed mass contribution of point or component i[kg]
- ri = (xi, yi)
- position of that mass[m]
- r_G
- centre of mass[m]
Point masses have no area, so only the discrete sum applies there; a composite body needs an explicit mass or area density per component before G is defined.
In the composite bookkeeping, a positive contribution adds material and a negative contribution subtracts removed material (a cutout). A negative contribution is an accounting term, not a physically negative mass.
G is mass-weighted, not area-weighted, so it is generally distinct from the geometric centroid. For a uniformly dense body they coincide. With non-uniform density they generally differ, although special symmetric mass distributions can still place them at the same point.
Assumptions
- · Planar point masses in one global x-y frame.
- · Mass must be finite and non-negative; zero total mass leaves G undefined.
- · Points have no geometric area, so a geometric centroid C is not defined.