Calculate the 2D center of mass for two to five weighted points, or find an equal-mass centroid with coordinate and mass unit conversions.

Required: enter mass, X, and Y for every visible point to find the center of mass.

Point 1
Point 2
Point 3

Center of Mass Formula

The following formula is used to calculate a center of mass of multiple point masses.

For point masses in 2D, compute each coordinate separately:
xcm = (m1x1 + m2x2 + … + mNxN) / (m1 + m2 + … + mN)
ycm = (m1y1 + m2y2 + … + mNyN) / (m1 + m2 + … + mN)

  • Where m is the mass of each point
  • x is the coordinate distance of each point along the x-axis
  • y is the coordinate distance of each point along the y-axis

To calculate a center of mass, multiply each point mass by its coordinate, add these values together, then divide by the sum of the point masses. Do this separately for the x-coordinate and y-coordinate.

Center of Mass Definition

The center of mass is the mass-weighted average position of an object or system of objects. In many problems (for example, translational motion under uniform gravity), the system behaves as if all its mass were concentrated at this point.

Center of Mass Example

FAQ

What is a center of mass?

A center of mass is the mass-weighted average position of an object or system. It is a single point that can be used to model the system’s translational motion (for example, under uniform gravity) as if the mass were concentrated there.

What is a point mass?

A point mass is an idealized model in which an object’s size is negligible compared with the distances involved, so its mass can be treated as concentrated at a single point.