Center of Mass Calculator

Add point masses with x and y coordinates to calculate total mass and the mass-weighted center coordinates.

—r̄ = Σmᵢrᵢ / Σmᵢ

—Total mass

—Center x

—Center y

—Point masses

Point-mass model. Coordinates may use any consistent length unit; the center is returned in that same unit.

Physics model preflight

Check the governing model before trusting the number

2D point-mass model

r̄ = Σmᵢrᵢ / Σmᵢ

Reading the current native inputs…

Point-mass coordinates with positive masses and one consistent coordinate unit. This is an idealized educational model: unit consistency and valid inputs do not guarantee that omitted effects are negligible in a real system.

State the model before trusting the number

Classical formulas are only as good as their assumptions and units. Air resistance, damping, deformation, non-constant forces and measurement uncertainty are not silently invented when the selected model does not include them.

Governing physics model

r̄ = Σmᵢrᵢ / Σmᵢ — 2D point-mass model.

How to verify the result

The center should stay inside the convex span of positive point masses; duplicating every mass by the same factor must not move it.

Domain and assumption boundary

Point-mass coordinates with positive masses and one consistent coordinate unit. The calculator does not silently add drag, damping, deformation, varying fields, relativistic effects, measurement uncertainty, or geometry that the selected model does not contain.