What is the center of mass?

The center of mass is the unique point where the weighted relative position of the distributed mass sums to zero. For a system of discrete masses it is the mass-weighted average of their positions.

What formula does this calculator use?

For each axis, COM = (m1*x1 + m2*x2 + ... + mn*xn) / (m1 + m2 + ... + mn). The same formula applies independently to Y and Z axes.

Can masses be negative?

Physically, masses must be positive. This calculator requires all mass values to be greater than zero and will show an error otherwise.

What units should I use?

The calculator is unit-agnostic. As long as you use consistent units for mass (kg, g, lb) and length (m, cm, ft), the result will be in those same units.

How many masses can I add?

You can add up to 20 point masses. For most physics and engineering problems this is more than sufficient.

What is the difference between center of mass and center of gravity?

In a uniform gravitational field they are identical. They differ only in non-uniform fields, such as very large objects spanning significant altitude differences.

Center Of Mass Calculator

Enter point masses with coordinates in 1D, 2D, or 3D space to instantly calculate the center of mass.

Point Masses

Center of Mass

Add at least two masses to compute the center of mass.

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Summary

The center of mass calculator finds the weighted average position of a system of point masses. Enter each mass and its coordinates, then the tool computes the centroid using the standard formula: each coordinate of the center of mass equals the sum of (mass × coordinate) divided by total mass. Supports 1D, 2D, and 3D configurations.

How it works

Select the number of dimensions: 1D, 2D, or 3D.
Add each point mass by entering its mass value and coordinates.
Click "Add Mass" to append more mass points to the system.
The center of mass coordinates update instantly as you type.
Remove any mass point by clicking the trash icon next to it.
Copy the result or clear all entries to start over.

Use cases

Physics homework: find the centroid of a multi-body system.
Engineering: locate the center of gravity for structural analysis.
Robotics: compute the balance point of a robot arm or chassis.
Astronomy: estimate the barycenter of a planetary system.
Game development: calculate equilibrium points for physics simulations.
Chemistry: determine molecular centroid positions.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu