Center of Gravity Calculator

Summary

Enter masses and their X/Y/Z coordinates to instantly find the combined center of gravity in 2D or 3D space.

How it works

1. Select 2D mode (X, Y) or 3D mode (X, Y, Z) depending on your problem.
2. Enter the mass and coordinates for each component in the table.
3. Click "Calculate CG" to compute the combined center of gravity and total first moments.
4. The tool computes intermediate first moments ΣM = Σ(m·r) and divides by total mass: CG = ΣM / Σm.
5. Review coordinates and moments, then copy the formatted result summary.
6. Add or remove rows as needed for up to 10 point masses.

Use cases

• Determine the CG of aircraft or spacecraft assemblies.
• Balance mechanical structures or vehicle chassis designs.
• Verify stability margins in structural engineering projects.
• Compute centroids for composite cross-sections in beam design.
• Check load distribution for shipping containers or cargo pallets.
• Analyze robotic arm balance and joint loading.
• Estimate the CG of assembled products during mechanical design.
• Validate finite-element model assumptions for mass distribution.

Frequently Asked Questions