Supply Chain
Center of Gravity (Facility Location) Calculator
Where to put the warehouse. Plot the places you ship to on any grid, weight each by how much moves there, and the centre of gravity is the point that balances them — the classic first answer to a distribution-centre question, and the one that stops an argument about which city "feels central" from being settled by whoever is loudest.
Inputs
- Locations you serve — Customers, stores, plants — whatever the freight actually runs between.
- Location 1 — across (x) — Any grid will do so long as every location uses the same one: map squares, miles east and north of a corner, or latitude and longitude as plain numbers.
- Location 1 — up (y)
- Location 1 — loads
- Location 2 — across (x)
- Location 2 — up (y)
- Location 2 — loads
- Location 3 — across (x)
- Location 3 — up (y)
- Location 3 — loads
- Location 4 — across (x)
- Location 4 — up (y)
- Location 4 — loads
How to use this calculator
- Put every location on one grid. Map squares, miles east and north of a corner, or latitude and longitude as plain numbers — anything works as long as all the locations use the same one.
- Weight each location by the thing that drives freight cost: truckloads, pallets, tons. Not revenue, and not customer count. A location with big revenue and one delivery a month barely moves a warehouse.
- Read the centre of gravity as a SEARCH AREA, not an address. It is a point on a flat grid with straight-line distances; roads, rivers, state lines and congestion are all still ahead of you.
- Compare it with the true minimum-distance point underneath. They differ because the centre of gravity balances squared distance, and when a few locations carry most of the volume the gap is worth knowing about.
- Compare both with the best site you already have. A building you own, staffed, with a lease already signed, often beats a greenfield optimum by more than the freight difference between them.
- Then price the things this ignores: land, labour, taxes, incentives, and whether you can hire there. They routinely outweigh the freight gap between two candidate sites fifty miles apart.
What each term means
- Centre of gravity
- The volume-weighted average position of everywhere you ship. It balances the map the way a fulcrum balances a beam, and it is the standard first answer to a location question.
- Load-distance
- Volume multiplied by distance, summed over every location. The proxy for freight cost that this whole method minimises, and the number to compare candidate sites on.
- Weber point
- The point that actually minimises weighted DISTANCE, found by iteration rather than a formula. The centre of gravity minimises weighted SQUARED distance, which is not the same thing and is why the two differ.
- Weighting
- What each location contributes to the pull. Use the unit your freight is billed in; weighting by revenue moves the warehouse toward your margin rather than toward your trucks.
- Greenfield
- A site chosen with no existing building to favour. The honest comparison is always against what you already have, because the incumbent site costs nothing to keep.
Educational disclaimer: Outputs are simplified educational estimates built from the numbers you enter — they are not financial, legal, tax, or investment advice, and real decisions deserve verified figures and qualified professionals.