What is the Federal Bridge Formula?
The Federal Bridge Formula (W = 500(LN/(N-1)+12N+36)) sets the maximum legal weight on any group of axles based on how far apart they are spread.
The Federal Bridge Formula (also called the Bridge Gross Weight Formula) sets the maximum weight allowed on any group of consecutive axles based on the number of axles and the distance between the outermost ones. It exists because weight concentrated over a short span stresses a bridge far more than the same weight spread out.
W = 500 × ( L·N / (N − 1) + 12·N + 36 )
- W = maximum weight (lb) on the group, rounded down to the nearest 500 lb
- L = distance (ft) between the extreme axles of the group
- N = number of axles in the group
The formula must hold for every group of consecutive axles on the vehicle — not only the outer pair — and the 20,000 lb single, 34,000 lb tandem, and 80,000 lb gross caps still apply.
Try it with real numbers on the Bridge Formula calculator. Note that Canada does not use a bridge formula — it regulates axle groups by fixed weight bands instead.
Check a real load in secondsLoadLegit turns axle weights into a pass/fail compliance verdict — federal Bridge Formula plus verified state and Canadian rules — and issues a shareable certificate. Try it free →
Related
Federal Bridge Formula calculatorFree Federal Bridge Formula calculator. Enter axle count and the spacing between the extreme axles to get the maximum legal weight (W = 500(LN/(N-1)+12N+36)).What is axle weight?Axle weight is the portion of a vehicle's total weight carried by a single axle or axle group — the number weigh stations and the Bridge Formula regulate.What is a tandem axle?A tandem axle is two axles spaced close together (typically 40–96 inches) that share a load as one group. The US federal tandem limit is 34,000 lb.What is a tridem axle?A tridem axle is a group of three axles spaced close together. Common in Canada, where a tridem group can be rated to roughly 21,000–24,000 kg by its spread.