Guides · LoadLegit · 2026-06-29

The Federal Bridge Formula, explained (with the exact math)

The Federal Bridge Formula (23 CFR 658.17) is the rule that catches drivers who thought they were legal. Your gross weight can be under 80,000 lb, every axle can be under its own limit — and you can still get a ticket, because a group of axles is carrying too much weight for how close together they are.

The formula

W = 500 × ( L·N / (N − 1) + 12·N + 36 )

• W — the maximum weight (lb) allowed on the axle group, rounded down to the nearest 500 lb, capped at 80,000 lb
• L — the distance in feet between the outermost axles of the group
• N — the number of axles in the group

The intuition: bridges care about how concentrated weight is. The same 80,000 lb spread over 51 feet stresses a bridge far less than 80,000 lb bunched into 40 feet, so tighter axle groups get lower limits.

A worked example

A standard 5-axle tractor–trailer with 51 ft from steer to rear trailer axle: W = 500 × (51×5/4 + 12×5 + 36) = 500 × 159.75 = 79,875 → rounded down to 79,500 lb. If you scaled 80,000 lb gross, you're legal on the gross limit and illegal on the bridge formula — by 500 lb.

That's the trap: the formula must hold for every consecutive group of two or more axles, not just the whole truck. Inner groups (like the drive-to-trailer tandem span) each get their own check.

The two fixed exceptions

Two limits always apply regardless of the formula: 20,000 lb on any single axle and 34,000 lb on a tandem group (axles 40–96 inches apart). The well-known "grandfather" exception also lets two consecutive tandems carry 34,000 lb each when the groups are at least 36 ft apart on a 5-axle rig.

How to check it without doing algebra at the scale

You can run this formula by hand, but nobody does at 5 a.m. in a truck stop. Enter your scale weights into our free axle weight calculator — it checks single, tandem, gross and the bridge formula instantly. See also: federal axle weight limits and how sliding tandems shifts weight.