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Federal Bridge Formula Calculator

Free bridge formula calculator. Enter the axle group length and axle count to get the maximum legal group weight, or flip it around and solve for the minimum spacing or minimum axle count you need. The rule, sometimes called the bridge law, is set by the Federal Bridge Formula at 23 CFR § 658.17.

Max weight

73,000 lb

max group weight

How it is calculated

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

W = 500 × ((40 × 5) / 4 + 60 + 36) = 73,000 lb (rounded to nearest 500)

W is the max allowed weight (lb) on the axle group, L is the distance from the first to the last axle of the group (ft), and N is the number of axles in the group.

How the Federal Bridge Formula works

The Federal Bridge Formula caps the gross weight on any group of consecutive axles based on the distance between the outermost axles of that group: W = 500 × ((L × N) / (N − 1) + 12N + 36). W is the maximum allowed weight in pounds, L is the distance from the first to the last axle of the group in feet, and N is the number of axles in the group. The result is rounded to the nearest 500 pounds, which is how the Federal Highway Administration publishes and enforces the limits.

The catch most people miss: a vehicle has to clear the formula on every consecutive subgroup of axles, not just the outer bridge from the first axle to the last. A long rig can pass on its full wheelbase and still fail on an interior tandem or tridem that sits too close together. That is why heavy-haul setups spread weight across more axles over a longer span.

Need the full picture? Check a real axle layout against per-state limits with the axle weight calculator (single, tandem, tridem and quad caps, GVW, lookup tables, and the permit ladder for all 48 states). Working the other direction, given a load weight: which rig clears the formula? Use the FBF solver to see tractor, jeep, trailer, and booster combinations that pass on every axle subset.

Frequently asked questions

What is the Federal Bridge Formula?
The Federal Bridge Formula (23 CFR § 658.17) caps the maximum legal weight on any group of consecutive axles based on the distance between them. The formula is W = 500 × ((L × N) / (N − 1) + 12N + 36), where W is the maximum allowed group weight in pounds, L is the distance from the first to the last axle of the group in feet, and N is the number of axles in the group. It exists because short, heavy axle groups concentrate load and damage bridge spans. Every consecutive subgroup of axles on a vehicle has to clear the formula independently, not just the outermost group.
How do you calculate the Federal Bridge Formula?
Plug the axle group length L (in feet) and the axle count N into W = 500 × ((L × N) / (N − 1) + 12N + 36), then round the result to the nearest 500 pounds. For example, a tandem (N = 2) spaced 4 feet apart gives W = 500 × ((4 × 2) / 1 + 24 + 36) = 500 × 68 = 34,000 lb, which is the federal tandem limit. This calculator does that math instantly and can also run it backwards: enter a target weight to get the minimum spacing or the minimum axle count you need.
What is the bridge formula weight for a tandem axle?
A tandem axle group is two axles. At the federal minimum tandem spacing of 4 feet, the bridge formula gives 34,000 lb, which matches the statutory tandem cap. Spreading the tandem wider raises the bridge-formula limit, but the flat 34,000 lb tandem cap still applies on the interstate, so the lower of the two governs. A tridem (three axles) at 8 feet works out to 42,000 lb by the formula; states publish their own tridem caps on top of that.
What do L, N, and W mean in the bridge formula?
W is the maximum weight in pounds allowed on the axle group. L is the wheelbase of the group: the distance in feet from the center of the first axle to the center of the last axle. N is the number of axles in the group. A wider L or a higher N both raise the allowed weight, which is why heavy-haul rigs add jeep dollies and boosters to spread weight across more axles over a longer span.
Why does the bridge formula round to 500 pounds?
The Federal Highway Administration publishes bridge-formula limits rounded to the nearest 500 pounds, and the statute is applied that way in the field. This calculator follows the same convention so the numbers match the values DOT officers and permit offices use. The raw formula output is rounded to the nearest 500 before it is reported as the legal limit.
Does the Federal Bridge Formula apply to overweight permit loads?
Per 23 CFR § 658.17(h), states have authority to waive the Federal Bridge Formula for nondivisible loads operating under permit. In practice most states still treat the formula as a baseline and run their own bridge-by-bridge structural analysis on top. Divisible loads almost never get a waiver. If your axle configuration cannot clear the formula, expect a state engineering review and a route survey, which add cost and lead time.
How is this different from the axle weight calculator and the FBF solver?
This page is the pure formula: give it any two of weight, length, and axle count and it returns the third. The axle weight calculator runs a full per-state compliance check (single, tandem, tridem and quad caps, GVW limits, lookup tables, and the permit ladder) for all 48 states. The FBF solver works the inverse problem for brokers: given a load weight, it returns the rig configurations (tractor, jeep, trailer, booster) that clear the formula on every consecutive axle subset.
This calculator is provided for planning purposes only and implements the federal formula at 23 CFR § 658.17. State limits, permit waivers, and posted bridge restrictions vary and change without notice. Verify current requirements with the relevant state DOT before moving a load.