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Federal bridge formula calculator

Type the axle positions and weights. Every group of two or more consecutive axles is checked — all of them — with the headroom left on each one.

Start from a common rig

Four real configurations, not demonstrations. Pick the closest and then edit the positions and weights — a preset only fills the form.

Axles, front to rear

Position is the distance in feet from the steer axle, so the first axle is always 0. Measure centre to centre, and for a wheel cluster use the centre of the cluster. Weight is what that axle actually carries, not its rating.

Up to 13 axles. Positions must increase front to rear; the calculator refuses to compute on impossible geometry rather than returning a number.

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How the answer is reached

Three checks, in order. Each single axle against the federal 20,000 lb limit. Then every group of two or more consecutive axles against the bridge formula, with the tandem cap applied by span and the two-tandem exception applied by geometry. Then the whole vehicle against the federal 80,000 lb gross limit.

The result is rounded to the nearest 500 lb with exact ties going down, which is what the statute and the published federal table both do — ordinary rounding sends halves up and would permit 500 lb the law does not.

The formula, the full table and the five cells where the published federal table contradicts the federal formula →

Once you know you need a permit

Questions

How many axle groups does this check?

Every group of two or more consecutive axles — N(N−1)/2 of them. A five-axle tractor-semitrailer has ten groups; a nine-axle heavy haul has thirty-six. The count is shown in the result so you can see it rather than take it on trust.

Why does my legal 5-axle van pass with 34,000 lb on each tandem?

Because of a statutory exception: two consecutive sets of tandem axles may each carry 34,000 lb — 68,000 lb between them — provided the outer axles of the two tandems are at least 36 ft apart. The bare formula at that geometry allows only 66,000, so a calculator implementing the formula alone flags every legal van in the country.

Does this work above 80,000 lb?

Yes, and that is deliberate. A group's bridge-formula allowance is capped by the vehicle's own gross weight, not by the federal 80,000 lb limit — clamping it at 80,000 fabricates overages of up to 25,500 lb on permitted heavy-haul loads whose groups are in fact compliant. The federal gross limit is still enforced, once, as a limit on the vehicle.

Does passing mean I need no permit?

Not on its own. This checks weight against federal limits. Size limits are set by each state, and several states publish axle or gross figures different from the federal ones. Use the axle weight checker to bring a state's own cited limits into the answer.