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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.

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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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Scope

What this answers, and where the answer stops

A weight check is not a route clearance. The three facts below are the whole boundary.

What it covers

Every group of two or more consecutive axles against 23 U.S.C. §127(a) — all of them, not the three anyone would name — plus the flat federal 20,000 lb single-axle, 34,000 lb tandem and 80,000 lb gross limits.

What it does not cover

A state's own axle and gross limits, seasonal (spring thaw) restrictions posted road by road, local bridge postings, and permit fees. Any one of them can make a rig that passes here illegal on a specific route.

What it costs

Nothing, and no account. Every input is in the request and every limit is compiled in, so the page renders and the endpoint answers with the database unreachable, and neither calls anything billable.

How it works

Three checks, in order

Describe the rig

Position is the distance in feet from the steer axle, measured centre to centre; weight is what that axle actually carries, not its rating. Start from one of 4 real configurations and edit from there.

Every group gets enumerated

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 80,000 lb.

Read the headroom, not just the verdict

Each group shows what it carries, what it is allowed and what is left. Allowances round to the nearest 500 lb with exact ties going down — what the statute and the published federal table both do, where ordinary rounding would permit 500 lb the law does not.

Why this one

Two things most free calculators get wrong

Every group, not the obvious three

Compliance is not "steer, drives, trailer tandems". It is every group of two or more consecutive axles — N(N−1)/2 of them. The classic failure is a rig whose every named group passes and whose interior span does not, and an interior span is exactly what a bridge cares about.

The count is returned with the result so you can see it rather than take it on trust.

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

Groups on a 5-axle tractor-semitrailer
10
Groups on a 9-axle heavy haul
36
Groups a named-group check looks at
3

It works above 80,000 lb, on purpose

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 there 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, which is what it is.

Federal single axle
20,000 lb
Federal tandem axle
34,000 lb
Federal gross weight
80,000 lb
FAQ

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.