How to Use the Federal Bridge Formula and Axle Weight Tables

The Federal Bridge Formula sets the maximum weight allowed on any group of consecutive axles on the Interstate System, based on how far apart the outer axles are spaced and how many axles fall between them. The formula is W = 500 × [LN / (N − 1) + 12N + 36], where W is the allowable gross weight in pounds, L is the distance in feet between the outermost axles of the group, and N is the number of axles in that group. Whatever the formula produces, three absolute ceilings still apply: 20,000 pounds on any single axle, 34,000 pounds on any tandem, and 80,000 pounds gross vehicle weight.¹

The Three Variables You Have to Measure

L is the distance between the outermost axles of the group you are checking, measured in feet from the center of the first axle to the center of the last. Fractional measurements are typically rounded to the nearest whole foot.

N is the number of axles in that group. Count every axle from front to back of the span, including trailer axles, lift axles, and pusher axles.¹

W is what the formula gives you back: the maximum allowable gross weight, in pounds, on that group of axles. The result is rounded to the nearest 500 pounds, and the rounding runs in the driver’s favor. A calculated 79,600 rounds up to 80,000, not down to 79,500.¹

A tandem axle, for the 34,000-pound cap, means two or more consecutive axles spaced more than 40 inches but not more than 96 inches apart.²

Running the Calculation Step by Step

The formula looks dense, but the arithmetic is basic once broken into steps. Take a three-axle group spanning 20 feet, so L = 20 and N = 3:

Multiply L by N: 20 × 3 = 60
Divide by (N − 1): 60 ÷ 2 = 30
Add 12N: 30 + 36 = 66
Add 36: 66 + 36 = 102
Multiply by 500: 102 × 500 = 51,000 pounds

That three-axle group can legally carry up to 51,000 pounds.³

Now a five-axle group spanning 51 feet, with L = 51 and N = 5: 51 × 5 = 255, divided by 4 = 63.75, plus 60 = 123.75, plus 36 = 159.75, times 500 = 79,875 pounds. Rounded, that is 80,000 pounds. In this case the formula and the gross vehicle weight cap arrive at the same number.³

Using the FHWA Bridge Table Instead

The Federal Highway Administration publishes a Bridge Gross Weight Formula Table that runs the calculation for every reasonable combination of L and N. Most drivers and enforcement officers work from the table rather than the equation, and it is the standard reference at weigh stations.³

The layout is simple. Distances in feet run down the left column, numbers of axles across the top row. Find your row, follow it across to your column, and the intersection is your maximum legal weight in pounds. Four axles at 35 feet gives 65,500 pounds. Four axles at 23 feet gives 57,500 pounds.³

The table already incorporates the 500-pound rounding built into the statute, so its figures are the legally defensible numbers. If a hand calculation disagrees with the table, the table controls. Carrying a printed copy or a digital version in the cab is standard practice for anyone hauling near the limits.

Check Every Axle Group, Not Just the Obvious Ones

Federal law requires that every combination of two or more consecutive axles satisfy the Bridge Formula, even when individual axle weights and the gross vehicle weight are within legal limits.³ This is where most overweight citations come from. A truck passes the single-axle and gross weight checks but fails on some interior group nobody thought to measure.

On a typical five-axle tractor-semitrailer, that means checking axles 1–2, 1–3, 1–4, 1–5, 2–3, 2–4, 2–5, 3–4, 3–5, and 4–5. Ten separate groups, each with its own distance, its own axle count, and its own limit from the table. A vehicle can be perfectly legal on nine of those groups and overweight on the tenth. Enforcement officers tend to focus on the interior combinations where weight concentrates.

The Two-Tandem Exception

One built-in exception matters for almost every long-haul operation. Two consecutive sets of tandem axles can each carry 34,000 pounds, for 68,000 pounds across the four axles, as long as the distance from the first axle of the front tandem to the last axle of the rear tandem is 36 feet or more.¹

Without the exception, the standard formula would cap that same four-axle group at roughly 66,000 to 67,500 pounds at 36 to 38 feet of spacing.⁴ Because standard tractor-semitrailers naturally place the drive tandems and trailer tandems in this range, the exception is what makes an 80,000-pound rig legal on its two main axle groups. A narrower version, with a reduced spacing requirement of 30 feet, applies to certain tank trailers, dump trailers, and ocean containers that were operating before September 1, 1989.¹

Rounding, Tolerances, and What Enforcement Actually Uses

The 500-pound rounding on W is the only cushion the formula gives you. The federal weight limits are inclusive of all tolerances, meaning no separate buffer sits on top of the published numbers.⁵

The one narrow exception involves portable wheel-load weighers, which are less accurate than permanent platform scales. When enforcement uses portable scales, a scale allowance factor may apply, but it can never exceed 5 percent.⁶ Some states have historically used penalty schedules that impose no fine below a certain overage, but federal regulations treat those as unauthorized tolerance provisions.⁵ Counting on an informal cushion is a gamble.

Steering axles have their own floor: states cannot restrict a steering axle to less than 20,000 pounds or the manufacturer’s axle rating, whichever is lower. General tire loads on other axles cannot be limited below 500 pounds per inch of tire or tread width.⁶

Where the 80,000-Pound Cap Does Not Apply

The formula and the 80,000-pound ceiling govern the Interstate System, but two situations put a truck outside that framework, and both are worth knowing before assuming a load is illegal.

First, grandfather rights. States that had higher weight limits in force before July 1, 1956, can continue enforcing those higher limits on the Interstate. A few states have their own statutory dates: Michigan uses May 1, 1982; Maryland uses June 1, 1993; Hawaii uses February 1, 1960; and New Hampshire has a January 1, 1987 date for specific routes.¹ Michigan allows up to 164,000 pounds for certain longer combination vehicles on the Interstate, and several other states permit configurations well above 100,000 pounds.⁷ These rights are frozen. No state can create new allowances above 80,000 pounds; it can only maintain what was already legal on its grandfather date.

Second, state-issued overweight permits for non-divisible loads. When a load cannot reasonably be broken into smaller pieces, states can issue permits that waive the Bridge Formula, axle limits, and gross weight cap. Federal law does not issue these; permitting happens at the state level.⁸ A load qualifies as non-divisible if splitting it would keep the vehicle from doing its job, destroy the value of the cargo, or take more than eight person-hours to disassemble with appropriate equipment.² Divisible loads generally cannot receive Interstate overweight permits unless a state has specific grandfathered authority or congressional authorization for that commodity or route.

For everything else, the workflow is the same before every trip near the limits: measure the axle spacings, look up each group in the FHWA table, confirm no single or tandem axle exceeds its cap, and verify the gross stays under 80,000 pounds. A few minutes with the table is cheaper than any fine the alternative produces.

1
Office of the Law Revision Counsel. 23 U.S.C. 127 – Vehicle Weight Limitations-Interstate System
2
eCFR. 23 CFR 658.5 – Definitions
3
Federal Highway Administration. Bridge Formula Weights
4
Federal Highway Administration. Federal Bridge Formula and Axle Weight Tables
5
eCFR. 23 CFR Part 658 – Truck Size and Weight, Route Designations
6
eCFR. 23 CFR 658.17 – Weight
7
Legal Information Institute. 23 CFR Appendix C to Part 658
8
Federal Highway Administration. Oversize/Overweight Load Permits