What is the Federal Bridge Gross Weight Formula?

 Truck drivers and department of transportation officials use The Federal Bridge Law Formula to determine the appropriate maximum gross weight of trucks. Truck axle weight limits by state vary. The formula is part of federal weight and size regulations regarding interstate commercial traffic also known as Bridge Laws. Preventing heavy vehicles from damaging roads and bridges is highly important.  Allowable weight depends on the number of axles a vehicle has and axle spacing. There are many axle spacing diagrams out there. An axle is a rod around which a wheel moves or rotates. Any kind of vehicle with wheels uses some kind of axle for those wheels to rotate on.

History of Federal Bridge Gross Weight Formula or Truck Axle Weight Limits by State

First, let's take a look at how this formula originated.  It started in 1913, only four states enacted the formula. Eventually, by 1933, all states had some form of truck weight regulation. Then, the Federal-Aid Highway Act of 1956 instituted the first federal truck weight regulation.

Formula Law

  In fact, weigh stations check each vehicle's gross weight and axle weight using a set of in-ground truck scales.

w=500\left({\frac {\ell n}{n-1}}+12n+36\right)
  • w = maximum weight in pounds that can be carried on a group of two or more axles to the nearest 500 pounds (230 kg)
  •  = spacing in feet between the outer axles of any two or more consecutive axles
  • n = number of axles being considered

As a matter of fact, the axle groups must comply with the bridge formula.

For example, the figure below shows the most common vehicle checked for compliance with weight limit requirements.

Although, the Bridge Formula applies to each combination of two or more axles, experience shows that axle combinations 1 through 3, 1 through 5, and 2 through 5 are critical and must be checked.

More importantly, any two axles must comply with the results of the formula. The axle groups 1–5, 1–3, and 2–5 are most critical. Indeed, this truck is not in violation of the formula.


Penalties for violating truck axle weight limits by state varies, as the states are responsible for enforcement and collection of fines. To learn state specific fine amounts contact the Department of Transportation.


1. Axles are measured to the nearest foot between the extremes on any group of two or more consecutive axles.

2. Gross weights for 5 and 6 axle vehicles apply to combinations only.

3. Two consecutive sets of tandems may carry 34,000 pounds each providing the overall distance between the first and last axles of such consecutive sets of tandems is 36 feet or more.

4. Also, if the distance between the centers of the first and third axles in a group of consecutive axles does not exceed 96 inches, the group is a tandem.

5. So, the maximum weight of any single axle is 20,000 pounds and the maximum weight of any tandem is 34,000.

6. To compensate for these weight restrictions, some tractors have a fifth wheel (also called as "slider"), that can slide forward or backward on the tractor frame. This sliding motion shifts and balances the trailer's kingpin weight put on each axle without moving the cargo around. Sliders let you adjust the wheelbase in order to be in compliance with the bridge law.