The Federal Bridge Gross Weight Formula, also known as Bridge Formula B or the Federal Bridge Formula, is a mathematical formula in use in the United States by truck drivers and Department of Transportation (DOT) officials to determine the appropriate maximum gross weight for a commercial motor vehicle (CMV) based on axle number and spacing. The formula is part of federal weight and size regulations regarding interstate commercial traffic (intrastate traffic is subject to state limits). The formula is necessary to prevent heavy vehicles from damaging roads and bridges. CMVs are most often tractor-trailers or buses, but the formula is of most interest to truck drivers due to the heavy loads their vehicles often carry.

Early 20th-century weight limits were enacted to protect dirt and gravel roads from damage caused by the solid wheels of heavy trucks. As time passed, truck weight limits focused primarily on gross weight limits (which had no prescribed limits on length). By 1974, bridges received special protection from increasing truck weight limits. The bridge formula law was enacted by the U.S. Congress to limit the weight-to-length ratio of heavy trucks, and to protect roads and bridges from the damage caused by the concentrated weight of shorter trucks. The formula effectively lowers the legal weight limit for shorter trucks, preventing them from causing premature deterioration of bridges and highway infrastructure.

Compliance with the law is checked when vehicles pass through a weigh station, often located at the borders between states or on the outskirts of major cities, where the vehicle may be weighed and measured. The one exception to the formula allows a standard five-axle semi-truck configuration to weigh the maximum legal gross weight. This exception was specifically requested by the American Trucking Associations to allow tank trucks to reach the maximum legal gross weight without violating the bridge formula law.

The first truck weight limits were enacted by four states in 1913, ranging from 18,000 pounds (8,200 kg) in Maine to 28,000 pounds (13,000 kg) in Massachusetts. These laws were passed to protect earth and gravel-surfaced roads from damage caused by the steel and solid rubber wheels of early heavy trucks. By 1933, all states had some form of truck weight regulation. The Federal-Aid Highway Act of 1956 instituted the first federal truck weight regulation (set at 73,280 pounds or 33,240 kilograms) and authorized the construction of the Interstate Highway System.

In the late 1950s, the American Association of State Highway and Transportation Officials (AASHTO) conducted a series of extensive field tests of roads and bridges to determine how traffic contributed to the deterioration of pavement materials. In 1964, the AASHTO recommended to Congress that a bridge formula table be used instead of a single gross weight limit for trucks. The Federal-Aid Highway Act Amendments of 1974 established the bridge formula as law, along with the gross weight limit of 80,000 pounds (36,000 kg). Current applications of the formula allow for up to 7 axles and 86 feet or more length between axle sets, and a maximum load of 105,500 lbs.

The formula was enacted as law to limit the weight-to-length ratio of a commercial motor vehicle (CMV). The formula is necessary to prevent the concentrated truck's axles from overstressing pavements and bridge members (possibly causing a bridge collapse). In simplified form, this is analogous to a person walking on thin ice. When standing upright, a person's weight is concentrated at the bottom of their feet, funneling all of their weight into a small area. When lying down, a person's weight is distributed over a much larger area. This difference in weight distribution would allow a person to cross an area of ice while crawling that might otherwise collapse under their body weight while standing up. For an overweight truck to comply with the formula, more axles must be added, the distance between axles must be increased, or weight must be removed.

While the Federal Motor Carrier Safety Administration (FMCSA), regulates safety for the U.S. trucking industry., the Federal Highway Administration (FHWA) oversees the State enforcement of truck the size and weight Federal limits set by Congress for the Federal Aid System as described in 23 CFR 658. The Federal size limits apply in all States to the National Network (NN) which is a network of Interstate Highways, U.S. Highways, and state highways. Provided the truck remains on the NN, in all States and a truck is not subject to State size limits. In a similar fashion, the Federal weight limits and the Federal Bridge Formula apply to the Interstate System in all States. The State truck size and weight regulations apply to the Federal Aid System routes that do not have Federal limits.

The weight and size of CMVs are restricted for practical and safety reasons. CMVs are restricted by gross weight (total weight of vehicle and cargo), and by axle weight (i.e., the weight carried by each tire). The federal weight limits for CMVs are 80,000 pounds (36,000 kg) for gross weight (unless the bridge formula dictates a lower limit), 34,000 pounds (15,000 kg) for a tandem axle, and 20,000 pounds (9,100 kg) for a single axle. A tandem axle is defined as two or more consecutive axles whose centers are spaced more than 40 inches (102 cm) but not more than 96 inches (244 cm) apart. Axles spaced less than 40 inches (102 cm) apart are considered a single axle.