The federal bridge formula decides how much weight any group of axles on your truck may carry on the Interstate, based on two things: how many axles are in the group and how far apart the outer axles of that group are.
What the formula is and where it comes from
The formula is federal law for the Interstate System. It is written in 23 CFR 658.17, and the variables are defined in 23 CFR 658.5. The regulation calls it the Bridge Gross Weight Formula.
It ties the weight a group of axles may carry to how far apart those axles are, so weight packed into a short space is limited more than weight spread out.
Section 658.17 applies to the National System of Interstate and Defense Highways and reasonable access to it. It does not set limits for other roads.
The three fixed limits, and how the formula sits under them
Section 658.17 sets three fixed limits on the Interstate:
- Single axle: 20,000 pounds on any one axle, including any one axle of a group.
- Tandem axle: 34,000 pounds. Under 658.5, a tandem is two or more consecutive axles whose centers are more than 40 inches and not more than 96 inches apart.
- Gross weight: 80,000 pounds, unless the bridge formula gives a lower figure.
The bridge formula works alongside these limits. It applies to the gross weight on any two or more consecutive axles. Every group must pass the formula, every axle must stay at or under 20,000 pounds, every tandem at or under 34,000 pounds, and the whole vehicle at or under 80,000 pounds. The lowest answer wins.
So the formula never lets you go above 80,000 pounds gross. In the words of the regulation, in no case may the total gross weight of a vehicle exceed 80,000 pounds.
How to read the formula
Here is the formula:
W = 500 × (L × N ÷ (N − 1) + 12 × N + 36)
The three letters mean:
- W is the overall gross weight allowed on the group of axles, in pounds, to the nearest 500 pounds.
- L is the distance in feet between the extreme axles of the group. That means the first axle to the last axle of the group you are checking.
- N is the number of axles in the group.
To use it, pick a group of consecutive axles. Count them. Measure from the center of the first axle in the group to the center of the last. Put the numbers in, work the brackets first, then multiply by 500. Round the result to the nearest 500 pounds.
Worked examples
These examples use the same math as the bridge formula calculator on this site. Each answer below matches what the calculator returns.
- 3 axles, 10 ft spread: formula 43,500 lb, allowed 43,500 lb
- 5 axles, 40 ft spread: formula 73,000 lb, allowed 73,000 lb
- 5 axles, 51 ft spread: formula 79,875 lb, allowed 80,000 lb after rounding
- 4 axles, 36 ft spread: formula 66,000 lb, allowed 66,000 lb
Example 1: three axles spread 10 feet
N = 3 and L = 10.
- L × N ÷ (N − 1) = 10 × 3 ÷ 2 = 15
- 12 × N = 12 × 3 = 36
- 15 + 36 + 36 = 87
- 500 × 87 = 43,500 pounds
This is already a multiple of 500, so no rounding is needed. A group of three axles with 10 feet between the outer axles may carry 43,500 pounds.
Example 2: a five-axle rig, 40 feet versus 51 feet
Take a five-axle tractor-semitrailer and check all five axles together.
At 40 feet from the steer axle to the last trailer axle:
- 40 × 5 ÷ 4 = 50
- 12 × 5 = 60
- 50 + 60 + 36 = 146
- 500 × 146 = 73,000 pounds
That rig cannot legally scale 80,000 pounds on the Interstate. It is capped at 73,000 pounds by its own axle spacing.
At 51 feet:
- 51 × 5 ÷ 4 = 63.75
- 12 × 5 = 60
- 63.75 + 60 + 36 = 159.75
- 500 × 159.75 = 79,875 pounds
Rounded to the nearest 500 pounds, that is 80,000 pounds. Stretch the outer spread to 60 feet and the formula gives 85,500 pounds, but the 80,000 pound gross limit still applies.
The figure below puts the two spreads side by side.
Example 3: the inner bridge on axles 2 through 5
Now look inside the same rig. Axles 2 and 3 are the drive tandem. Axles 4 and 5 are the trailer tandem. Say the distance from axle 2 to axle 5 is 36 feet.
N = 4 and L = 36.
- 36 × 4 ÷ 3 = 48
- 12 × 4 = 48
- 48 + 48 + 36 = 132
- 500 × 132 = 66,000 pounds
The formula alone gives 66,000 pounds for those four axles. But 658.17 has an exception for exactly this layout: two consecutive sets of tandem axles may carry 34,000 pounds each if the overall distance between the first and last axle is 36 feet or more. At 36 feet, the two tandems may carry 34,000 pounds each, or 68,000 pounds together. Below 36 feet, the exception does not apply and the formula figure governs.
Note that the site's calculator returns the plain formula figure, 66,000 pounds, for this input. Apply the tandem exception yourself when your layout fits it.
The figure below shows the group and both figures.
Why spreading axles helps
Look at the formula again. L sits on top of the fraction. Every extra foot between the outer axles adds weight to W. With five axles, each foot of spread adds 500 × 5 ÷ 4, or 625 pounds, before rounding.
That is why sliding a trailer tandem back, or running a longer wheelbase, can make the same load legal.
Adding an axle raises W too, because N appears in the 12 × N term. The extra axle still has to stay within the 20,000 pound single axle limit.
Common misreads
Only checking the whole truck. The formula applies to any group of two or more consecutive axles. Checking steer to last axle is not enough. You also have to check inner groups, such as axles 2 through 5, and axles 1 through 3. A truck can pass on its outer bridge and fail on an inner one.
Assuming every five-axle rig gets 80,000 pounds. It does not. Example 2 shows a 40-foot spread stops at 73,000 pounds. In that example, the formula reaches 80,000 pounds after rounding only at 51 feet.
Measuring the wrong distance. L runs from the first axle to the last axle of the group you are checking. It is not the trailer length or the overall length of the rig.
Forgetting there is no tolerance. Under 658.17, the axle, tandem, gross and formula weights include all tolerances, enforcement or otherwise. The one exception is a scale allowance for portable wheel-load weighers, which may never exceed 5 percent.
State permits, and why posted limits may differ
States may issue special permits for nondivisible vehicles or loads without regard to the axle, gross or bridge formula limits. That is how an overweight load that cannot be broken down moves legally. The permit, not the formula, then sets what you may carry and where.
Posted limits can also differ from the federal numbers for other reasons:
- Grandfather rights. The fixed limits in 658.17 do not apply to single axle, tandem axle or gross weights that a state legally allowed on July 1, 1956. The axle group requirement does not apply to vehicles grandfathered under state axle group tables or formulas on January 4, 1975.
- Specific exceptions. Section 658.17 lists other carve-outs for certain vehicles and routes.
- Roads off the Interstate. Section 658.17 covers the Interstate and reasonable access to it. Other roads follow state rules.
On the Interstate, a state may not enforce limits lower than 20,000 pounds on a single axle, 34,000 pounds on a tandem, or the bridge formula weights up to 80,000 pounds, except as the regulation provides. Check the state's own rules before you plan a route.
Check your own numbers
Use the bridge formula calculator to run any axle count and spread. Run it once for the whole truck, then once for each inner group. For state permit rules, start at the oversize and overweight permit pages, which cite each state's official sources.
Related guides
Weight is one side of a permit. These guides cover the rest of the move:
- trip permits versus IRP and IFTA
- pilot car basics and escort triggers
- how to read a state oversize permit