Federal Bridge Formula Calculator
Calculate the maximum legal gross weight for a group of truck axles using the Federal Bridge Gross Weight Formula (23 CFR 658.17).
How this calculator works
Truck weight limits aren’t just about the total number on the scale — how far apart the axles sit matters just as much. This calculator applies the federal Bridge Formula to a group of axles, using the spacing between the first and last axle in the group along with the number of axles, to find the maximum gross weight allowed for that group.
Formula: W = 500 × ((L × N ÷ (N − 1)) + 12N + 36), where W is the maximum gross weight in pounds, L is the distance in feet between the first and last axle of the group, and N is the number of axles in that group. This is the US federal formula (23 CFR 658.17, commonly called the “Bridge Formula” or “Bridge Law”) that limits truck weight based on axle spacing, not just total weight, to protect bridges from concentrated loads.
Worked example
20 ft axle spread, 3 axles in the group:
- L × N ÷ (N − 1) = 20 × 3 ÷ 2 = 30
- 12N = 12 × 3 = 36
- Sum: 30 + 36 + 36 = 102
- W = 500 × 102 = 51,000 lb maximum gross weight for that axle group
Notes
The Bridge Formula exists because a heavy load concentrated on closely-spaced axles stresses a bridge span more than the same total weight spread over a longer wheelbase — it’s why longer trucks are allowed more total weight than shorter ones carrying the same axle count.
This is a federal formula, but it interacts with state-specific weight limits and permit rules, so a specific route’s actual legal limit can differ.
How to use
Enter the distance in feet between the first and last axle of the group and the number of axles in that group. The calculator returns the maximum legal gross weight for that axle group under the federal formula, which you can then cross-check against state limits for your route.
This is the federal formula for legal gross vehicle weight (23 CFR 658.17), not a structural capacity calculation. Confirm with your carrier’s DOT compliance department or state permitting office for your specific route and vehicle configuration.
Frequently asked questions
What is the Federal Bridge Formula?
It's a US federal regulation (23 CFR 658.17), commonly called the Bridge Formula or Bridge Law, that sets the maximum legal gross weight for a group of truck axles based on how far apart those axles are spaced and how many axles are in the group, rather than just capping total vehicle weight.
Why does axle spacing matter for weight limits?
A heavy load concentrated on closely-spaced axles puts more stress on a bridge span than the same total weight spread over a longer wheelbase. The Bridge Formula limits weight based on spacing specifically to protect bridges from that concentrated-load stress, which is why longer trucks are allowed more total weight than shorter ones carrying the same number of axles.
Does the federal Bridge Formula override state weight limits?
No. The federal formula sets a baseline, but it interacts with state-specific weight limits and permit rules, so the actual legal limit for a specific route can differ from the federal calculation. Carriers need to check both federal and state requirements for the route being used.
What counts as an axle group under the Bridge Formula?
An axle group is any set of two or more consecutive axles on a vehicle, measured from the first axle to the last axle in that set. The formula can be applied to different axle groupings on the same vehicle, and each grouping has its own maximum gross weight result.
Estimates only. Verify quantities with your supplier before purchasing.