The Federal Bridge Formula Explained, With Worked Examples

You can be under 80,000 lb gross, under 34,000 on each tandem, and still be overweight on the Interstate. The federal bridge formula limits the weight on every group of axles in a row, and if your axles are too close together, it can hold you below those numbers. Here's how it works and how to check your own rig.

The formula

W = 500 × (L × N ÷ (N − 1) + 12 × N + 36)

• W is the most the axle group may carry, rounded to the nearest 500 lb.
• L is the distance in feet between the first and last axle of the group, center to center.
• N is the number of axles in the group.

It applies to every group of two or more consecutive axles: the whole truck (the "outer bridge"), the tractor, the trailer, and everything in between. FHWA says that on a typical 5-axle tractor-semitrailer, axles 1 through 3, 1 through 5, and 2 through 5 are the ones that usually decide it.

The other federal limits

• Any single axle: 20,000 lb. Axles 40 inches or less apart count as one axle.
• A tandem (axles more than 40 and not more than 96 inches apart): 34,000 lb. The tandem limit replaces the formula for those axles.
• Gross: 80,000 lb on the Interstate, unless the formula gives less.
• Two tandems in a row may carry 34,000 lb each if the first and last axles of the two tandems are 36 feet or more apart, even though the formula alone would allow only 66,000 to 67,500 lb on tandems 36 to 38 feet apart.

Worked example: a 5-axle tractor-trailer

This is FHWA's own example. Steer axle 12,000 lb; drives and trailer tandem 17,000 lb per axle; 80,000 lb gross. Axle 1 to axle 3 is 20 feet, axle 2 to axle 5 is 35 feet, and axle 1 to axle 5 is 51 feet. The single, tandem, and gross limits all pass. Now the bridge groups:

• Axles 1 to 3 (tractor): 500 × (20 × 3 ÷ 2 + 36 + 36) = 500 × 102 = 51,000 lb. The actual weight is 12,000 + 17,000 + 17,000 = 46,000 lb. Legal.
• Axles 1 to 5 (outer bridge): 500 × (51 × 5 ÷ 4 + 60 + 36) = 79,875, which rounds to 80,000 lb. The actual weight is 80,000 lb. Legal, just.
• Axles 2 to 5: 500 × (35 × 4 ÷ 3 + 48 + 36) = 65,333, which rounds to 65,500 lb. The actual weight is 4 × 17,000 = 68,000 lb. Over by 2,500 lb.

The fix is to move the trailer tandem back. At 36 feet from axle 2 to axle 5, the two-tandem exception kicks in and those four axles may carry 34,000 + 34,000 = 68,000 lb. On a trailer with sliding tandems, that means moving them back, which also shifts weight between the drives and the trailer axles, so recheck both tandems afterward.

A straight truck example

FHWA's second example is a 4-axle single-unit truck: 12,000 lb on the steer and 15,000 lb on each of three rear axles, 57,000 lb gross. Axles 1 to 4 are 23 feet apart: 500 × (23 × 4 ÷ 3 + 48 + 36) = 57,333, rounded to 57,500 lb. That passes. But the three rear axles span only 9 feet: 500 × (9 × 3 ÷ 2 + 36 + 36) = 42,750, which FHWA rounds down to 42,500 lb. They carry 45,000. Over by 2,500 lb. Closely spaced axles are where the formula bites hardest.

Rounding

FHWA's bridge table rounds to the nearest 500 lb, and when the answer lands exactly halfway, it rounds down. Five axles over 30 feet works out to 66,750 lb, and the table lists 66,500. The table also reads spacings in whole feet. Anything more than 8 but less than 9 feet uses the 8-foot row, so two axles 97 inches apart may carry 38,000 lb.

State limits and grandfather rights

These are the federal Interstate limits. Some states kept higher weights they allowed before the federal limits took effect, and states set their own limits on other roads. Before you load heavy for a particular state, look it up in truck weight limits by state.

Check your rig

Measure center to center between each pair of axles, enter the spacings and your scale ticket weights in the bridge formula calculator, and it checks every axle group and shows the math. If you're planning the whole trip, the hours of service calculator helps with the driving side.