Federal Bridge Gross Weight Formula
This guide describes the bridge formula of 23 CFR 658.17(e): what it is, why it is necessary and how it is applied to a vehicle.
Source 23 CFR 658.17(e)Figures verified against the published regulation on November 1, 2026
What is the bridge formula?
23 CFR 658.17(e) limits the overall gross weight on any group of two or more consecutive axles to the weight given by the following formula.
W = 500 × ( LN ÷ (N − 1) + 12N + 36 )
- W is the overall gross weight on the group, in pounds, to the nearest 500 lb.
- L is the distance in feet between the outer axles of the group.
- N is the number of axles in the group.
The weight on a group may not exceed the gross vehicle weight limit of 80,000 lb, whatever the formula yields, and each single axle and tandem axle within the group remains subject to its own limit.
Why is the bridge formula necessary?
A given weight concentrated over a short length produces greater stress in a bridge than the same weight distributed over a greater length. The formula therefore relates the permissible weight on a group of axles to both the number of axles and the distance between them. An additional axle, or a greater distance between the outer axles, increases the permissible weight. For this reason, vehicles intended to carry heavier loads are commonly built with more axles or with greater axle spacing.
How is the bridge formula applied?
Consider a five-axle tractor-semitrailer with a distance of 51 ft between the steering axle and the rearmost trailer axle. In this case N is 5 and L is 51.
W = 500 × ( 51 × 5 ÷ 4 + 12 × 5 + 36 ) = 500 × 159.75 = 79,875 lb
Rounded to the nearest 500 lb, the result is 80,000 lb. At a span of 51 ft, the five axles may therefore carry the full gross vehicle weight limit of 80,000 lb; at any shorter span they may not. At a span of 45 ft, the same five axles are limited to 76,000 lb.
The formula is then applied to each shorter group of consecutive axles within the vehicle. The drive tandem and the trailer tandem, for example, together form a group of four axles. Where the distance between the outer axles of that group is 36 ft or more, the two-tandem exception permits 68,000 lb on the group, whereas the formula alone yields 66,000 lb for four axles at 36 ft.
Table of permissible weights
The following table gives the maximum weight permitted by the formula for selected spans and numbers of axles, before the single axle and tandem axle limits within the group are applied. A dash indicates that the formula permits more than the gross vehicle weight limit.
| Distance between outer axles | 2 axles | 3 axles | 4 axles | 5 axles | 6 axles |
|---|---|---|---|---|---|
| 10 ft | 40,000 lb | 43,500 lb | 48,500 lb | 54,000 lb | 60,000 lb |
| 20 ft | 50,000 lb | 51,000 lb | 55,500 lb | 60,500 lb | 66,000 lb |
| 30 ft | 60,000 lb | 58,500 lb | 62,000 lb | 66,500 lb | 72,000 lb |
| 36 ft | 66,000 lb | 63,000 lb | 66,000 lb | 70,500 lb | 75,500 lb |
| 40 ft | 70,000 lb | 66,000 lb | 68,500 lb | 73,000 lb | 78,000 lb |
| 45 ft | 75,000 lb | 69,500 lb | 72,000 lb | 76,000 lb | – |
| 51 ft | – | 74,000 lb | 76,000 lb | 80,000 lb | – |
Distances are rounded down to whole feet, which yields the more restrictive limit, and weights are rounded to the nearest 500 lb, consistent with the table published by the Federal Highway Administration.
Application in MaxLoader
A five-axle tractor-semitrailer has ten groups of two or more consecutive axles, each of which is subject to the formula. MaxLoader calculates the load on each axle from the position of the cargo, applies the formula to every group and reports, for each group, the load, the limit and the margin.
Plan a load against these limits, or calculate the limits for a particular vehicle with the Bridge Formula Calculator. See also Federal Truck Size and Weight Limits.