The Federal Bridge Formula calculates a weight value for a group of two or more consecutive axles based on axle count and the distance between the first and last axles. The table below shows selected results for groups of two through five axles, rounded to the nearest 500 pounds. These are arithmetic results—not stand-alone legal weight allowances. Single-axle, tandem-axle, gross vehicle weight, and other applicable restrictions must also be checked.
Federal Bridge Formula Reference Table
Each row represents one axle group, not necessarily the entire truck. Outer-axle spacing is the distance between the centers of the first and last axles in that group.
| Axles in group (N) | Outer-axle spacing (L), feet | Rounded formula result, pounds |
|---|---|---|
| 2 | 8 | 38,000 |
| 2 | 20 | 50,000 |
| 2 | 40 | 70,000 |
| 3 | 10 | 43,500 |
| 3 | 20 | 51,000 |
| 3 | 40 | 66,000 |
| 4 | 10 | 48,500 |
| 4 | 20 | 55,500 |
| 4 | 40 | 68,500 |
| 5 | 10 | 54,500 |
| 5 | 20 | 60,500 |
| 5 | 40 | 73,000 |
Values are calculated from the formula described in FHWA’s Bridge Formula Weights, with halfway results rounded upward for this table. No separate axle or vehicle weight caps have been applied to these figures. In particular, the 38,000-pound result for two axles spaced exactly 8 feet apart does not replace the standard 34,000-pound federal tandem limit.
Formula, Units, and Rounding
The Federal Bridge Formula is:
[
W = 500\left(\frac{LN}{N-1} + 12N + 36\right)
]
Where:
- (W) is the calculated axle-group weight in pounds, rounded to the nearest 500 pounds.
- (L) is the distance in feet between the centers of the outermost axles in the group.
- (N) is the number of consecutive axles in that group, including both outer axles and every axle between them.
The formula applies to groups of at least two axles; it cannot be used with (N = 1). Enter spacing in feet, not inches. For example, 20 feet 6 inches is 20.5 feet. FHWA defines the formula variables and explains their use in its bridge-weight guidance.
For four axles spanning 20 feet:
[
W = 500\left(\frac{20 \times 4}{4-1} + 12 \times 4 + 36\right)
= 55{,}333.33\text{ lb}
]
Rounded to the nearest 500 pounds, the result is 55,500 pounds.
Keep full precision until the final rounding step. For the five-axle, 10-foot row, the unrounded result is 54,250 pounds—exactly halfway between 54,000 and 54,500 pounds. This table uses the round-half-up convention and displays 54,500 pounds.
Why Formula Results Can Exceed an Applicable Weight Limit
The standard federal framework includes a 20,000-pound single-axle limit, a 34,000-pound tandem-axle limit, and an 80,000-pound gross vehicle weight limit, with the Bridge Formula potentially requiring a lower weight. These requirements apply together rather than as alternatives. The federal regulation addresses the Interstate System and reasonable access; it is not a universal weight table for every road. See 23 CFR § 658.17.
Two entries illustrate why the arithmetic column must not be read as a loading allowance:
- Two axles spaced 8 feet apart produce 38,000 pounds under the formula. However, 8 feet equals 96 inches, which falls within the federal tandem-spacing definition: more than 40 inches and no more than 96 inches. The standard tandem limit is therefore 34,000 pounds, not 38,000 pounds.
- Two axles spaced 20 feet apart produce 50,000 pounds under the formula. Under the standard 20,000-pound individual-axle limit, those two axles could carry no more than 40,000 pounds combined, even though the formula result is higher.
Recognized exceptions and grandfather provisions can change the applicable limits for particular vehicles or operations. Posted bridge limits, state requirements, and any permit conditions also require route-specific review; a formula result alone does not establish permission to operate.
The Two-Tandem Exception
A specific federal exception allows two consecutive sets of tandem axles to carry 34,000 pounds each when the distance between the first axle of the first tandem and the last axle of the second tandem is at least 36 feet. This permits 68,000 pounds across the two tandems under that exception, even where the ordinary four-axle formula calculation would produce a lower figure.
The exception does not raise the standard 34,000-pound limit on either tandem or eliminate the need to check the vehicle’s other axle groups and gross weight.
How to Use the Table With Axle Weights
- Identify the consecutive axle group being checked. Do not skip an axle within the group.
- Count its axles and measure the center-to-center distance between its first and last axles.
- Find the matching row, or calculate the result directly if the spacing is not listed.
- Add the measured weights on all axles in that group.
- Compare that total with the rounded formula result, then check the separate axle, tandem, gross weight, and applicable route requirements.
Checking only the group spanning the entire vehicle is not enough. Interior groups must also satisfy the applicable requirements. FHWA illustrates this with a five-axle vehicle weighing 80,000 pounds: its full five-axle group satisfies the bridge check, but axles 2 through 5 carry 68,000 pounds across 35 feet, exceeding that four-axle group’s 65,500-pound formula value by 2,500 pounds.
The table gives selected spacing examples rather than a complete bridge-weight chart. Use the exact axle count and measured spacing for the group under review; do not substitute a nearby row or treat a higher formula value as additional payload capacity.