Federal Bridge Formula Calculator
A federal bridge formula calculator applies W = 500 × (LN ÷ (N − 1) + 12N + 36): 3 axles spread over 20 ft may carry up to 51,000 lb under the federal rule.
How much weight can my axles carry?
A federal bridge formula calculator works out the most weight a group of truck axles may carry on the Interstate System. It uses W = 500 × (L × N ÷ (N − 1) + 12N + 36), where L is the distance in feet from the first to the last axle in the group and N is how many axles are in the group. Three axles spread over 20 ft give 500 × (30 + 36 + 36) = 51,000 lb.
Enter the axle spread and the number of axles. Enter at least 2 axles; the formula divides by N − 1, so a single axle has no bridge formula result (single axles have their own 20,000 lb federal limit).
The formula in plain words
- Spacing term = L × N ÷ (N − 1)
- Axle term = 12 × N
- Weight = 500 × (spacing term + axle term + 36)
Each extra foot of spread adds weight, and each extra axle adds weight. The 500 multiplier converts the sum into pounds.
Worked examples
All results match the calculator.
- Three-axle group spread over 20 ft
- Spacing term: 20 × 3 ÷ 2 = 30
- Axle term: 12 × 3 = 36
- Sum: 30 + 36 + 36 = 102
- W = 51,000 lb
- Five-axle tractor-semitrailer, 51 ft from steer axle to rear axle
- Spacing term: 51 × 5 ÷ 4 = 63.75
- Axle term: 12 × 5 = 60
- Sum: 63.75 + 60 + 36 = 159.75
- W = 79,875 lb, which the official table rounds to 80,000 lb
That is why roughly 51 ft of outer bridge is the length a standard five-axle rig needs to use the full 80,000 lb gross limit.
- Tandem drive axles 4 ft apart
- Spacing term: 4 × 2 ÷ 1 = 8
- Axle term: 24
- Sum: 8 + 24 + 36 = 68
- W = 34,000 lb, matching the federal tandem axle limit
Formula results for common groups
| Axles | Spread | Formula result | Note |
|---|---|---|---|
| 2 | 4 ft | 34,000 lb | Equals tandem limit |
| 2 | 8 ft | 38,000 lb | Still a tandem; 34,000 lb cap applies |
| 3 | 10 ft | 43,500 lb | Tridem or tandem plus lift axle |
| 3 | 20 ft | 51,000 lb | Calculator default |
| 4 | 30 ft | 62,000 lb | Straight truck with pusher and tag |
| 4 | 36 ft | 66,000 lb | |
| 5 | 40 ft | 73,000 lb | Short tractor-trailer |
| 5 | 51 ft | 79,875 lb | Table shows 80,000 lb |
| 5 | 60 ft | 85,500 lb | 80,000 lb gross cap applies |
Limits that sit on top of the formula
The bridge formula is one test among several. On the Interstate System:
- Single axle: 20,000 lb.
- Tandem axle (axle centers more than 40 in and no more than 96 in apart): 34,000 lb.
- Gross vehicle weight: 80,000 lb.
- Every axle group must also pass the bridge formula.
There is a known exception: two consecutive tandems may carry 34,000 lb each when the first and last axles of those tandems are at least 36 ft apart, even where the formula gives slightly less. State routes, grandfathered state limits, and permits add further rules.
Why the tandem cap matters
The formula alone would let two axles 8 ft apart carry 38,000 lb. Because they still count as a tandem, the 34,000 lb cap applies instead.
How to measure axle spread
- Measure center to center of the axle hubs, not tire edge to tire edge.
- Round to the nearest foot. The official table uses whole feet.
- Check every grouping, not only the outer bridge. A short drive tandem can fail even when the whole truck passes.
- Count lift axles only when they are down and carrying load.
Common mistakes
- Treating the formula result as the legal limit. The single, tandem, and gross caps can be lower.
- Measuring to the kingpin. The bridge is axle to axle.
- Ignoring state law. Off the Interstate, state limits may be higher or lower.
- Forgetting the payload’s position. Even within limits, shifting the load can overload one group.
Related calculators
For moving heavy loads on site, the dumpster weight calculator and pounds to tons calculator help estimate payload, and the truck turning radius calculator checks site access. This is a planning tool, not legal advice. Confirm compliance with the official Bridge Table, your state DOT, or a licensed transportation engineer.
Frequently asked questions
What is the Federal Bridge Formula?
It is the federal rule in 23 CFR 658.17, often called Bridge Formula B, that limits how much weight any group of two or more consecutive axles may carry on the Interstate System, based on the number of axles and the distance between the first and last axle in the group. It protects bridges by stopping heavy loads from being packed onto short wheelbases.
Why does axle spacing matter for weight limits?
A bridge span feels the load on whatever axles are on it at once. The same 60,000 lb spread over 40 ft stresses a short span far less than 60,000 lb bunched over 20 ft. So the formula lets a group carry more weight the longer it is and the more axles share the load.
Does the bridge formula result override other limits?
No. The lowest applicable limit wins. On the Interstate System the federal limits are 20,000 lb on a single axle, 34,000 lb on a tandem axle, and 80,000 lb gross vehicle weight, along with the bridge formula. States set limits on other roads and issue overweight permits, so check the route.
What counts as an axle group under the Bridge Formula?
Any two or more consecutive axles, measured from the center of the first to the center of the last, in feet. A five-axle tractor-trailer is checked several ways: the steer axle through the last trailer axle, the drive tandem alone, the trailer tandem alone, the drive axles through the trailer axles, and so on. Every grouping must pass.
Why does the official bridge table differ slightly from my result?
The published Bridge Table rounds results to the nearest 500 lb, while this calculator shows the unrounded formula value. For 5 axles over 51 ft the formula gives 79,875 lb, which the table lists as 80,000 lb. Use the official table or your state DOT for compliance decisions.
Estimates only. Verify quantities with your supplier before purchasing.