Federal Bridge Formula Calculator
Formula B — commonly called the bridge formula or bridge law — determines the maximum weight any group of consecutive axles can carry based on axle count and spacing. Overweight violations are costly and put unnecessary stress on axles, bearings, and suspension components.
Enter your axle count and the distance between your outermost axles below to get an estimated maximum legal gross weight under the federal formula.
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What the Bridge Formula Is and Why It Exists
Formula B was created to protect bridges and pavement from concentrated axle loads. Rather than setting one flat weight limit for every truck, the bridge law scales the allowable weight based on how many axles are carrying the load and how far apart they're spaced — spreading a heavier load over more axles, or over a longer wheelbase, is allowed to carry more total weight than the same axles packed close together.
Formula B: The Math Behind It
The formula is written as: W = 500 [ LN/(N-1) + 12N + 36 ], where W is the maximum weight in pounds, L is the distance in feet between the outer axles of the group, and N is the number of axles in that group.
Worked Example
For a 3-axle group (N=3) spanning 20 feet (L=20): W = 500 [ (20×3)/(3-1) + 12(3) + 36 ] = 500 [ 30 + 36 + 36 ] = 500 × 102 = 51,000 lbs. That's the maximum weight this axle group can legally carry under the bridge law, regardless of what the individual axle limits below would otherwise allow.
Single-Axle and Tandem-Axle Weight Limits
Two flat federal limits apply on top of the bridge law calculation: a single axle is capped at 20,000 lbs, and a tandem-axle group (two axles spaced 40 inches to 96 inches apart) is capped at 34,000 lbs. Whichever number is lower — the flat axle cap or the bridge law result for that axle group — is the one that governs.
Bridge Table Reference
| Axle Spacing (ft) | 2 Axles | 3 Axles | 4 Axles |
|---|---|---|---|
| 4 | 34,000 | — | — |
| 8 | 34,000 | 42,500 | — |
| 12 | 34,000 | 45,700 | 50,000 |
| 20 | 34,000 | 51,000 | 58,000 |
| 30 | — | 58,000 | 66,500 |
These values come directly from the published FHWA bridge table and match the results of Formula B for each spacing and axle-count combination — use it as a quick cross-check against the calculator above.
State Bridge Laws vs. Federal Law
The federal bridge law sets the baseline for the Interstate highway system, but individual states can adopt their own bridge formula variations or additional weight restrictions on state and local roads. Arizona and Nevada largely mirror the federal formula on Interstate routes like I-40 and I-15, but county roads and posted bridges may carry lower limits — always check posted signage, since a load legal under the federal formula can still be a violation on a locally restricted route.
Steer Axle Limits
The steer axle has its own practical ceiling separate from the bridge formula math: most steer axles are rated by the manufacturer between 12,000 and 13,200 lbs, and many states enforce a 12,000-lb steer axle limit regardless of what the tire and suspension are physically rated to carry. Exceeding the steer axle's rated capacity affects handling and braking long before it becomes a bridge-formula violation, so it should be checked independently of the axle-group calculation above.
Why Weight Distribution Matters Beyond Compliance
Chronic overloading — even when it isn't flagged at a scale — accelerates wear on axles, wheel bearings, brake components, and suspension bushings. Uneven weight distribution from a shifted load or worn suspension components can push one axle group over its bridge-formula limit even when the gross vehicle weight is legal overall, which is a common and easily overlooked cause of scale violations.
Purpose and Practical Use of the Calculator
This tool gives a fast field estimate so you can plan loading and axle spacing before you hit a scale — not a substitute for a certified scale ticket. Always verify actual weight at a certified truck scale before your trip, especially when you're close to a calculated limit, and remember that axle repairs and suspension maintenance directly affect how evenly your load's weight is actually distributed across each axle group.
Frequently Asked Questions
What is an example of the bridge formula?
For a 3-axle group spanning 20 feet, Formula B gives W = 500[(20×3)/(3-1) + 12(3) + 36] = 500 × 102 = 51,000 lbs, meaning that axle group's maximum legal weight under the federal bridge law is 51,000 pounds.
What is Federal Bridge Formula B?
Formula B is the federal calculation — W = 500[LN/(N-1) + 12N + 36] — that sets the maximum weight allowed on a group of axles based on the number of axles (N) and the distance in feet between the outer axles (L), protecting bridges and pavement from concentrated loads.
Can my steer axle be over 12,000 lbs?
It depends on the state and the axle's manufacturer rating. Many states cap steer axles at 12,000 lbs regardless of the bridge formula result, while some allow up to 13,200 lbs if the axle and tires are rated for it. Check your state's specific regulations before loading near that limit.
What is the purpose of the bridge formula?
The bridge formula exists to protect bridges and roadways from damage caused by concentrated axle loads. It allows heavier gross weights when the load is spread across more axles or a longer wheelbase, rather than applying one flat weight limit to every truck configuration.