Bridge Formula Calculator
Calculate maximum legal weight by axle spacing using Federal Bridge Formula B.
About this calculator
The Federal Bridge Formula (Formula B) is the equation that keeps a truck's gross weight from being carried on too few, too-closely-spaced axles -- a bridge built to a published AASHTO design load can be damaged by concentrated axle loads even when the truck's total weight is under 80,000 lbs, because it's the load per foot of span that stresses a bridge deck, not the total weight alone. Formula B, codified at 23 CFR 658.17 (23 U.S.C. 127), sets the maximum weight W (in lbs) a group of axles can carry as W = 500 x [(L x N) / (N - 1) + 12N + 36], where L is the distance in feet between the outermost axles of the group and N is the number of axles in that group. Spreading the same weight over a longer wheelbase, or adding another axle, both raise the legal limit -- that's the formula's whole purpose: reward axle spread and axle count, penalize concentrated load.
This calculator evaluates one axle group at a time (the way a real weigh-station scale check does), reporting the Bridge Formula maximum, the 80,000 lb federal gross-vehicle-weight cap, and -- specifically for a 2-axle group spaced between 40 and 96 inches (3.33 to 8 ft), which federal law defines as a tandem axle -- the 34,000 lb tandem-axle limit. That tandem limit is an INDEPENDENT cap: Formula B alone permits more than 34,000 lbs on a 2-axle group once the spacing passes roughly 7 ft, but 23 U.S.C. 127 still holds a legally-defined tandem to 34,000 lbs regardless of what the formula computes, so the calculator reports whichever of the three limits is lowest as the effective legal weight. A full truck combination is checked group by group this way -- steer axle, drive tandem, trailer tandem or tridem -- not as one number for the whole vehicle, and state permit programs, bridge-specific postings, and non-Interstate roads can all impose additional limits this federal formula does not capture.
Inputs
Results
Bridge Formula Max Weight
79,875 lbs
≈ 7 elephants
Effective Limit
79,875 lbs
≈ 7 elephants
Figures current as of 2019. Source: 23 U.S.C. § 127; 23 CFR 658.17, Appendix C (Federal Bridge Formula); FHWA-HOP-19-028, Federal Size Regulations for Commercial Motor Vehicles
How to Use This Calculator
- Enter the Number of Axles in the axle group being evaluated.
- Set the Outer Axle Spacing in feet (distance from first to last axle in the group).
- Enter the Actual Weight on the axle group in lbs.
- Review the Bridge Formula Max Weight, Compliance Status (legal or over), and Over/Under Limit.
- If over the limit on Formula B alone, check Min Spacing for Weight to see what axle spread would satisfy the formula -- but note it doesn't account for the independent 80,000 lb GVW or 34,000 lb tandem caps, so it isn't a guaranteed fix when one of those is the binding constraint.
How the result changes with Outer Axle Spacing
| Outer Axle Spacing | Bridge Formula Max Weight | Effective Limit |
|---|---|---|
| 26 | 64,250 lbs | 64,250 lbs |
| 38 | 71,750 lbs | 71,750 lbs |
| 60 | 85,500 lbs | 80,000 lbs |
What each input means
- Number of Axles
- Number of axles in the group being evaluated.
- Outer Axle Spacing
- Distance in feet between the first and last axle of the group.
- Actual Weight on Group
- Actual weight on the axle group being evaluated.
What each result means
- Min Spacing for Weight
- Spacing that would satisfy Formula B alone. Does not account for the independent 80,000 lb GVW cap or 34,000 lb tandem cap -- if Actual Weight already exceeds either of those, no amount of spacing makes the load legal.
How this is calculated
Worked example, using the default values
- Identify Input Parameters3 parametersNumber of Axles = 5, Outer Axle Spacing = 51, Actual Weight on Group = 75000 = 3 input(s) provided
- Calculate Bridge Formula Max WeightBridge Formula Max Weight79875 = 79875
- Calculate Effective LimitEffective Limit79875 = 79875
- Calculate Compliance StatusLegal = Legal
- Calculate Weight per AxleWeight per Axle15000 = 15000
Figures and sources
- Federal Bridge Formula B and federal weight limits (80,000 lb GVW / 34,000 lb tandem-axle) (2019) — 23 U.S.C. § 127; 23 CFR 658.17, Appendix C (Federal Bridge Formula); FHWA-HOP-19-028, Federal Size Regulations for Commercial Motor Vehicles
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does spreading axles farther apart raise the legal weight limit?
Because Formula B is protecting bridges from concentrated load, not protecting the road surface or the truck's own components. A given total weight applied over a longer wheelbase spreads the bending stress a bridge span experiences over more of its length, so federal law rewards a longer axle spread (larger L) or an added axle (larger N) with a higher legal weight for that axle group. This is why a 5-axle tractor-trailer can legally gross 80,000 lbs while a 2-axle straight truck cannot -- more axles spread farther apart carry more weight without exceeding any single bridge span's design load.
My 2-axle group passes Formula B -- why does this calculator still say it's overweight?
Because federal law (23 U.S.C. 127) sets 34,000 lbs as an independent ceiling on any "tandem axle" -- two axles spaced more than 40 and not more than 96 inches (3.33 to 8 ft) apart -- regardless of what Formula B alone would allow at that spacing. Once a 2-axle group's spacing passes roughly 7 ft, Formula B's own number climbs above 34,000 lbs, but the tandem cap still governs. This calculator reports the lowest of the Bridge Formula result, the 34,000 lb tandem cap (when it applies), and the 80,000 lb federal gross weight limit as the effective legal weight for the group.
Does this calculator check my entire truck's weight at once?
No -- it evaluates a single axle group, the same unit the Bridge Formula itself governs and the same way a weigh-station officer checks a scale ticket. A tractor- trailer is checked group by group: steer axle, drive tandem, and trailer tandem or tridem each have their own spacing and weight, and each must independently satisfy Formula B before the overall 80,000 lb gross vehicle weight is even relevant. This calculator itself checks Formula B and, when the group is a 2-axle tandem, the 34,000 lb tandem cap -- it does not check the 20,000 lb single-axle cap, since that limit applies to a single axle rather than an axle group and this tool's minimum group size is two axles; verify a steer axle's weight against 20,000 lbs separately.
What does 'Min Spacing for Weight' tell me if I'm over the limit?
It rearranges Formula B to solve for the axle spacing L that would make your entered Actual Weight exactly legal under the formula alone, holding the number of axles fixed -- in effect, how far apart the axles would need to be spread to carry that weight. It does not account for the independent 34,000 lb tandem-axle cap or the 80,000 lb GVW cap, both of which apply regardless of spacing. If Actual Weight already exceeds 80,000 lbs, no amount of axle spread makes the load legal -- Formula B only governs how weight is distributed across a group's axles, not the truck's total weight, so the fix in that case is removing weight, not spreading axles further. Likewise, for a 2-axle group already at or under the 34,000 lb tandem cap, no extra spacing is needed; the Min Spacing figure is only a real route to legality when Formula B itself, not one of the two independent caps, is the binding constraint.
Are the 80,000 lb and 34,000 lb limits the same on every road?
No -- those are the federal limits for the Interstate Highway System under 23 U.S.C. 127. States can and do set different limits on non-Interstate roads, and many issue overweight/oversize permits that allow higher weights on specific routes under specific conditions. Bridges can also carry their own posted weight limits below the federal formula's result. Always confirm against the specific state and route before relying on a Formula B calculation alone for a real trip.
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