What the bridge formula is protecting
The bridge formula exists to protect bridges, not pavement. A bridge span responds to how much weight arrives at once and how tightly that weight is packed. Eighty thousand pounds spread over fifty-one feet of truck loads a span far more gently than the same eighty thousand pounds squeezed into thirty feet, because the shorter truck concentrates its mass over a smaller fraction of the span at any moment.
Congress therefore wrote a rule that ties allowable weight to axle spacing. Codified at 23 U.S.C. § 127 and applied on the Interstate System, it says that for any group of two or more consecutive axles, allowable weight rises as the group gets longer and as the number of axles in the group grows. Three separate statutory caps sit on top of it: 20,000 lb on a single axle, 34,000 lb on a tandem, and 80,000 lb gross.
The subtlety that catches drivers out is the phrase any group. It is not enough for the outer bridge to check out and the tandems to be under 34,000 lb each. Every interior combination has to pass too — steer plus drives, drives plus trailer tandem, and every other consecutive run. Enforcement checks them all, and the group that fails is usually one nobody looked at.
Reading the formula term by term
The formula is W = 500 × [ (L × N) ÷ (N − 1) + 12N + 36 ], and each piece does a specific job.
L is the distance in feet between the extreme axles of the group, measured centre to centre and rounded to the nearest foot in the published tables. N is the number of axles in the group. The first term, (L × N) ÷ (N − 1), is the one that rewards length: stretch the group out and allowable weight climbs roughly linearly. The 12N term rewards adding axles, and the constant 36 sets the floor.
Notice the formula is undefined at N = 1, which is why a single axle is governed by the flat 20,000 lb statutory limit instead. Notice too that the formula alone would permit far more than 80,000 lb on a long, many-axled combination; the gross cap is what stops it. Both facts explain why the calculation is always a minimum of several numbers rather than one evaluation.
The result is rounded to the nearest 500 lb, which is how the FHWA publishes its bridge table. That rounding is not decorative: at 50 ft on five axles the raw formula gives 79,250 lb and the table shows 79,500 lb, which is a real 250 lb of headroom.
One more definition matters. A tandem for weight purposes is two axles spaced more than 40 inches and not more than 96 inches apart. Spread the pair beyond 8 ft and the 34,000 lb tandem cap no longer applies; the pair is then limited by the bridge formula and by the 20,000 lb single-axle limit on each axle, which is why spread-axle trailers can legally carry more on the rear group.
Worked example: a five-axle tractor-semitrailer at 80,000 lb
You are running 12,000 lb on the steer, 34,000 lb on the drives and 34,000 lb on the trailer tandem — 80,000 lb gross. The tractor wheelbase from steer to front drive axle is 16.00 ft, both tandems are set at 4.33 ft (52 in), and the trailer tandems are pinned so the front drive axle to front trailer axle distance is 36.00 ft.
- Drive tandem. Two axles at 4.33 ft. The formula gives 500 × [(4.33 × 2) ÷ 1 + 24 + 36] = 500 × 68.66 = 34,330 → 34,500 lb, but the statutory tandem cap holds it at 34,000 lb. Actual 34,000 — legal, with nothing spare.
- Trailer tandem. Identical spacing, identical result: 34,000 lb. Legal.
- Steer plus drives. Three axles spanning 16.00 + 4.33 = 20.33 ft. 500 × [(20.33 × 3) ÷ 2 + 36 + 36] = 500 × 102.495 = 51,247 → 51,000 lb. Actual 12,000 + 34,000 = 46,000. Legal with 5,000 lb to spare.
- Drives plus trailer tandem. Four axles spanning 36.00 + 4.33 = 40.33 ft. 500 × [(40.33 × 4) ÷ 3 + 48 + 36] = 500 × 137.773 = 68,887 → 69,000 lb. Actual 34,000 + 34,000 = 68,000. Legal with 1,000 lb to spare.
- All five axles. Span 16.00 + 36.00 + 4.33 = 56.33 ft. 500 × [(56.33 × 5) ÷ 4 + 60 + 36] = 500 × 166.41 = 83,206, above the statutory maximum, so allowable gross is 80,000 lb. Actual 80,000. Legal, exactly at the cap.
Now slide the trailer tandems forward so the drive-to-trailer distance drops from 36.00 ft to 28.00 ft. The four-axle span becomes 32.33 ft and its limit becomes 500 × [(32.33 × 4) ÷ 3 + 84] = 500 × 127.107 = 63,553 → 63,500 lb. The drives and trailer tandem still carry 68,000 lb between them, so that group is now 4,500 lb over. The outer span also shortens to 48.33 ft, capping gross at 500 × [(48.33 × 5) ÷ 4 + 96] = 78,206 → 78,000 lb, so gross is 2,000 lb over as well.
This is the trap worth remembering: sliding the tandems moves weight between the drives and the trailer axles, but the four-axle group contains both, so its total is unchanged. Sliding forward makes that group's limit smaller while its weight stays the same. No amount of sliding fixes it — only more spacing or less cargo does.
Which adjustment fixes which failure
Match the failing group to the right lever, because the wrong one wastes a trip across the scale.
Drives over, trailer tandem under. Slide the fifth wheel rearward. Moving the fifth wheel back shifts trailer weight off the drives and onto the trailer axles. Each hole is typically worth a few hundred pounds.
Trailer tandem over, drives under. Slide the trailer tandems rearward. Moving the axles back moves the load's centre of gravity forward relative to them, taking weight off the trailer group and putting it on the drives.
Steer over. This is usually a fifth-wheel position problem in the other direction, or genuinely heavy equipment on the tractor. Federal law caps a single axle at 20,000 lb, and many states allow more on a steering axle, but tire load ratings frequently bind before the law does — check the sidewall rating multiplied by two.
A multi-axle group over while its members are individually legal. This is the bridge formula proper, and it means the group is too short for the weight it carries. Sliding tandems changes the split within the group, not the total, so the only remedies are a longer spacing or removing cargo. On a trailer with a sliding suspension, moving the tandems rearward lengthens the drives-to-trailer span and raises that group's limit, which is the one case where sliding does help.
Gross over. Only cargo comes off. No redistribution changes the total.
Aim to leave a margin rather than sit exactly at the limit. Fuel burn moves weight off the drives as the trip goes on, cargo settles, and platform scales differ from one another by a few hundred pounds. Loading to 79,000 lb gross rather than 80,000 gives you room for all three.
Bridge formula allowable weights by span and axle count
| Span L (ft) | 2 axles | 3 axles | 4 axles | 5 axles |
|---|---|---|---|---|
| 4 | 34,000 | — | — | — |
| 8 | 38,000 | 42,000 | — | — |
| 20 | 50,000 | 51,000 | 55,500 | — |
| 28 | 58,000 | 57,000 | 60,500 | 65,500 |
| 32 | 62,000 | 60,000 | 63,500 | 68,000 |
| 36 | 66,000 | 63,000 | 66,000 | 70,500 |
| 40 | 70,000 | 66,000 | 68,500 | 73,000 |
| 44 | 74,000 | 69,000 | 71,500 | 75,500 |
| 48 | 78,000 | 72,000 | 74,000 | 78,000 |
| 52 | 80,000 | 75,000 | 76,500 | 80,000 |
Two-axle values above 34,000 lb apply only to a spread pair wider than 8 ft; a true tandem is held to 34,000 lb by statute regardless of what the formula gives. At a fixed span the two-axle column can exceed the three-axle column because (L × N) ÷ (N − 1) falls as N rises — at L = 40 it is 80 for two axles and 60 for three — and the 12N term does not fully make that up. Real trucks do not hold span fixed while adding axles. Dashes mark spans too short to accommodate that many axles in practice.
Federal limits, state limits and permits
The numbers here are the federal limits that apply on the Interstate System under 23 U.S.C. § 127. Off the Interstate, states set their own limits, and several carry grandfathered allowances that predate the federal rule and differ from it. States also issue overweight and oversize permits that authorise loads above these figures on specified routes, and permitted configurations frequently have their own axle spacing requirements. Treat this calculator as the federal baseline check and the permit or the state manual as the operative rule wherever you are actually running.
Mistakes that produce a legal-looking truck that scales overweight
- Checking only the outer bridge. Interior groups fail far more often than the full-length group, and the four-axle drives-to-trailer group is the usual culprit.
- Measuring spacing to the trailer kingpin instead of the axles. The formula uses axle centres. The kingpin is not an axle.
- Forgetting that spacing changes when you slide. Every pin hole changes L for two different groups at once.
- Assuming a spread axle is a tandem. Beyond 8 ft it is not, which raises the pair's limit but also means each axle carries its own 20,000 lb single-axle limit.
- Loading to exactly 80,000 lb. Fuel burn, cargo settling and scale-to-scale variation all move the number after you leave the shipper.
- Ignoring the steer axle's tires. Tire load rating often binds below the legal axle limit, and a blown steer tire is a far worse outcome than a citation.
- Applying federal numbers off the Interstate. State limits and grandfathered allowances differ, sometimes in your favour and sometimes not.
Where axle weight fits with the rest of the load decision
Weight distribution starts at the dock, not the scale. Where the heavy pallets sit in the trailer determines the split between drives and trailer tandems before the driver ever touches a slide. A load built with the heavy freight over the tandems and the light freight in the nose behaves completely differently from the reverse, and the pallet pattern calculator gives you the per-pallet gross weight you need to plan that.
Whether weight or cube fills the trailer first is a density question. Dense freight hits 80,000 lb with the trailer half empty; bulky freight cubes out well below the weight limit. The crossover is what the freight density and class calculator quantifies, and it is also what decides whether the load is priced on weight or on space.
On the carrier's side, a load that cannot be made legal is a load that cannot be taken at any rate, which makes this calculation part of the same decision as the cost per mile analysis: a permit, a re-work at the shipper or a return trip all land on the cost side of the ledger.
The underlying idea — a weight distribution constrained by where it sits relative to fixed reference points — is the same one that governs aircraft weight and balance, and the moment arithmetic behind a forklift's derated capacity. In all three, the total weight is only half the question; where it is decides the rest.