How the bridge formula really works
The federal formula is W = 500 × (LN/(N−1) + 12N + 36). FHWA defines the letters plainly: "L = the distance in feet between the outer axles of any group", "N = the number of axles in the group", and "W = the overall gross weight on any group of two or more consecutive axles to the nearest 500 pounds." Three flat caps sit on top of the formula, quoted from the same publication: "single axles are limited to 20,000 pounds, and axles spaced more than 40 inches and not more than 96 inches apart (tandem axles) are limited to 34,000 pounds. Gross vehicle weight is limited to 80,000 pounds."
The phrase that catches people is any group of two or more consecutive axles. On a five-axle tractor-trailer that is ten separate groups, not one: axles 1–2, 1–3, 1–4, 1–5, 2–3, 2–4, 2–5, 3–4, 3–5, and 4–5. Each has its own L, its own N, and therefore its own ceiling. The underlying regulation says the same thing — 23 CFR 658.17 bars operating on an Interstate highway "when the gross weight on two or more consecutive axles exceeds the limitations prescribed by the following formula." Nothing in that sentence narrows the test to the outer span. So this checker builds every group, computes each one, sorts them by how much room is left, and puts the tightest at the top of the table.
Why distance and axle count buy allowance
Read the formula as a machine and it tells you what to do about a tight number. W climbs with L, so spreading the same load over a longer wheelbase raises the ceiling. W climbs with N as well, so an extra axle in the group raises it — which is why a lift axle changes the answer here, but only if you actually enter it, with its own weight and spacing. The 12N + 36 term is a fixed allowance that grows purely with axle count; LN/(N−1) is where distance does its work. Before rounding, one additional foot of L is worth exactly 500 × N/(N−1) pounds: 1,000 lb on a two-axle group, 750 on three, about 667 on four, 625 on five. That is also the price of a sloppy measurement — half a foot of error on a five-axle span is more than 300 pounds of allowance you either have or do not.
Rounding, and where it helps
W is taken "to the nearest 500 pounds," and that rounding is not always downward. FHWA's own published example is the classic five-axle rig with 51 feet between the steer axle and the rearmost trailer axle: 500 × (51×5/4 + 60 + 36) = 79,875, which rounds up to the 80,000 shown in FHWA's table. That vector is wired into this site's automated test suite, so if the arithmetic on this page ever drifts away from FHWA's, the build fails before it ships.
A legal gross weight that still comes back over
Here is the failure that outer-span-only calculators miss. You can reproduce it in the tool above. Take a five-axle combination carrying 12,000 lb on the steer and 17,000 lb on each of the other four axles. Gross is 80,000 — right at the cap, not a pound past it. Enter the spacings as 18.0 ft steer to first drive, 4.3 ft across the drive tandem, 25.0 ft from rear drive to front trailer axle, and 4.3 ft across the trailer tandem.
Now look at what comes back. The outer span is 51.6 ft across five axles, which computes to 80,250 and is then held at the 80,000 cap, so axles 1–5 show a margin of exactly zero. The drive tandem carries 34,000 against its 34,000 cap. The trailer tandem carries 34,000 against 34,000. Gross, both tandems, and the full span are all at the line and none of them past it. But axles 2–5 form a group too: L = 4.3 + 25.0 + 4.3 = 33.6 ft, N = 4, so W = 500 × (33.6×4/3 + 48 + 36) = 64,400, rounded to 64,500. That group is carrying 68,000 lb. It is over by 3,500, and the tool reports "Over on at least one check" despite every headline figure clearing.
That is not a contrived setup. It is what a trailer with the tandems racked forward looks like, and the group that comes up short is the one nobody puts on a scale by itself.
The 36-foot exception, and the inch that decides it
FHWA carves out one exception: "two consecutive sets of tandem axles may carry 34,000 pounds each if the overall distance between the first and last axles of these tandems is 36 feet or more." The regulation words it the same way. On the rig above, that span is the axles 2–5 group again — first axle of the drive tandem to last axle of the trailer tandem.
Slide the trailer tandems until that distance measures 35.9 ft and the exception does not apply. The raw formula gives 500 × (35.9×4/3 + 84) = 65,933, rounded to 66,000, against 68,000 actual — over by 2,000. Move rearward 1.2 inches to a measured 36.0 ft and the exception switches on: allowed becomes 68,000, actual is 68,000, margin zero. Same tractor, same trailer, same axle weights. One and a fifth inches of trailer position separates a number that clears from one that does not.
This is exactly why the line above the inputs says measured spacing beats guessed spacing. Anywhere near the 36-foot boundary, a tape measure is worth more than a recollection.
What sliding the tandems actually changes
Two things at once, and this page only sees one of them unless you tell it both. Repositioning the trailer tandems changes the spacing you type here, which changes L for every group that spans them. It also redistributes weight between the trailer axles and the tractor axles, which changes the numbers in the weight column. Slide back three holes, re-run this page with the old weights, and you have an answer for a truck that does not exist.
Do it in order: work the weight transfer first on the tandem slide calculator, then bring the new weights and the new spacing back here and re-check every group. The two pages answer different questions. That one estimates where the pounds move. This one runs the federal arithmetic on the arrangement you end up with.
What this checker tests, and in what order
There is nothing hidden in the sequence. Every axle is measured against the 20,000-lb single-axle cap. Every consecutive group of two or more axles is then assembled, its L summed from the spacings you entered, and its W computed and rounded to the nearest 500. Any two-axle group whose spacing falls inside the tandem window — more than 40 inches and not more than 96 inches, which is 3.33 ft to 8.00 ft — is additionally held to 34,000. Any four-axle group built from two qualifying tandems spanning 36 ft or more receives the 68,000 allowance. Every group is capped at 80,000, and the sum of the axle weights you entered is checked against the 80,000 gross limit. Results are sorted by remaining margin, tightest first, and any group with under 1,000 lb of room is highlighted so a near miss does not hide in the middle of the table.
The form accepts anywhere from two to nine axles, which covers a straight truck through a heavy multi-axle configuration. Spacing takes decimals, so four feet six inches is 4.5 — not 4.6.
Fewer axles is not a simpler problem, just a smaller one. Delete two rows and enter a three-axle straight truck at 12,000 lb on the steer and 17,000 on each rear axle, spaced 15.0 and 4.3 ft. Gross is 46,000, comfortably beneath the federal ceiling, and the 1–3 span allows 50,500 against 46,000 carried. The binding row is again the rear tandem: 34,000 allowed, 34,000 loaded, zero margin. Adding a single hundred pounds to either rear axle pushes that row negative while gross barely twitches. The lesson generalizes: gross is only one row in the table, and as every example on this page shows, it is not necessarily the row that binds.
Reading the results table
Four columns: the group being tested with its L and N spelled out, what the federal arithmetic allows that group, what you said it actually carries, and the margin between them. A negative margin marks the group as over. Rows are ordered tightest first, so the row you care about is never buried — you read downward from your worst case, not hunting for it.
The setup loaded by default is an ordinary five-axle van: 11,800 lb steer, 16,500 on each drive axle, 16,900 on each trailer axle, spaced 16.0 / 4.3 / 32.4 / 4.3 ft. Press the button and gross comes to 78,600 with 1,400 lb to spare. The full span, L = 57.0 ft across five axles, computes to 83,625 raw and is held at the 80,000 cap, leaving that same 1,400. The 2–5 group runs L = 41.0 ft, N = 4, allowed 69,500 against 66,800 actual. Yet the tightest row in the whole table is the trailer tandem: 33,800 lb against 34,000, a margin of 200 pounds. Fourteen hundred pounds of headroom on gross, two hundred on the axle group that actually decides the outcome. That gap is the entire argument for checking groups instead of totals.
One quirk worth naming while you are looking at that row. At 4.3 ft the tandem's own formula result is 34,300, but the flat 34,000 tandem cap governs, so the table shows 34,000. At exactly 4.0 ft the formula returns 34,000 too — that is the crossover — and any tighter than that the formula itself falls below the cap and becomes the binding constraint. Whichever of the two is smaller is the number you get.
What these numbers cannot see
This page computes federal Interstate limits from figures you type in. Plenty sits outside that frame, and the gap is where trouble tends to live.
23 CFR 658.17 applies to "the National System of Interstate and Defense Highways and reasonable access thereto." The last few miles to a shipper on a county road are a separate legal question with a potentially different answer. States set their own limits off the Interstate system. Federal grandfather provisions leave some states with weight limits vested by Congress on a specific date, so an identical rig can be measured against different ceilings in different places. A permit replaces the ceiling entirely. A posted bridge overrides everything on this page with a number painted on a sign. Seasonal frost and thaw restrictions come and go on a schedule no formula predicts. Tire, axle, and suspension ratings can bind before any legal limit does.
And the arithmetic is only ever as good as what you feed it. This tool cannot know whether the steer weight you typed is current, whether the spacing came off a tape or off memory, or whether the freight shifted forty miles back. It reports what your own numbers say against the federal figures. It does not tell you that you are legal, and it is not built to — that call belongs to the scale, the officer, and the regulation.
When the margin comes back thin
A group showing a few hundred pounds of room is a planning problem, not a verdict. Three things move a tight number honestly, and one thing does not.
Re-measure. Find the group flagged tightest, look at which spacings feed its L, and put a tape on them center to center. Given what a foot of L is worth, a guess that is off by a foot is off by hundreds of pounds of allowance.
Re-weigh. A single gross ticket tells you almost nothing about interior groups. A scale that splits steer, drives, and trailer gives you inputs worth entering; anything coarser leaves you estimating the very numbers the formula is most sensitive to.
Reposition. Slide the tandems, move the fifth wheel, or get the load reworked at the dock — then re-enter both the revised weights and the revised spacings and run every group again from scratch. Do not patch one field and assume the rest held.
What never moves a tight number is optimism. The formula has no opinion about your appointment time, and neither does the scale.