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Bridge Formula Calculator

How much can your dump truck haul legally? Enter the axles and the spacing between them. Get the most the truck may gross on the Interstate, the axle group that sets it, what a lift axle changes, and your legal payload.

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The math, shown transparently

Every rule below comes from the statute or regulation cited in the sources. The math is locked in a unit test against FHWA’s Bridge Table.

// Every group of 2 or more axles in a row, steer included

W = 500 × (L × N / (N − 1) + 12 × N + 36)

// to the nearest 500 lb; an exact half rounds down (FHWA)

// L = first to last axle in feet, rounded down to whole feet

// Limits that replace or sit on top of the formula

40 in or less apart: one axle, 20,000 lb

over 40 in to 96 in: tandem, 34,000 lb

two tandems 36 ft or more first to last: 34,000 lb each

any one axle: 20,000 lb; whole truck: 80,000 lb

// The answer

max legal gross = the most weight that fits every limit at once

The max legal gross is not just the smallest number in the table. A tandem dump’s axle limits alone allow 20,000 lb + 34,000 lb = 54,000 lb, which can be more than the formula allows on the whole truck, or less. The calculator finds the heaviest load that keeps every axle and every group under its limit at the same time. Because each limit covers a run of axles in a row, that answer is the cheapest way to split the truck into runs, each counted at its limit, and the calculator shows one axle load split that reaches it.

Rounding L down is our choice, not the law. 23 U.S.C. 127 and 23 CFR 658.17 do not say how to round a fractional foot. FHWA’s table prints its “more than 8, less than 9” row at the 8 ft values, and rounding down can only understate the limit, never overstate it. In metric, metres are converted to feet first, then rounded down.

Worked examples

Tandem dump: 17 ft 6 in, 4 ft 6 in

Example spacing to show the rules, not a standard truck. Measure yours.

  • Axles 1 to 2: 17 ft 6 in, L 17 ft, N 2: 500 × 94 = 47,000 lb (the other limits hold it to 40,000 lb).
  • Axles 2 to 3: 54 in, tandem: 34,000 lb.
  • Axles 1 to 3: 22 ft, L 22 ft, N 3: 500 × 105 = 52,500 lb.

Max legal gross: 52,500 lb, set by axles 1 to 3 (Bridge Formula: 52,500 lb, the outer bridge). The axle limits alone would allow 54,000 lb. One split that reaches it: steer 18,500, axle 2 17,000, axle 3 17,000 lb.

Tri-axle at FHWA Figure 8 spacing: 14 ft, 4 ft 6 in, 4 ft 6 in

FHWA’s Figure 8 spacing. FHWA shows no lift axle; we treat axle 2 as one to show the difference.

  • Axles 1 to 2: 14 ft, L 14 ft, N 2: 500 × 88 = 44,000 lb (the other limits hold it to 40,000 lb).
  • Axles 2 to 3: 54 in, tandem: 34,000 lb.
  • Axles 3 to 4: 54 in, tandem: 34,000 lb.
  • Axles 1 to 3: 18 ft 6 in, L 18 ft, N 3: 500 × 99 = 49,500 lb.
  • Axles 2 to 4: 9 ft, L 9 ft, N 3: 500 × 85.5, an exact half, rounded down to 85 = 42,500 lb.
  • Axles 1 to 4: 23 ft, L 23 ft, N 4: 500 × 114.67, rounded to 115 = 57,500 lb.

Lift axle down: 57,500 lb, set by axles 1 to 4 (Bridge Formula: 57,500 lb, the outer bridge). Axles 2 to 4 can never carry more than 42,500 lb, so the steer has to carry at least 15,000 lb. One split that reaches it: steer 15,000, axle 2 14,000, axle 3 14,000, axle 4 14,500 lb.

  • Axles 1 to 3: 18 ft 6 in, L 18 ft, N 2: 500 × 96 = 48,000 lb (the other limits hold it to 40,000 lb).
  • Axles 3 to 4: 54 in, tandem: 34,000 lb.
  • Axles 1 to 4: 23 ft, L 23 ft, N 3: 500 × 106.5, an exact half, rounded down to 106 = 53,000 lb.

Lift axle up (axles 1, 3, 4, 18 ft 6 in, 4 ft 6 in): 53,000 lb, set by axles 1 to 4 (Bridge Formula: 53,000 lb, the outer bridge). Down allows 4,500 lb more on paper.

Tandem dump pulling a tandem pup: 17 ft 6 in, 4 ft 6 in, 27 ft, 4 ft 6 in

Example spacing to show the rules, not a standard truck. Measure yours.

  • Axles 1 to 2: 17 ft 6 in, L 17 ft, N 2: 500 × 94 = 47,000 lb (the other limits hold it to 40,000 lb).
  • Axles 2 to 3: 54 in, tandem: 34,000 lb.
  • Axles 3 to 4: 27 ft, L 27 ft, N 2: 500 × 114 = 57,000 lb (the other limits hold it to 40,000 lb).
  • Axles 4 to 5: 54 in, tandem: 34,000 lb.
  • Axles 1 to 3: 22 ft, L 22 ft, N 3: 500 × 105 = 52,500 lb.
  • Axles 2 to 4: 31 ft 6 in, L 31 ft, N 3: 500 × 118.5, an exact half, rounded down to 118 = 59,000 lb (the other limits hold it to 54,000 lb).
  • Axles 3 to 5: 31 ft 6 in, L 31 ft, N 3: 500 × 118.5, an exact half, rounded down to 118 = 59,000 lb (the other limits hold it to 54,000 lb).
  • Axles 1 to 4: 49 ft, L 49 ft, N 4: 500 × 149.33, rounded to 149 = 74,500 lb (the other limits hold it to 72,500 lb).
  • Axles 2 to 5: 36 ft, L 36 ft, N 4: 500 × 132 = 66,000 lb, raised to 68,000 lb by the 36 ft exception.
  • Axles 1 to 5: 53 ft 6 in, L 53 ft, N 5: 500 × 162.25, rounded to 162 = 81,000 lb, held to the 80,000 lb gross limit.

Max legal gross: 80,000 lb, set by the 80,000 lb federal gross limit. One split that reaches it: steer 15,000, axle 2 15,500, axle 3 16,000, axle 4 16,500, axle 5 17,000 lb.

Move the pup 1 in closer (26 ft 11 in from axle 3 to 4) and axles 2 to 5 span 35 ft 11 in: the exception is lost and they drop to 65,500 lb. The gross is still 80,000 lb, because the steer can take the rest. With a 12,000 lb steer rating it cannot: 80,000 lb at 36 ft but 77,500 lb at 35 ft 11 in.

How to use the calculator

  1. Set the axles. Add or remove axles until the list matches your truck, up to 9. Axle 1 is the steer. A truck and pup is one list, front to back.
  2. Measure every spacing. Center of axle to center of axle, in feet and inches (or metres). Enter each one between the axles it separates.
  3. Mark lift axles. Tick Lift axle on any axle that raises. The calculator works the truck with those axles down and up.
  4. Add the steer rating and empty weight. Optional. The steer rating counts when it is under 20,000 lb. The empty weight off a scale ticket gives your legal payload.
  5. Read the result. Max legal gross, the axle group that sets it, every group’s limit, one load split that reaches it, and your payload with a link into the dump truck load calculator.

Sources and assumptions

Frequently asked questions

How much can a tri-axle dump truck haul legally?

It depends on the axle spacing. On FHWA’s Figure 8 spacing (steer, then 14 ft, 4 ft 6 in, 4 ft 6 in between axles), the Bridge Formula allows 57,500 lb gross on the Interstate. FHWA shows no lift axle there, but if axle 2 were one (our assumption, to show the effect), the truck could gross 53,000 lb with it up. Your legal payload is that gross minus your empty weight off a scale ticket. If a pusher sits within 96 in of the back axle, all three axles share the 34,000 lb tandem limit, so the pusher adds less than you might think. Enter your own spacings in the calculator for your truck.

How much can a tandem dump truck haul legally?

Under the federal limits, at most 54,000 lb gross on the Interstate from the axle limits (20,000 lb on the steer plus 34,000 lb on the tandem), and often less once the Bridge Formula is applied. With 17 ft 6 in, 4 ft 6 in spacing, the whole truck spans 22 ft and the formula allows 52,500 lb. Subtract your empty weight for the payload.

Do lift axles help?

On paper they can. Down, a lift axle adds to N and spreads the load, so the formula allows more: 4,500 lb more on FHWA’s Figure 8 spacing with axle 2 treated as a lift axle (57,500 lb down, 53,000 lb up; the lift axle is our assumption, FHWA shows none). But federal law does not address lift axles. In a 2000 study FHWA wrote that “Federal TS&W laws, as well as most State laws, do not address the use of lift axles.” States have their own rules, so the calculator shows both numbers and promises nothing about either.

What is the bridge formula?

A federal limit on the weight of every group of two or more axles in a row: W = 500 × (L × N / (N − 1) + 12N + 36), where L is the distance in feet from the group’s first axle to its last and N is the number of axles in the group, to the nearest 500 lb. FHWA rounds an exact half down. Congress enacted it in 1975 to limit the weight-to-length ratio of a vehicle crossing a bridge. It applies on the Interstate along with the 20,000 lb single axle, 34,000 lb tandem and 80,000 lb gross limits, and every group has to pass, not just the whole truck.

Does the steer axle count?

Yes. Groups that start at the steer axle count like any other; FHWA’s own worked checks add up axles 1 through 3 and 1 through 4. The steer axle also has the 20,000 lb single axle limit, and a state may hold it to the manufacturer’s rating when that is lower (23 CFR 658.17(f)). Enter your rating and the calculator uses it.

What is the 36 foot exception?

Two consecutive tandems may carry 34,000 lb each when the first axle of the front tandem is 36 ft or more from the last axle of the rear one (23 CFR 658.17(e)). Without it the formula would allow only 66,000 lb to 67,500 lb on tandems 36 to 38 ft apart. For a tandem dump pulling a tandem pup at 36 ft, axles 2 to 5 get 68,000 lb; at 35 ft 11 in they get 65,500 lb. The statute’s 30 ft rule for dump trailers covers only vehicles from before September 1, 1989, and the calculator does not apply it.

Is there a weight tolerance?

No. The federal axle, tandem, gross and Bridge Formula limits are “inclusive of all tolerances” (23 CFR 658.17(g)). The only exception is a scale allowance of up to 5 percent when weighing on portable wheel-load scales. The calculator adds no tolerance.

Do state limits differ?

Yes. The federal limits cover the Interstate and reasonable access to it (23 CFR 658.17(a)). Other roads follow state law, and some states allow more on the Interstate under grandfather rights. A posted bridge limit overrides all of it. Check your state DOT before you load to the number; FHWA’s compilation of state laws (laws as of 2012) is a starting point. Canada is not modeled.

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