Choose formula weight, span from unrounded weight, or whole-number axle counts from unrounded weight. Convert pounds, kilograms, US short tons and metric tonnes. This is formula arithmetic, not legal loading clearance.

Federal Bridge Formula arithmetic for one axle group. This is not a legal loading clearance: other axle, vehicle, route and permit limits still apply.

Center of the first axle to center of the last axle in this group. Unit changes convert the value.

Whole-number count, 2–1,000 supported for arithmetic; this is not a permitted configuration range.

Federal Bridge Formula Weight Formula

The Federal Bridge Formula uses axle-group span and axle count. Forward results are rounded to the nearest 500 lb; raw values remain visible. Other limits and exceptions require separate checks.

W = 500 × ((L × N) / (N - 1) + 12 × N + 36)
L = ((W / 500) - 12 × N - 36) × ((N - 1) / N)
12 × N² + (L - 12 - A) × N + A = 0, where A = (W / 500) - 36
  • W = raw formula weight in pounds for the equations below; the forward output also shows nearest-500-lb rounding
  • L = axle group span, in feet, measured from the center of the first axle to the center of the last axle in the group
  • N = number of axles in the group
  • A = intermediate value used when solving for the number of axles

Choose a solve mode and fill the displayed fields. Weight mode shows the rounded formula value and raw arithmetic. Inverse modes solve the unrounded equality, not minimum legal spacing or the minimum axle count for a requested load. Axle-count mode checks every integer from 2 to 1,000 and reports all matches; no exact match is an error. This supported calculation range is not a permitted vehicle range.

Common Bridge Formula Reference Values

These examples show raw formula values before nearest-500-lb rounding, with L in feet and weight in pounds. The 51,333 lb entry is displayed to the nearest pound.

Axles in Group (N) Axle Group Span (L) Bridge Formula Weight
2 4 ft 34,000 lb
3 8 ft 42,000 lb
4 14 ft 51,333 lb
5 40 ft 73,000 lb
5 51 ft 79,875 lb

Unit Conversions Used for Bridge Formula Inputs

Input Type Unit Conversion to Formula Unit
Distance inches 1 in = 1/12 ft
Distance centimeters 1 cm = 0.032808399 ft
Distance meters 1 m = 3.280839895 ft
Weight kilograms 1 kg = 2.204622622 lb
Weight short tons 1 short ton = 2,000 lb
Weight metric tons 1 metric ton = 2,204.622622 lb

Example Calculations

Example 1: Calculate formula weight

Suppose the axle group span is 51 ft and the group has 5 axles.

W = 500 × ((51 × 5) / (5 - 1) + 12 × 5 + 36)
W = 500 × (63.75 + 60 + 36) = 79,875 lb

The raw formula value is 79,875 lb; rounded to the nearest 500 lb, it is 80,000 lb. This alone is not loading clearance.

Example 2: Solve span from unrounded weight

Suppose the unrounded formula weight is 60,000 lb and the axle group has 4 axles.

L = ((60000 / 500) - 12 × 4 - 36) × ((4 - 1) / 4)
L = (120 - 48 - 36) × 0.75 = 27 ft

The raw equality gives 27 ft. This is not a minimum legal-spacing determination.

FAQs

What distance should you use for L?

Use the distance between the extreme axles in the axle group. That means measuring from the center of the first axle in the group to the center of the last axle in the same group. Do not add the spaces between every axle separately unless you are using them to find the total first-to-last axle span.

Why does the number of axles need to be 2 or greater?

The formula contains N - 1 in the denominator. If N is 1, the formula would require division by zero. The Bridge Formula is used for axle groups, so the axle count must be at least 2.

Is the Bridge Formula result always the legal maximum vehicle weight?

Not necessarily. The formula gives a maximum based on axle spacing and axle count for the axle group. Other limits can still apply, such as single axle limits, tandem axle limits, gross vehicle weight limits, permit rules, and state-specific requirements. Use the lowest applicable limit when checking compliance.