Calculate federal bridge formula weight, axle-group span, or axle count from two inputs and convert between lbs, kg, short tons, or metric tons.
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Federal Bridge Formula Weight Formula
The Federal Bridge Formula estimates the maximum allowable weight for an axle group based on the spacing between the first and last axle in the group and the number of axles in that group.
- W = Bridge Formula weight, in pounds
- 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
If you enter L and N, the calculator solves for the maximum Bridge Formula weight. If you enter W and N, it solves for the axle group span needed for that weight. If you enter W and L, it solves the quadratic equation for N. In actual vehicle use, N should be a whole-number axle count.
Common Bridge Formula Reference Values
These examples use the Federal Bridge Formula with L in feet and the result in pounds.
| 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 maximum Bridge Formula weight
Suppose the axle group span is 51 ft and the group has 5 axles.
The Bridge Formula weight is 79,875 lb.
Example 2: Calculate required axle group span
Suppose the desired Bridge Formula weight is 60,000 lb and the axle group has 4 axles.
The required axle group span is 27 ft.
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.
