About the Federal Bridge Formula Calculator
This bridge formula calculator applies the US Federal Bridge Gross Weight Formula, W = 500 × (LN/(N − 1) + 12N + 36), which limits the weight on any group of two or more consecutive axles on the Interstate System according to how many axles are in the group and how far apart the outer axles are. Enter the number of axles and the distance between the first and last axle of the group to see the maximum allowable weight, then enter the actual weight to check compliance.
It is built for truck drivers, dispatchers, fleet managers and trailer buyers checking a configuration before loading. The calculator also applies the other federal limits from 23 U.S.C. 127 and 23 CFR 658.17: 20,000 lb on a single axle, 34,000 lb on a tandem (axles more than 40 inches and not more than 96 inches apart), an 80,000 lb gross vehicle limit, and the exception allowing two consecutive tandems to carry 34,000 lb each when the first and last axles are at least 36 feet apart.
Results are rounded to the nearest 500 lb, with exact halves rounded down as in FHWA’s Bridge Table (federal figures current as of 2026). The Bridge Table lists whole feet only and federal law sets no rule for fractions, so this calculator conservatively drops fractional feet; some states round to the nearest foot instead. Check every critical group — typically axles 1–3 (tractor), 2–5 (tandems) and 1–5 (whole vehicle). States can have grandfathered higher limits, different limits off the Interstate, and permit rules; always confirm with the state where you operate.
With the default inputs, the maximum allowable weight is 80,000 lb. Change any value above to recalculate instantly.
How to use the federal bridge formula calculator
- 1Pick the axle group to check, for example axles 1–5 (whole rig) or 2–5 (drive and trailer tandems).
- 2Enter the number of axles in that group.
- 3Measure the distance in feet from the center of the first axle to the center of the last axle.
- 4Enter the actual weight on that group from a scale ticket.
- 5Read the maximum allowable weight and repeat for every critical group.
Formula and method
W is the maximum overall gross weight on any group of two or more consecutive axles, to the nearest 500 pounds; L is the distance in feet between the outer axles of the group; and N is the number of axles in the group. Longer spacing and more axles spread the load over a bridge, so the formula allows more weight. FHWA’s Bridge Table rounds down when a result falls exactly halfway between 500 lb steps, and lists whole feet; fractional feet are dropped here as a conservative choice.
The single-axle limit (20,000 lb) replaces the formula for axles 40 inches or less apart, and the tandem limit (34,000 lb) replaces it for axles more than 40 and not more than 96 inches apart. Gross vehicle weight cannot exceed 80,000 lb. Two consecutive tandem sets may carry 34,000 lb each if the first and last axles are 36 ft or more apart, even though the formula alone would allow only 66,000–67,500 lb at 36–38 ft.
- W
- Maximum gross weight on the axle group, lb (nearest 500)
- L
- Distance between the outer axles of the group, ft
- N
- Number of axles in the group
Worked examples
5-axle tractor-semitrailer, 51 ft outer bridge
W = 500 × (51 × 5 ÷ 4 + 60 + 36) = 500 × 159.75 = 79,875 lb, which rounds to 80,000 lb. That equals the gross limit, so an 80,000 lb load on axles 1–5 complies — matching FHWA’s worked example.
Axles 2–5 at 35 ft carrying 68,000 lb
W = 500 × (35 × 4 ÷ 3 + 48 + 36) = 65,333 lb, rounded to 65,500 lb. The 36 ft tandem exception does not apply at 35 ft, so 68,000 lb on these axles is 2,500 lb over.
Tandems spread to 36 ft — exception applies
At 36 ft the formula gives 500 × (48 + 48 + 36) = 66,000 lb, but because the group is two consecutive tandems at least 36 ft apart, each may carry 34,000 lb — 68,000 lb in total.
3 axles at 9 ft (single-unit truck rear group)
W = 500 × (9 × 3 ÷ 2 + 36 + 36) = 42,750 lb, exactly halfway between 500 lb steps, so it rounds down to 42,500 lb (FHWA policy). A 45,000 lb load is 2,500 lb over.
Frequently asked questions
What is the federal bridge formula?+
It is W = 500 × (LN/(N − 1) + 12N + 36), where W is the maximum weight in pounds on any group of two or more consecutive axles, L is the distance in feet between the outer axles of the group, and N is the number of axles. It is set by 23 U.S.C. 127 for the Interstate System.
What are the federal axle weight limits?+
On the Interstate System federal limits are 20,000 lb on a single axle, 34,000 lb on a tandem axle group and 80,000 lb gross vehicle weight, plus the Bridge Formula for every group of axles. Some states keep higher grandfathered limits.
Which axle groups do I need to check?+
Every group of two or more consecutive axles must comply, but for a typical 5-axle tractor-semitrailer FHWA notes the critical groups are axles 1–3, 2–5 and 1–5. If those pass, the others normally will too.
What is the 36-foot tandem exception?+
Federal law lets two consecutive sets of tandem axles carry 34,000 lb each (68,000 lb) if the distance between the first and last axles of those tandems is 36 ft or more, even when the formula would give slightly less.
Does the bridge formula apply on state roads?+
The federal formula applies on the Interstate System and to reasonable access routes. States set their own limits on other roads and can issue permits for heavier loads, so check the rules of each state on your route.
Results are general estimates and not legal advice. Laws vary by jurisdiction — consult a qualified attorney.