Total number of axles in the group under consideration (Min: 2).
Please enter a valid number of axles (2-15).
Distance in feet between the center of the first axle and the center of the last axle.
Please enter a valid distance (min 8 feet).
Maximum Allowable Gross Weight
80,000
Pounds (lbs)
Calculated Formula Weight
80,000 lbs
Average Weight per Axle
16,000 lbs
Compliance Status
Standard Limit
Formula used: W = 500 [ (LN / (N-1)) + 12N + 36 ]
Weight Limit Visualization
Chart shows maximum weight allowance (Y) based on bridge length (X) for 5 axles.
Compliance Reference Table
Parameter
Value
Description
Axle Count (N)
5
Number of axles in group
Bridge Length (L)
51 ft
Distance between outer axles
Raw Formula Result
80,000
Unrounded calculation
Applicable Limit
80,000 lbs
Lesser of Formula B or 80k cap
What is a Bridge Weight Calculator?
A bridge weight calculator is an essential compliance tool used by logistics managers, truck drivers, and civil engineers to determine the maximum gross weight a vehicle can legally carry across a bridge without causing structural damage. In the United States, this calculation is governed by the Federal Bridge Gross Weight Formula, commonly referred to as Bridge Formula B.
This tool ensures that heavy vehicles distribute their load effectively across axles. By spreading weight over a longer distance (wheelbase) and more axles, the stress on bridge components is reduced. Violating these weight limits can result in severe fines, vehicle impoundment, and long-term infrastructure damage.
This calculator is designed for fleet operators, owner-operators, and dispatchers who need to verify that their axle configurations and loads comply with federal regulations before hitting the road.
Bridge Formula and Mathematical Explanation
The Federal Bridge Gross Weight Formula is derived from engineering principles intended to prevent overstressing bridges. The formula calculates the maximum allowable weight ($W$) based on the number of axles and the distance between them.
The Official Formula:
W = 500 [ (LN / (N – 1)) + 12N + 36 ]
Variable Definitions
Variable
Meaning
Unit
Typical Range
W
Maximum weight on the axle group
Pounds (lbs)
34,000 – 80,000+
L
Distance between outer axles
Feet (ft)
8 – 60+
N
Number of axles in the group
Count (Integer)
2 – 9+
Note: The final result $W$ is typically rounded to the nearest 500 pounds. Additionally, except for special permits, the gross vehicle weight is generally capped at 80,000 lbs on Interstate highways, even if the formula allows for more.
Practical Examples of Weight Compliance
Example 1: Standard 5-Axle Semi-Truck
Consider a standard tractor-trailer with 5 axles and a wheelbase (distance from steering axle to rear trailer axle) of 51 feet.
Even though the truck might physically hold more material, legally it is limited to 47,500 lbs on federal bridges to prevent concentrated stress damage.
How to Use This Bridge Weight Calculator
Identify the Axle Group: Determine if you are calculating the weight for the entire vehicle (gross weight) or a specific inner group of axles (e.g., the tandem drive axles).
Count Axles (N): Enter the total number of axles in the group you are measuring.
Measure Distance (L): Measure the distance in feet from the center of the first axle in the group to the center of the last axle in the group.
Input Values: Enter these numbers into the calculator fields above.
Analyze Result: The calculator provides the maximum legal weight. If your actual scale weight exceeds this number, you must reduce the load or adjust axle spacing (slide the tandems).
Key Factors That Affect Bridge Weight Results
Several variables influence the allowable weight limit beyond just the raw formula:
Axle Spacing: Spreading axles further apart (increasing $L$) generally increases the allowable weight because the load is distributed over a larger span of the bridge.
Number of Axles: Adding an axle (increasing $N$) reduces the weight carried by each individual tire and contact point, allowing for a higher total gross weight.
Federal vs. State Limits: While the federal limit is 80,000 lbs, many states have "grandfathered" rights allowing higher weights on non-interstate roads or specific corridors.
Tire Width Exceptions: Some regulations allow for higher weights per axle if wide-base "super single" tires are used, though this varies by jurisdiction.
Steering Axle Limits: The steering axle is often limited to 12,000 lbs or 20,000 lbs regardless of the bridge formula result.
Permitting: Oversize/Overweight (OS/OW) permits override these standard calculator results, allowing for significantly heavier loads under controlled conditions.
Frequently Asked Questions (FAQ)
What is the maximum weight allowed without a permit?
On the US Interstate system, the maximum gross vehicle weight is generally 80,000 pounds, provided the vehicle also complies with the Federal Bridge Formula for axle spacing.
Does the bridge formula apply to all roads?
It primarily applies to the Interstate Highway System. However, many states have adopted it for state highways, while others use different tables or flat limits for non-interstate roads.
Why does a shorter truck have a lower weight limit?
A shorter truck concentrates its entire weight on a smaller section of a bridge span. This creates a higher "bending moment," which increases structural stress. Lowering the weight limit prevents the bridge from cracking or failing.
What happens if I violate the bridge formula?
Violations result in fines that scale with the amount of excess weight. In severe cases, the vehicle may be placed "out of service" until the load is reduced or shifted.
Can I increase my legal weight by sliding my trailer axles?
Yes. Sliding trailer axles backward increases the distance ($L$) between the tractor drive axles and trailer axles, potentially increasing your allowable gross weight under the bridge formula.
What is the "Exception" regarding 34,000 lbs?
A specific exception allows two consecutive sets of tandem axles to carry 34,000 pounds each if the overall distance between the first and last axles of these tandems is 36 feet or more.
Does this calculator handle "spread axle" trailers?
Yes. Spread axles (typically spaced 10 feet apart) are treated as two single axles rather than a tandem group, often allowing for 20,000 lbs per axle (40,000 lbs total) instead of the standard 34,000 lbs for a closed tandem.
How accurate is this bridge weight calculator?
This calculator uses the exact Federal Bridge Formula B math. However, local state laws, seasonal weight restrictions, and bridge postings always take precedence over the theoretical formula.
Related Tools and Internal Resources
Explore more tools to manage your fleet's compliance and efficiency:
// Initialize calculator logic
function calculateBridgeWeight() {
var numAxlesInput = document.getElementById("numAxles");
var distanceInput = document.getElementById("axleDistance");
var N = parseFloat(numAxlesInput.value);
var L = parseFloat(distanceInput.value);
// Validation
var errorAxles = document.getElementById("error-axles");
var errorDist = document.getElementById("error-distance");
var isValid = true;
if (isNaN(N) || N 15) {
errorAxles.style.display = "block";
isValid = false;
} else {
errorAxles.style.display = "none";
}
if (isNaN(L) || L = 250) {
finalWeight = rawWeight + (500 – remainder);
} else {
finalWeight = rawWeight – remainder;
}
}
// Cap at 80,000 for standard display unless calculation is specifically for OS/OW contexts,
// but the formula can go higher. We will show the formula limit but note the cap.
// For the Main Result, we usually cap at 80k for standard users, but let's show the Formula Result
// and note the compliance.
// However, standard 80k limit applies to Gross Weight.
// If N >= 5 and L is sufficient, it hits 80k. Formula can yield higher for longer combos (e.g. 9 axles).
// Let's display the Formula Result as primary, but cap visually if it exceeds 80k with a note,
// OR just show the raw formula limit which is what the user asked for.
// Decision: Show Formula Limit.
// Update UI
document.getElementById("mainResult").innerText = formatNumber(finalWeight);
document.getElementById("formulaResult").innerText = formatNumber(finalWeight) + " lbs";
var avgWeight = Math.round(finalWeight / N);
document.getElementById("avgAxleWeight").innerText = formatNumber(avgWeight) + " lbs";
var status = document.getElementById("complianceStatus");
if (finalWeight > 80000) {
status.innerText = "Exceeds 80k (Permit Req)";
status.style.color = "#dc3545"; // Red
} else {
status.innerText = "Within Standard Limits";
status.style.color = "#28a745"; // Green
}
updateTable(N, L, rawWeight, finalWeight);
drawChart(N, L, finalWeight);
document.getElementById("chartAxleCount").innerText = N;
}
function formatNumber(num) {
return num.toString().replace(/\B(?=(\d{3})+(?!\d))/g, ",");
}
function resetCalculator() {
document.getElementById("numAxles").value = 5;
document.getElementById("axleDistance").value = 51;
document.getElementById("error-axles").style.display = "none";
document.getElementById("error-distance").style.display = "none";
calculateBridgeWeight();
}
function copyResults() {
var n = document.getElementById("numAxles").value;
var l = document.getElementById("axleDistance").value;
var res = document.getElementById("mainResult").innerText;
var text = "Bridge Weight Calculation:\n" +
"Axles: " + n + "\n" +
"Distance: " + l + " ft\n" +
"Max Allowable Weight: " + res + " lbs\n" +
"Generated by Bridge Weight Calculator.";
var tempInput = document.createElement("textarea");
tempInput.value = text;
document.body.appendChild(tempInput);
tempInput.select();
document.execCommand("copy");
document.body.removeChild(tempInput);
var btn = document.querySelector(".btn-copy");
var originalText = btn.innerText;
btn.innerText = "Copied!";
setTimeout(function(){ btn.innerText = originalText; }, 2000);
}
function updateTable(n, l, raw, final) {
var tbody = document.getElementById("breakdownTable");
tbody.innerHTML =
"
Axle Count (N)
" + n + "
Number of axles in group
" +
"
Bridge Length (L)
" + l + " ft
Distance between outer axles
" +
"
Formula Result
" + formatNumber(final) + " lbs
Rounded to nearest 500 lbs
" +
"
Federal Cap
80,000 lbs
General Interstate Max
";
}
function drawChart(currentN, currentL, currentWeight) {
var canvas = document.getElementById("weightChart");
var ctx = canvas.getContext("2d");
// Handle High DPI
var dpr = window.devicePixelRatio || 1;
var rect = canvas.getBoundingClientRect();
canvas.width = rect.width * dpr;
canvas.height = rect.height * dpr;
ctx.scale(dpr, dpr);
var width = rect.width;
var height = rect.height;
var padding = 40;
var graphWidth = width – (padding * 2);
var graphHeight = height – (padding * 2);
// Clear canvas
ctx.clearRect(0, 0, width, height);
// Chart Settings
var minL = 10;
var maxL = 80;
var minW = 30000;
var maxW = 100000;
// Draw Axes
ctx.beginPath();
ctx.strokeStyle = "#666";
ctx.lineWidth = 1;
// Y Axis
ctx.moveTo(padding, padding);
ctx.lineTo(padding, height – padding);
// X Axis
ctx.lineTo(width – padding, height – padding);
ctx.stroke();
// Draw Labels
ctx.fillStyle = "#333";
ctx.font = "12px Arial";
ctx.textAlign = "center";
ctx.fillText("Length (ft)", width / 2, height – 5);
ctx.save();
ctx.translate(10, height / 2);
ctx.rotate(-Math.PI / 2);
ctx.fillText("Max Weight (lbs)", 0, 0);
ctx.restore();
// Draw Grid and Ticks
ctx.strokeStyle = "#eee";
// X Ticks
for (var i = minL; i <= maxL; i += 10) {
var x = padding + ((i – minL) / (maxL – minL)) * graphWidth;
ctx.beginPath();
ctx.moveTo(x, padding);
ctx.lineTo(x, height – padding);
ctx.stroke();
ctx.fillText(i, x, height – padding + 15);
}
// Y Ticks
ctx.textAlign = "right";
for (var i = minW; i <= maxW; i += 10000) {
var y = (height – padding) – ((i – minW) / (maxW – minW)) * graphHeight;
ctx.beginPath();
ctx.moveTo(padding, y);
ctx.lineTo(width – padding, y);
ctx.stroke();
ctx.fillText(i/1000 + "k", padding – 5, y + 4);
}
// Draw Curve for current N
ctx.beginPath();
ctx.strokeStyle = "#004a99";
ctx.lineWidth = 2;
for (var xVal = minL; xVal = minL && currentL <= maxL) {
var ptX = padding + ((currentL – minL) / (maxL – minL)) * graphWidth;
var ptY = (height – padding) – ((currentWeight – minW) / (maxW – minW)) * graphHeight;
ctx.beginPath();
ctx.arc(ptX, ptY, 6, 0, 2 * Math.PI);
ctx.fillStyle = "#28a745";
ctx.fill();
ctx.strokeStyle = "white";
ctx.lineWidth = 2;
ctx.stroke();
}
}
// Initial load
window.onload = function() {
calculateBridgeWeight();
};