Hex Weight Calculation Formula Calculator | Professional Metal Weight Estimator
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Total Estimated Weight
0.00
kg
Formula Used: Weight = (0.866 × AF²) × Length × Density
Weight vs. Length Analysis
Weight Reference Table
| Length |
Weight (Selected Material) |
Weight (Steel Reference) |
Volume |
Calculated values based on current Across Flats (AF) dimension.
What is the Hex Weight Calculation Formula?
The hex weight calculation formula is a mathematical method used by engineers, machinists, and material purchasers to determine the mass of a hexagonal (six-sided) metal bar. Unlike round bars or square tubing, hexagonal bars have a unique cross-sectional geometry that requires a specific geometric constant to calculate area accurately.
This calculation is critical in manufacturing and logistics. Knowing the precise weight of raw materials ensures accurate shipping cost estimation, structural load planning, and material costing. Whether you are working with steel, aluminum, or brass, the core geometry remains the same, while the material density changes the final result.
Common misconceptions include treating a hex bar as a round bar with a diameter equal to the "across flats" distance. This leads to significant errors, as the area of a hexagon is approximately 10% greater than the inscribed circle but less than the circumscribed circle.
Hex Weight Calculation Formula and Mathematical Explanation
To calculate the weight of a hexagonal bar, you must first determine its volume and then multiply by the material's density. The formula is derived from the geometry of a regular hexagon.
Weight (W) = Area (A) × Length (L) × Density (ρ)
Step 1: Calculate Cross-Sectional Area
Hex bars are measured by the distance "Across Flats" (AF), which is the perpendicular distance between opposite parallel sides. The area formula is:
Area ≈ 0.866025 × (AF)²
Note: The constant 0.866025 is derived from √3 / 2.
Step 2: Calculate Volume
Multiply the cross-sectional area by the length of the bar.
Volume = Area × Length
Step 3: Calculate Weight
Multiply the volume by the specific density of the material.
Variables Table
| Variable |
Meaning |
Metric Unit |
Imperial Unit |
| AF |
Distance Across Flats |
Millimeters (mm) |
Inches (in) |
| L |
Length of Bar |
Meters (m) |
Feet (ft) |
| ρ (Rho) |
Material Density |
g/cm³ or kg/m³ |
lbs/in³ |
| W |
Total Weight |
Kilograms (kg) |
Pounds (lbs) |
Key variables used in hex weight calculation.
Practical Examples (Real-World Use Cases)
Example 1: Manufacturing a Steel Drive Shaft
Scenario: A machine shop needs to order 100 meters of 25mm hex steel bar (Mild Steel) for production.
- Input (AF): 25 mm
- Input (Length): 100 m (total)
- Material: Mild Steel (Density ~7.85 g/cm³)
Calculation:
- Area = 0.866 × 25² = 541.25 mm² = 5.4125 cm²
- Volume = 5.4125 cm² × 10,000 cm (100m) = 54,125 cm³
- Weight = 54,125 × 7.85 = 424,881 grams = 424.88 kg
Financial Impact: If steel costs $1.50/kg, the raw material cost is approximately $637.32.
Example 2: Brass Fittings for Plumbing
Scenario: A workshop uses 1-inch hex brass bars. They have a 12-foot bar.
- Input (AF): 1.0 inch
- Input (Length): 12 feet (144 inches)
- Material: Brass (Density ~0.307 lb/in³)
Calculation:
- Area = 0.866 × 1.0² = 0.866 in²
- Volume = 0.866 in² × 144 in = 124.704 in³
- Weight = 124.704 × 0.307 = 38.28 lbs
How to Use This Hex Weight Calculator
- Select Unit System: Choose between Metric (mm/kg) or Imperial (inch/lbs) based on your supplier's specifications.
- Choose Material: Select the metal type from the dropdown. If you have a specific alloy not listed, select "Custom" and enter the density manually.
- Enter Dimensions: Input the "Across Flats" dimension and the total length of the bar.
- Review Results: The calculator instantly provides the total weight, cross-sectional area, and volume.
- Cost Estimation: Optionally, enter the price per unit of weight to get an estimated total material cost.
Key Factors That Affect Hex Weight Results
Several factors can influence the accuracy of your weight calculations and financial estimates:
- Material Density Variations: Not all "Steel" is the same. Stainless steel (304) is slightly denser than mild steel. Always verify the specific alloy grade.
- Dimensional Tolerances: Manufacturing standards (like ASTM A29) allow for slight variations in the "Across Flats" dimension. A bar sold as 25mm might actually be 25.1mm, slightly increasing weight.
- Corner Radius: Hex bars are not always perfectly sharp at the corners. Rounded corners (radii) slightly reduce the total cross-sectional area and weight compared to the theoretical formula.
- Length Precision: Cutting allowances (kerf) and rough cuts mean a "6-meter bar" might be slightly longer to allow for finishing, adding to the billable weight.
- Surface Finish: Plating or coating (like zinc or chrome) adds negligible weight but significant cost.
- Scrap Rates: When calculating financial requirements, always account for the unusable ends of the bar (drops) that cannot be machined into parts.
Frequently Asked Questions (FAQ)
Is the hex weight formula different for aluminum vs. steel?
No, the geometric formula for volume ($Area \times Length$) is identical. Only the density value changes. Aluminum is roughly 1/3 the weight of steel.
What is "Across Flats" vs. "Across Corners"?
"Across Flats" is the distance between parallel flat sides (where a wrench fits). "Across Corners" is the distance between opposite points. This calculator uses "Across Flats" as it is the industry standard for sizing.
How accurate is this calculator?
It is mathematically precise based on theoretical dimensions. However, real-world weights may vary by 1-3% due to manufacturing tolerances and corner radii.
Can I calculate the weight of a hollow hex bar?
This specific tool is for solid bars. For hollow bars, you would calculate the weight of the outer hex and subtract the weight of the inner hole (volume of the void).
Why is the constant 0.866 used?
The area of a hexagon is composed of 6 equilateral triangles. The math simplifies to $\frac{\sqrt{3}}{2} \times d^2$. Since $\frac{\sqrt{3}}{2} \approx 0.866025$, this constant is used for quick calculation.
Does this calculator account for shipping pallets?
No, this calculates the net weight of the metal only. Gross shipping weight will be higher due to pallets, banding, and packaging.
How do I convert density from g/cm³ to lbs/in³?
Multiply the g/cm³ value by 0.03613. For example, Steel (7.85 g/cm³) × 0.03613 ≈ 0.283 lbs/in³.
Why is knowing the weight important for quoting?
Raw material is often sold by weight, not length. Accurate weight calculation allows machine shops to quote jobs precisely without underestimating material costs.
Related Tools and Internal Resources
Enhance your manufacturing and financial planning with these related tools:
// Global Variables
var chartInstance = null;
var ctx = document.getElementById('weightChart').getContext('2d');
// Initialization
window.onload = function() {
calculateHexWeight();
};
function updateLabels() {
var system = document.getElementById('unitSystem').value;
var afLabel = document.getElementById('afLabel');
var lengthLabel = document.getElementById('lengthLabel');
var priceLabel = document.getElementById('priceLabel');
var densityLabel = document.getElementById('densityLabel');
var afInput = document.getElementById('acrossFlats');
var lenInput = document.getElementById('length');
if (system === 'metric') {
afLabel.innerText = "Distance Across Flats (mm)";
lengthLabel.innerText = "Length (meters)";
priceLabel.innerText = "Material Cost ($ per kg)";
densityLabel.innerText = "Custom Density (g/cm³)";
afInput.placeholder = "e.g., 20";
lenInput.placeholder = "e.g., 1";
} else {
afLabel.innerText = "Distance Across Flats (inches)";
lengthLabel.innerText = "Length (feet)";
priceLabel.innerText = "Material Cost ($ per lb)";
densityLabel.innerText = "Custom Density (lbs/in³)";
afInput.placeholder = "e.g., 1.0";
lenInput.placeholder = "e.g., 10″;
}
calculateHexWeight();
}
function calculateHexWeight() {
// 1. Get Inputs
var system = document.getElementById('unitSystem').value;
var materialSelect = document.getElementById('material');
var af = parseFloat(document.getElementById('acrossFlats').value);
var length = parseFloat(document.getElementById('length').value);
var price = parseFloat(document.getElementById('pricePerUnit').value);
var customDensityInput = document.getElementById('customDensity');
// Handle Custom Density Visibility
var densityVal = 0;
if (materialSelect.value === 'custom') {
document.getElementById('customDensityGroup').style.display = 'block';
densityVal = parseFloat(customDensityInput.value);
} else {
document.getElementById('customDensityGroup').style.display = 'none';
densityVal = parseFloat(materialSelect.value);
}
// 2. Validation
var isValid = true;
if (isNaN(af) || af <= 0) {
document.getElementById('afError').style.display = 'block';
isValid = false;
} else {
document.getElementById('afError').style.display = 'none';
}
if (isNaN(length) || length <= 0) {
document.getElementById('lengthError').style.display = 'block';
isValid = false;
} else {
document.getElementById('lengthError').style.display = 'none';
}
if (materialSelect.value === 'custom' && (isNaN(densityVal) || densityVal 0) {
totalCost = weight * price;
}
// 4. Update DOM
document.getElementById('totalWeight').innerText = formatNumber(weight);
document.getElementById('weightUnit').innerText = wUnit;
document.getElementById('crossArea').innerText = formatNumber(area) + " " + areaUnit;
document.getElementById('totalVolume').innerText = formatNumber(volume) + " " + volUnit;
document.getElementById('weightPerLength').innerText = formatNumber(weightPerLen) + " " + wUnit + "/" + lenUnit;
if (totalCost > 0) {
document.getElementById('totalCost').innerText = "$" + formatNumber(totalCost, 2);
} else {
document.getElementById('totalCost').innerText = "-";
}
updateTable(weightPerLen, lenUnit, wUnit, system, area, volUnit);
drawChart(weight, length, system, wUnit, lenUnit, af, densityVal, materialSelect.value);
}
function updateTable(weightPerUnit, lenUnit, wUnit, system, area, volUnit) {
var tbody = document.getElementById('tableBody');
tbody.innerHTML = "";
// Generate 5 rows: 1x, 2x, 5x, 10x, 20x length units
var multipliers = [1, 2, 5, 10, 20];
// Steel Reference Density
var steelDensity = (system === 'metric') ? 7.85 : (7.85 * 0.0361273);
// Current Area is already calculated in calculateHexWeight but we need it here.
// Re-calculate area for reference column logic simplicity
// Actually, we can just ratio the weights based on density if we knew current density.
// Let's recalculate steel weight per unit length.
var af = parseFloat(document.getElementById('acrossFlats').value);
var hexConstant = 0.866025404;
var steelWeightPerUnit = 0;
var volumePerUnit = 0;
if (system === 'metric') {
var afCm = af / 10;
var areaCm2 = hexConstant * Math.pow(afCm, 2);
var volPerM_cm3 = areaCm2 * 100; // 1m = 100cm
steelWeightPerUnit = (volPerM_cm3 * 7.85) / 1000; // kg/m
volumePerUnit = volPerM_cm3; // cm³ per m
} else {
var areaIn2 = hexConstant * Math.pow(af, 2);
var volPerFt_in3 = areaIn2 * 12; // 1ft = 12in
steelWeightPerUnit = volPerFt_in3 * (7.85 * 0.0361273); // lbs/ft
volumePerUnit = volPerFt_in3; // in³ per ft
}
for (var i = 0; i < multipliers.length; i++) {
var len = multipliers[i];
var rowWeight = weightPerUnit * len;
var refWeight = steelWeightPerUnit * len;
var rowVol = volumePerUnit * len;
var tr = document.createElement('tr');
tr.innerHTML =
"
" + len + " " + lenUnit + " | " +
"
" + formatNumber(rowWeight) + " " + wUnit + " | " +
"
" + formatNumber(refWeight) + " " + wUnit + " | " +
"
" + formatNumber(rowVol) + " " + volUnit + " | ";
tbody.appendChild(tr);
}
}
function drawChart(currentWeight, currentLength, system, wUnit, lenUnit, af, currentDensity, matType) {
// Simple Canvas Chart Implementation
var canvas = document.getElementById('weightChart');
var ctx = canvas.getContext('2d');
// Reset canvas
ctx.clearRect(0, 0, canvas.width, canvas.height);
// Set dimensions
var width = canvas.width = canvas.offsetWidth;
var height = canvas.height = canvas.offsetHeight;
var padding = 50;
var chartWidth = width – (padding * 2);
var chartHeight = height – (padding * 2);
// Data Generation: 0 to 2x current length
var steps = 5;
var maxLen = Math.ceil(currentLength * 1.5);
if (maxLen < 5) maxLen = 5;
var dataPoints = [];
var refPoints = []; // Steel
var labels = [];
// Calculate Steel Density for reference
var steelDensity = (system === 'metric') ? 7.85 : (7.85 * 0.0361273);
var activeDensity = (system === 'metric') ? currentDensity : (matType === 'custom' ? currentDensity : currentDensity * 0.0361273);
var hexConstant = 0.866025404;
var area = 0;
if (system === 'metric') {
area = hexConstant * Math.pow((af/10), 2); // cm²
} else {
area = hexConstant * Math.pow(af, 2); // in²
}
var maxY = 0;
for (var i = 0; i maxY) maxY = w;
if (refW > maxY) maxY = refW;
}
// Draw Axes
ctx.beginPath();
ctx.strokeStyle = '#ddd';
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 Grid & Labels
ctx.fillStyle = '#666′;
ctx.font = '12px Arial';
ctx.textAlign = 'right';
// Y Axis Labels
for (var i = 0; i <= 5; i++) {
var yVal = (maxY / 5) * i;
var yPos = (height – padding) – ((yVal / maxY) * chartHeight);
ctx.fillText(formatNumber(yVal, 1), padding – 10, yPos + 4);
// Grid line
ctx.beginPath();
ctx.strokeStyle = '#eee';
ctx.moveTo(padding, yPos);
ctx.lineTo(width – padding, yPos);
ctx.stroke();
}
// X Axis Labels
ctx.textAlign = 'center';
for (var i = 0; i < labels.length; i++) {
var xPos = padding + ((i / steps) * chartWidth);
ctx.fillText(labels[i], xPos, height – padding + 20);
}
// Axis Titles
ctx.save();
ctx.translate(15, height / 2);
ctx.rotate(-Math.PI / 2);
ctx.textAlign = 'center';
ctx.fillText("Weight (" + wUnit + ")", 0, 0);
ctx.restore();
ctx.fillText("Length (" + lenUnit + ")", width / 2, height – 10);
// Draw Lines
function drawLine(points, color) {
ctx.beginPath();
ctx.strokeStyle = color;
ctx.lineWidth = 3;
for (var i = 0; i < points.length; i++) {
var x = padding + ((i / steps) * chartWidth);
var y = (height – padding) – ((points[i] / maxY) * chartHeight);
if (i === 0) ctx.moveTo(x, y);
else ctx.lineTo(x, y);
}
ctx.stroke();
}
// Draw Steel Reference (Grey)
drawLine(refPoints, '#999');
// Draw Selected Material (Blue)
drawLine(dataPoints, '#004a99');
// Legend
ctx.fillStyle = '#004a99';
ctx.fillRect(width – 150, padding, 15, 15);
ctx.fillStyle = '#333';
ctx.textAlign = 'left';
ctx.fillText("Selected Material", width – 130, padding + 12);
ctx.fillStyle = '#999';
ctx.fillRect(width – 150, padding + 25, 15, 15);
ctx.fillStyle = '#333';
ctx.fillText("Steel (Reference)", width – 130, padding + 37);
}
function formatNumber(num, decimals) {
if (decimals === undefined) decimals = 2;
return num.toLocaleString('en-US', { minimumFractionDigits: decimals, maximumFractionDigits: decimals });
}
function resetCalculator() {
document.getElementById('unitSystem').value = 'metric';
document.getElementById('material').value = '7.85';
document.getElementById('acrossFlats').value = '';
document.getElementById('length').value = '';
document.getElementById('pricePerUnit').value = '';
document.getElementById('customDensity').value = '1.0';
updateLabels();
resetOutputs();
}
function resetOutputs() {
document.getElementById('totalWeight').innerText = "0.00";
document.getElementById('crossArea').innerText = "-";
document.getElementById('totalVolume').innerText = "-";
document.getElementById('weightPerLength').innerText = "-";
document.getElementById('totalCost').innerText = "-";
document.getElementById('tableBody').innerHTML = "";
// Clear chart
var canvas = document.getElementById('weightChart');
var ctx = canvas.getContext('2d');
ctx.clearRect(0, 0, canvas.width, canvas.height);
}
function copyResults() {
var weight = document.getElementById('totalWeight').innerText;
var unit = document.getElementById('weightUnit').innerText;
var area = document.getElementById('crossArea').innerText;
var vol = document.getElementById('totalVolume').innerText;
var cost = document.getElementById('totalCost').innerText;
var text = "Hex Weight Calculation Results:\n";
text += "Total Weight: " + weight + " " + unit + "\n";
text += "Cross-Sectional Area: " + area + "\n";
text += "Total Volume: " + vol + "\n";
text += "Estimated Cost: " + cost + "\n";
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);
}