Paper Core Weight Calculator

Paper Core Weight Calculator | Professional Industrial Tool :root { –primary: #004a99; –secondary: #003377; –success: #28a745; –bg-color: #f8f9fa; –text-color: #333; –border-color: #ddd; –white: #ffffff; } body { font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif; line-height: 1.6; color: var(–text-color); background-color: var(–bg-color); margin: 0; padding: 0; } .container { max-width: 900px; margin: 0 auto; padding: 20px; background-color: var(–white); box-shadow: 0 0 20px rgba(0,0,0,0.05); } header, footer { text-align: center; padding: 20px 0; border-bottom: 1px solid var(–border-color); margin-bottom: 30px; } header h1 { color: var(–primary); margin: 0; font-size: 2.2rem; } h2, h3, h4 { color: var(–primary); margin-top: 1.5em; } /* Calculator Styles */ .loan-calc-container { background-color: #fff; border: 1px solid var(–border-color); border-radius: 8px; padding: 30px; box-shadow: 0 4px 12px rgba(0,0,0,0.05); margin-bottom: 40px; } .input-group { margin-bottom: 20px; display: flex; flex-direction: column; } .input-group label { font-weight: 600; margin-bottom: 8px; color: var(–secondary); } .input-group input, .input-group select { padding: 12px; border: 1px solid #ccc; border-radius: 4px; font-size: 16px; width: 100%; box-sizing: border-box; transition: border-color 0.3s; } .input-group input:focus { border-color: var(–primary); outline: none; box-shadow: 0 0 0 3px rgba(0, 74, 153, 0.1); } .helper-text { font-size: 0.85rem; color: #666; margin-top: 5px; } .error-msg { color: #dc3545; font-size: 0.85rem; margin-top: 5px; display: none; } .btn-container { display: flex; gap: 15px; margin-top: 25px; flex-wrap: wrap; } button { padding: 12px 24px; border: none; border-radius: 4px; font-size: 16px; cursor: pointer; font-weight: 600; transition: background 0.3s; } .btn-reset { background-color: #6c757d; color: white; } .btn-reset:hover { background-color: #5a6268; } .btn-copy { background-color: var(–primary); color: white; } .btn-copy:hover { background-color: var(–secondary); } /* Results Section */ #results-area { margin-top: 30px; padding-top: 20px; border-top: 2px solid var(–bg-color); } .primary-result { background-color: #e8f4fd; border-left: 5px solid var(–primary); padding: 20px; margin-bottom: 20px; border-radius: 0 4px 4px 0; } .primary-result h3 { margin: 0 0 10px 0; font-size: 1.1rem; color: var(–secondary); } .primary-result .value { font-size: 2.5rem; font-weight: 700; color: var(–primary); } .intermediate-results { display: flex; flex-wrap: wrap; gap: 15px; margin-bottom: 25px; } .result-card { flex: 1; min-width: 140px; background: #f8f9fa; padding: 15px; border-radius: 6px; border: 1px solid #eee; text-align: center; } .result-card .label { font-size: 0.9rem; color: #555; margin-bottom: 5px; } .result-card .res-value { font-size: 1.4rem; font-weight: bold; color: var(–success); } .formula-explainer { background: #fff3cd; padding: 15px; border-radius: 6px; color: #856404; font-size: 0.95rem; margin-bottom: 25px; } /* Table & Chart */ table { width: 100%; border-collapse: collapse; margin: 20px 0; font-size: 0.95rem; } th, td { padding: 12px; text-align: left; border-bottom: 1px solid #ddd; } th { background-color: var(–primary); color: white; } tr:nth-child(even) { background-color: #f2f2f2; } .chart-container { margin: 30px 0; padding: 20px; background: white; border: 1px solid #eee; border-radius: 8px; text-align: center; } canvas { max-width: 100%; height: auto; } /* SEO Article Styles */ article { margin-top: 50px; padding-top: 20px; border-top: 1px solid #eee; } article p { margin-bottom: 1.5em; text-align: justify; } .toc-list li { margin-bottom: 8px; } .faq-item { margin-bottom: 20px; } .faq-item h4 { margin-bottom: 8px; color: var(–secondary); } .internal-links ul { list-style-type: none; padding: 0; } .internal-links li { margin-bottom: 10px; padding: 10px; background-color: #f1f8ff; border-radius: 4px; } .internal-links a { color: var(–primary); text-decoration: none; font-weight: 600; } .internal-links a:hover { text-decoration: underline; }

Paper Core Weight Calculator

Instantly calculate the weight, volume, and material usage for paper cores and tubes.

The inside diameter of the tube (standard is 76mm or 3 inches).
Please enter a valid positive number.
Thickness of the paperboard wall in millimeters.
Please enter a valid positive thickness.
Total length of the core in millimeters.
Please enter a valid positive length.
Specific gravity of the paperboard. Standard Kraft paper is approx 0.7 – 0.9 g/cm³.
Please enter a valid density (0.1 – 2.0).
Number of cores to calculate total batch weight.
Please enter a valid quantity.

Single Core Weight

0.00 kg
Total Batch Weight
0.00 kg
Volume per Core
0.00 cm³
Outer Diameter (OD)
0.00 mm
Logic Used: Weight = Volume × Density. We calculate the hollow cylinder volume by subtracting the inner cylinder volume from the outer cylinder volume based on the input wall thickness and length.
Specification Value Unit
Inner Radius0mm
Outer Radius0mm
Cross-Section Area0cm²
Material Density0g/cm³
Table 1: Technical Geometric Breakdown of the Core

Sensitivity Analysis: Weight vs. Wall Thickness

Comparison of current configuration vs +/- 20% thickness variation

What is a Paper Core Weight Calculator?

A paper core weight calculator is an essential digital tool designed for packaging engineers, logistics managers, and procurement specialists in the manufacturing sector. It determines the precise mass of paper tubes, cardboard cores, and fiber cores used for winding materials such as film, foil, tape, textiles, and paper.

Knowing the exact weight of these cores is critical for shipping cost estimation, inventory management, and ensuring that winding machinery is not overloaded. While paper cores may seem lightweight individually, in high-volume industrial applications, the total weight of thousands of cores significantly impacts the Gross Vehicle Weight (GVW) during transport. This paper core weight calculator helps eliminate guesswork by using geometric physics to provide accurate weight data based on standard dimensions.

Paper Core Weight Calculator Formula

To understand how a paper core weight calculator works, one must look at the geometry of a hollow cylinder. The calculation involves determining the volume of the material used in the wall of the core and multiplying it by the density of the paperboard.

The mathematical derivation used in our tool is as follows:

Step 1: Determine Dimensions

  • ID (Inner Diameter): The diameter of the hole.
  • WT (Wall Thickness): The thickness of the cardboard.
  • OD (Outer Diameter): Calculated as ID + (2 × WT).
  • L (Length): The total length of the tube.

Step 2: Calculate Volume

The volume (V) of the material is the volume of the outer cylinder minus the volume of the inner void:

V = π × L × [ (OD/2)² – (ID/2)² ]

Step 3: Calculate Weight

Finally, weight is derived by applying the material density (ρ):

Weight = Volume × Density

Variables Table

Variable Meaning Common Unit Typical Range
ODOuter Diametermm / inches50 – 300 mm
IDInner Diametermm / inches25 – 254 mm
LLengthmm / m100 – 6000 mm
ρ (Rho)Paper Densityg/cm³0.65 – 0.95
Table 2: Key Variables in Core Weight Calculation

Practical Examples of Core Weight Calculation

Example 1: Standard Shipping Tape Core

Consider a manufacturer producing packing tape. They need to calculate the weight of the core to estimate shipping costs for a pallet of 5,000 rolls.

  • ID: 76 mm (3 inches)
  • Wall Thickness: 3 mm
  • Length: 50 mm
  • Density: 0.75 g/cm³

Using the paper core weight calculator, the outer diameter is 82 mm. The calculated volume of material is roughly 37.2 cm³. Multiplying by the density, the weight per core is approximately 27.9 grams. For 5,000 cores, the total weight added to the shipment is roughly 139.5 kg.

Example 2: Heavy Duty Textile Tube

A textile mill uses long, thick cores for winding heavy carpets.

  • ID: 100 mm
  • Wall Thickness: 10 mm
  • Length: 3000 mm (3 meters)
  • Density: 0.85 g/cm³

Here, the OD becomes 120 mm. The volume of material is substantial due to the length and thickness. The calculator reveals a single core weight of roughly 8.8 kg. Knowing this helps the mill ensure their forklift load limits are respected when moving crates of these cores.

How to Use This Paper Core Weight Calculator

  1. Enter Inner Diameter: Input the internal diameter of the core in millimeters. This is often standard (e.g., 76mm, 152mm).
  2. Specify Wall Thickness: Enter how thick the cardboard wall is. Do not enter the outer diameter directly; the tool calculates OD for you.
  3. Input Length: Provide the total length of the tube in millimeters.
  4. Adjust Density: The default is set to 0.75 g/cm³, which is standard for Kraft paper. If you are using high-density pressed board, increase this value.
  5. Set Quantity: Enter the number of cores to see the total batch weight.
  6. Analyze Results: Use the generated chart to see how sensitive the weight is to thickness variations, helping you optimize material usage.

Key Factors That Affect Paper Core Weight

When using a paper core weight calculator, it is important to understand that several physical factors can influence the final result slightly.

  • Moisture Content: Paper is hygroscopic. A core stored in a humid warehouse can weigh 5-8% more than a bone-dry core due to absorbed water.
  • Paper Grade & Density: Not all cardboard is created equal. Recycled paperboard often has a different density profile compared to virgin Kraft linerboard.
  • Adhesive Weight: Cores are made by spiral winding paper strips with glue. The amount of sodium silicate or starch adhesive used adds mass that pure volume calculations might slightly underestimate.
  • Manufacturing Tolerances: A "5mm" wall thickness might actually vary between 4.8mm and 5.2mm in production, affecting the unit weight.
  • Crush Strength Requirements: Higher crush strength requirements usually dictate higher density paper or thicker walls, directly increasing weight.
  • Diameter Variations: Even a small increase in Outer Diameter (due to loose winding) increases the volume of material significantly because volume increases with the square of the radius.

Frequently Asked Questions (FAQ)

1. How accurate is this paper core weight calculator?

This tool uses precise geometric formulas. However, actual weight may vary by +/- 5% due to glue weight, moisture content, and paper density variations.

2. What is the standard density for paper cores?

Standard industrial paper cores typically have a density between 0.7 g/cm³ and 0.9 g/cm³. High-performance cores may exceed 0.95 g/cm³.

3. Can I calculate the weight of plastic cores?

Yes. Simply change the "Density" input to match your plastic material (e.g., PVC is approx 1.4 g/cm³, PP is approx 0.9 g/cm³).

4. Why do I need to input wall thickness instead of OD?

In manufacturing, cores are often specified by ID and Wall Thickness. However, if you only have OD, you can calculate thickness as (OD – ID) / 2.

5. Does this calculator account for the glue?

Glue weight is generally included in the average density figure. If you have a specific composite density, enter it in the density field for better accuracy.

6. What is the difference between spiral and convolute cores?

Spiral cores are continuous wound, while convolute are straight wound. This calculator works for both as it calculates based on total material volume.

7. How do I convert inches to millimeters?

Multiply your inch value by 25.4. For example, a 3-inch core is 76.2 mm.

8. Why is the total batch weight important?

For logistics, knowing the total batch weight helps in maximizing container loads without exceeding legal weight limits.

Related Tools and Internal Resources

© 2023 Industrial Packaging Tools. All rights reserved.

// Initialize calculator on load window.onload = function() { calculateCoreWeight(); }; function calculateCoreWeight() { // 1. Get Inputs var idElem = document.getElementById("coreID"); var thickElem = document.getElementById("coreThickness"); var lenElem = document.getElementById("coreLength"); var denElem = document.getElementById("paperDensity"); var qtyElem = document.getElementById("quantity"); // Parse values var id_mm = parseFloat(idElem.value); var thick_mm = parseFloat(thickElem.value); var len_mm = parseFloat(lenElem.value); var density = parseFloat(denElem.value); var qty = parseInt(qtyElem.value); // Reset errors document.getElementById("err-coreID").style.display = "none"; document.getElementById("err-coreThickness").style.display = "none"; document.getElementById("err-coreLength").style.display = "none"; document.getElementById("err-paperDensity").style.display = "none"; document.getElementById("err-quantity").style.display = "none"; var hasError = false; // Validation if (isNaN(id_mm) || id_mm <= 0) { document.getElementById("err-coreID").style.display = "block"; hasError = true; } if (isNaN(thick_mm) || thick_mm <= 0) { document.getElementById("err-coreThickness").style.display = "block"; hasError = true; } if (isNaN(len_mm) || len_mm <= 0) { document.getElementById("err-coreLength").style.display = "block"; hasError = true; } if (isNaN(density) || density <= 0) { document.getElementById("err-paperDensity").style.display = "block"; hasError = true; } if (isNaN(qty) || qty <= 0) { document.getElementById("err-quantity").style.display = "block"; hasError = true; } if (hasError) return; // 2. Perform Calculations // Convert dimensions to cm for density calculation (g/cm3) var id_cm = id_mm / 10; var thick_cm = thick_mm / 10; var len_cm = len_mm / 10; var innerRadius_cm = id_cm / 2; var outerRadius_cm = innerRadius_cm + thick_cm; // Volume = pi * h * (R_out^2 – R_in^2) var volume_cm3 = Math.PI * len_cm * (Math.pow(outerRadius_cm, 2) – Math.pow(innerRadius_cm, 2)); var weight_g = volume_cm3 * density; var weight_kg = weight_g / 1000; var total_weight_kg = weight_kg * qty; var outerDiameter_mm = id_mm + (2 * thick_mm); // Cross section area (cm2) var area_cm2 = Math.PI * (Math.pow(outerRadius_cm, 2) – Math.pow(innerRadius_cm, 2)); // 3. Update UI document.getElementById("res-singleWeight").innerHTML = weight_kg.toFixed(3) + " kg / " + weight_g.toFixed(0) + " g"; document.getElementById("res-totalWeight").innerText = total_weight_kg.toFixed(2) + " kg"; document.getElementById("res-volume").innerText = volume_cm3.toFixed(1) + " cm³"; document.getElementById("res-od").innerText = outerDiameter_mm.toFixed(1) + " mm"; // Update Table document.getElementById("tab-ir").innerText = (id_mm / 2).toFixed(1); document.getElementById("tab-or").innerText = (outerDiameter_mm / 2).toFixed(1); document.getElementById("tab-area").innerText = area_cm2.toFixed(2); document.getElementById("tab-density").innerText = density.toFixed(2); // 4. Update Chart updateChart(weight_g, density, len_cm, innerRadius_cm, thick_cm); } function resetCalculator() { document.getElementById("coreID").value = "76"; document.getElementById("coreThickness").value = "5"; document.getElementById("coreLength").value = "1000"; document.getElementById("paperDensity").value = "0.75"; document.getElementById("quantity").value = "100"; calculateCoreWeight(); } function copyResults() { var w = document.getElementById("res-singleWeight").innerText; var t = document.getElementById("res-totalWeight").innerText; var text = "Paper Core Weight Calculation:\n" + "Single Core Weight: " + w + "\n" + "Total Batch Weight: " + t + "\n" + "Calculated on Industrial Tools."; 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); } // Canvas Chart Implementation function updateChart(currentWeightG, density, lenCm, irCm, thickCm) { var canvas = document.getElementById("weightChart"); var ctx = canvas.getContext("2d"); var width = canvas.width; var height = canvas.height; // Clear canvas ctx.clearRect(0, 0, width, height); // Data Generation: Sensitivity Analysis (-20% thickness, Current, +20% thickness) // Scenario 1: Thinner wall (-20%) var th1 = thickCm * 0.8; var or1 = irCm + th1; var vol1 = Math.PI * lenCm * (Math.pow(or1, 2) – Math.pow(irCm, 2)); var w1 = vol1 * density; // Scenario 2: Current var w2 = currentWeightG; var vol2 = w2 / density; // Scenario 3: Thicker wall (+20%) var th3 = thickCm * 1.2; var or3 = irCm + th3; var vol3 = Math.PI * lenCm * (Math.pow(or3, 2) – Math.pow(irCm, 2)); var w3 = vol3 * density; // Data series var weights = [w1, w2, w3]; var volumes = [vol1, vol2, vol3]; // secondary series var labels = ["-20% Thickness", "Current", "+20% Thickness"]; // Scaling var maxWeight = Math.max(w1, w2, w3) * 1.2; var chartHeight = height – 60; var barWidth = 60; var gap = (width – 100) / 3; var startX = 80; var startY = height – 40; // Draw Axis ctx.beginPath(); ctx.strokeStyle = "#ccc"; ctx.moveTo(50, 20); ctx.lineTo(50, startY); ctx.lineTo(width – 20, startY); ctx.stroke(); // Colors var colorPrimary = "#004a99"; var colorSecondary = "#28a745"; // Draw Bars for (var i = 0; i < 3; i++) { var x = startX + (i * gap); // Bar 1: Weight (Primary) var barH = (weights[i] / maxWeight) * chartHeight; ctx.fillStyle = colorPrimary; ctx.fillRect(x, startY – barH, barWidth, barH); // Label Values ctx.fillStyle = "#333"; ctx.font = "bold 12px Arial"; ctx.fillText((weights[i]/1000).toFixed(2) + "kg", x, startY – barH – 5); // X-Axis Labels ctx.fillStyle = "#555"; ctx.font = "12px Arial"; ctx.fillText(labels[i], x, startY + 20); // Draw secondary point (Volume) – visualized as a line node // Scale volume to match chart area roughly for visualization // Just displaying volume as text inside the bar for simplicity in strict JS env without complex secondary axis logic ctx.fillStyle = "#fff"; ctx.font = "11px Arial"; ctx.fillText(Math.round(volumes[i]) + "cm³", x + 10, startY – 10); } // Legend ctx.fillStyle = colorPrimary; ctx.fillRect(width – 120, 20, 15, 15); ctx.fillStyle = "#333"; ctx.font = "12px Arial"; ctx.fillText("Weight (kg)", width – 100, 32); ctx.fillStyle = "#555"; ctx.fillText("*Volume cm³ inside bar", width – 140, 50); }

Leave a Comment