Hollow Cone Weight Calculator
Calculate volume, mass, and material costs for engineering and fabrication
Millimeters (mm)
Centimeters (cm)
Meters (m)
Inches (in)
Feet (ft)
The radius of the outer edge of the cone base.
Must be positive.
The radius of the hollow center (must be smaller than outer radius).
Must be smaller than outer radius.
The vertical height from base to tip.
Steel (7850 kg/m³)
Aluminum (2700 kg/m³)
Cast Iron (7200 kg/m³)
Copper (8960 kg/m³)
Gold (19300 kg/m³)
Plastic – Polystyrene (1050 kg/m³)
Concrete (2400 kg/m³)
Water (1000 kg/m³)
Custom Density…
Enter 0 if unknown.
Total Weight
0.00 kg
Based on selected material density
Total Volume
0.00 m³
Total Cost
$0.00
Slant Height
0.00 mm
Detailed Breakdown
| Parameter | Value |
|---|
Material Weight Comparison
Comparison of your object's weight across common materials.
What is a Hollow Cone Weight Calculator?
A hollow cone weight calculator is a specialized engineering tool designed to determine the mass, volume, and material cost of a conical shell or a cone with a hollow center. Unlike a standard cone volume calculator, this tool accounts for the void space inside the object, making it essential for calculating the raw material requirements for funnels, hoppers, traffic cones, and architectural spires.
Engineers, fabricators, and logistics coordinators use this calculator to estimate shipping loads and material costs before production begins. By inputting geometric dimensions—specifically the outer radius, inner radius, and height—along with the material density, users can obtain precise weight data critical for structural analysis and budgeting.
Hollow Cone Formula and Mathematical Explanation
To calculate the weight of a hollow cone, we must first determine the volume of the material itself. This is done by calculating the volume of the outer cone and subtracting the volume of the inner void (the inner cone).
Volume Formula:
V = (1/3) × π × h × (R² – r²)
Weight Formula:
W = V × ρ
V = (1/3) × π × h × (R² – r²)
Weight Formula:
W = V × ρ
Where:
| Variable | Meaning | Typical Unit |
|---|---|---|
| V | Volume of material | m³ or in³ |
| h | Vertical Height | m, mm, in |
| R | Outer Base Radius | m, mm, in |
| r | Inner Base Radius | m, mm, in |
| ρ (rho) | Material Density | kg/m³ or lbs/in³ |
Note: This formula assumes the inner and outer cones share the same height, representing a cone with a conical hole. For sheet metal cones with uniform wall thickness, the calculation is often approximated using lateral surface area multiplied by thickness.
Practical Examples
Example 1: Steel Industrial Hopper
A fabrication shop needs to build a steel hopper funnel. The outer radius at the top is 1 meter, the inner radius is 0.95 meters (5cm wall thickness equivalent at the rim), and the height is 2 meters.
- Material: Steel (7850 kg/m³)
- Outer Radius (R): 1.0 m
- Inner Radius (r): 0.95 m
- Height (h): 2.0 m
- Calculation: V = (1/3) × π × 2 × (1² – 0.95²) ≈ 0.204 m³
- Total Weight: 0.204 m³ × 7850 kg/m³ ≈ 1,601 kg
Example 2: Plastic Traffic Cone
A manufacturer is designing a large custom traffic cone using Polystyrene.
- Material: Plastic (1050 kg/m³)
- Outer Radius: 200 mm (0.2 m)
- Inner Radius: 190 mm (0.19 m)
- Height: 600 mm (0.6 m)
- Result: The calculator determines the volume is approximately 0.00245 m³, resulting in a weight of roughly 2.57 kg.
How to Use This Hollow Cone Weight Calculator
- Select Units: Choose your preferred measurement system (Millimeters, Meters, Inches, etc.).
- Enter Dimensions: Input the Outer Base Radius, Inner Base Radius, and vertical Height. Ensure the Inner Radius is smaller than the Outer Radius.
- Choose Material: Select a material from the dropdown list (e.g., Steel, Aluminum) to automatically apply standard density values. If using a unique alloy, select "Custom" and enter the density manually.
- Review Costs: Optionally, enter the cost per kilogram/pound to get an estimated total material cost.
- Analyze Results: View the calculated Weight, Volume, and Surface Area in the results panel. Use the "Copy Results" button to save the data for your reports.
Key Factors That Affect Hollow Cone Weight
Several variables influence the final weight and cost of a hollow cone structure:
- Material Density: This is the most significant factor. A gold cone will weigh nearly 20 times more than a water-filled cone of the same dimensions due to density differences (19,300 kg/m³ vs 1,000 kg/m³).
- Wall Thickness: The difference between the outer radius (R) and inner radius (r) defines the wall thickness. Even a small increase in thickness can significantly increase volume and weight.
- Height vs. Radius Ratio: A taller cone with a narrow base may have the same volume as a short, wide cone, but the structural center of gravity will differ.
- Manufacturing Tolerances: In real-world fabrication, sheet metal rolling or casting may result in slight variations in wall thickness, affecting the actual weight by ±5%.
- Weld Material: For fabricated metal cones, the weight of welding rods used to join seams is often added to the theoretical weight (usually estimated at 1-2%).
- Surface Coatings: Paint, galvanization, or rubber linings add additional weight that is not calculated in the raw geometric formula.
Frequently Asked Questions (FAQ)
What is the difference between a hollow cone and a frustum?
A hollow cone comes to a sharp point (vertex), whereas a frustum is a "truncated" cone with the tip cut off, leaving two flat parallel bases. If your object has a flat top and bottom, you should use a frustum calculator.
Can I calculate the weight of a sheet metal cone?
Yes. To do this, set the Outer Radius to your desired dimension and set the Inner Radius to (Outer Radius – Sheet Thickness). This approximates the volume of the sheet metal used.
How do I convert cubic meters to kilograms?
You multiply the volume in cubic meters by the material density in kg/m³. For example, 1 m³ of steel weighs 7,850 kg.
Does this calculator account for the base plate?
No, this calculator determines the weight of the conical shell (lateral walls) only. If your cone has a solid base plate closing the bottom, calculate the weight of a cylinder/disk with height equal to the plate thickness and add it to the result.
Why is the inner radius required?
The inner radius defines the "hollow" part. Without it, the formula would calculate a solid cone. The difference between the outer and inner radii represents the material volume.
What is the density of mild steel?
Mild steel typically has a density of approximately 7,850 kg/m³ (or 7.85 g/cm³). This is the default value used in our calculator for "Steel".
Is the slant height different from the vertical height?
Yes. Vertical height is the straight distance from base to tip. Slant height is the distance along the angled side. Slant height is always longer than vertical height and is used to calculate surface area.
Can I use this for liquid volume?
Yes. If you want to know how much liquid a cone holds, set the Inner Radius to 0 (treating the liquid as a solid cone) and use the density of the liquid (e.g., Water = 1000 kg/m³).
Related Tools and Internal Resources
Expand your engineering toolkit with these related calculators:
- Metal Weight Calculator – Calculate weights for plates, bars, and tubes.
- Cylinder Volume Calculator – Determine volume and capacity for tanks and pipes.
- Frustum Weight Calculator – For truncated cones and hoppers.
- Sheet Metal Cost Estimator – Estimate fabrication costs based on surface area.
- Tank Capacity Calculator – Calculate liquid volume for various tank shapes.
- Structural Beam Load Calculator – Analyze load-bearing capacities for steel beams.