Cone Lateral Surface Area Calculator

Compute the lateral surface area of a cone and the sector angle required for sheet metal fabrication. Essential for students, welders, and engineers.

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About

Fabricating a cone from a flat sheet of material requires more than just knowing its height and radius. You need to know the "developed" shape specifically the Lateral Surface Area and the Sector Angle for the flat pattern. The Cone Lateral Surface Area Calculator bridges the gap between theoretical geometry and practical fabrication.

This tool is indispensable for sheet metal workers, HVAC technicians making funnels or transitions, and students studying solid geometry. By inputting the basic dimensions, you instantly get the area for material cost estimation and the precise angle needed to cut the sector from a flat plate, saving time on trial-and-error cardboard mockups.

cone surface-area fabrication sheet-metal

Formulas

The lateral surface area L (excluding the base) depends on the radius r and the slant height s. The slant height is the distance from the apex to the edge of the base.

s = √r2 + h2

Once s is found, the area is:

L = π r s

For fabrication, the flat pattern Sector Angle θ (in degrees) is calculated as:

θ = 360 × (rs)

Reference Data

MaterialDensity (kg/m³)Application Notes
Mild Steel7,850Standard for general fabrication/hoppers.
Stainless Steel (304)8,000Food grade funnels, chemical tanks.
Aluminum (6061)2,700Lightweight ducts, decorative cones.
Copper8,960Roofing spires, distillery equipment.
Titanium4,500High-performance aerospace parts.
Cardboard/Paper600-800Prototyping and crafts.
Glass2,500Laboratory funnels.
Concrete2,400Civil engineering structures.

Frequently Asked Questions

Lateral Area covers only the curved 'side' of the cone (the part you would wrap around). Total Surface Area includes the Lateral Area plus the area of the circular base (Pi * r^2). For making a funnel (open bottom), you only need the Lateral Area.
To make a cone from a flat sheet: 1) Draw a circle with radius equal to the Slant Height (s). 2) Measure the Sector Angle (θ) at the center. 3) Cut out that pie slice. 4) Roll the slice until the straight edges meet. This forms your cone.
The Slant Height is the actual distance usually measured on the physical material. However, in drawings, usually the vertical Height (h) is given. This calculator computes the Slant Height for you using the Pythagorean theorem.
No, this tool is for full cones (coming to a sharp point). For a truncated cone (like a bucket or lampshade), you need a specific 'Cone Frustum Calculator'.