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Cone Frustum Surface Area Calculator

Surface areas of a truncated cone.

Result

109.9557
201.0619

How it is calculated

Enter the two circle radii r1 and r2 and the perpendicular height h between them, in one length unit. The tool first finds the slant height s = √(h² + (r1 − r2)²), the length of the sloping side. Lateral area is π × (r1 + r2) × s. Total area adds both circular ends: π × (r1 + r2) × s + π × r1² + π × r2². Both are rounded to 4 decimals. All three inputs must be above zero, so a full cone (r2 = 0) is not accepted. If r1 = r2 the shape is a cylinder and the formulas still work. The larger radius can go in either box.

Worked example

A bucket-shaped frustum has radii 5 and 2 and height 4. Slant height: r1 − r2 = 3, so s = √(16 + 9) = √25 = 5. Lateral area: π × 7 × 5 = 35π = 109.9557. The two end circles are π × 25 = 78.5398 and π × 4 = 12.5664, which together make 91.1062. Total area: 109.9557 + 91.1062 = 201.0619, in square units of whatever unit you entered.

Try this example →

Common mistakes

  • Entering diameters instead of radii. Halve each diameter first; otherwise every area is far too large (the end circles alone are four times too large).
  • Using the slant height as the height. The tool computes the slant height itself from the perpendicular height.
  • Reading the total area as material for an open container. A bucket or cup has only one end cap, so add just the base circle to the lateral area instead of using the total.
  • Entering 0 for the top radius to model a cone. The tool requires both radii to be above zero, so use a very small value or a dedicated cone calculator.

About this calculator

A frustum is what remains of a cone after its tip is sliced off by a plane parallel to the base, leaving two circular faces of different radii (r1 and r2) connected by a slanted lateral surface. Its lateral surface area is π(r1 + r2) × s, where s is the slant height found from the Pythagorean relationship s = √(h² + (r1 − r2)²); adding the two circular end caps, πr1² and πr2², gives the total surface area.

This shape and its formulas are everywhere in manufacturing and design: paper and plastic cups, lampshades, buckets, funnels, traffic cones with flattened tops, and pipe reducers are all frustums, and knowing the surface area is essential for calculating how much material (sheet metal, cardboard, plastic) is needed to produce them at scale. Architects and engineers also use frustum geometry for tapered concrete columns, silos and chimney sections.

With the top and bottom radii and the height of the truncated cone, it works out the slant and gives the lateral surface area and the total area including both circular ends.

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