Cone Surface Area Calculator

SA = πr² + πrl, where l = √(r² + h²) is the slant height.

Inputs

Result

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General calculation reads

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How to use this calculator

  • Enter base radius and height.
  • Read SA (with or without base).

About this calculator

A cone's surface has two parts: lateral (curved side) and base (circle). Lateral surface = πr × slant, where slant = √(r² + h²). Total SA = πr² + πr × slant = πr(r + slant). Many real cones are open (party hats, ice cream cones) — use just the lateral. The lateral, when unrolled, is a circular sector of radius = slant, arc-length = circumference of base = 2πr.

Frequently asked

Why slant height for lateral?+
The lateral surface, when flattened, is a circle sector with radius = slant and arc length = 2πr (the cone's base circumference).
Open-top cone (party hat)?+
Just the lateral: πr × slant. No base, no top.
Slant from radius and height?+
Pythagorean: slant² = r² + h². Slant is hypotenuse of a right triangle with legs r and h.
Cone vs. pyramid SA?+
Same idea (lateral + base). Cone has one curved lateral; pyramid has multiple triangular faces.
Real-world cone surfaces?+
Loudspeaker cones, traffic cones, ice cream wafers, witch hats, conical roof tiles.

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