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Cone Surface Area Calculator

Calculate the surface area of a cone with πr(r + √(r² + h²)). Includes the formula, a worked example, and reference sizes for ice cream cones and funnels.

Perpendicular height

Calculate surface area of cone

Formula

textsurfacearea=pir2+pirell\\text{surface area} = \\\\pi r^2 + \\\\pi r \\\\ell

Where r is the radius and ℓ is the slant height.

Factorized:

textsurfacearea=pir(r+ell)\\text{surface area} = \\\\pi r(r + \\\\ell)

If you know the height h instead:

ell=sqrtr2+h2\\\\ell = \\\\sqrt{r^2 + h^2}

Worked example

Calculate the surface area of a cone with radius 6 cm and height 8 cm:

First find the slant height:

ell=sqrt62+82=sqrt36+64=sqrt100=10textcm\\\\ell = \\\\sqrt{6^2 + 8^2} = \\\\sqrt{36 + 64} = \\\\sqrt{100} = 10 \\\\text{ cm}

Now calculate surface area:

textsurfacearea=pitimes6(6+10)=pitimes6times16=96pi\\text{surface area} = \\\\pi \\\\times 6(6 + 10) = \\\\pi \\\\times 6 \\\\times 16 = 96\\\\piapprox96times3.1416=301.59textcm2\\\\approx 96 \\\\times 3.1416 = 301.59 \\\\text{ cm}^2

Result: 301.59 cm²

How to use

  1. Enter the radius of the cone base
  2. Enter either the height or the slant height
  3. Click "Calculate" to see the surface area

Related formulas

  • Volume: frac13pir2h\\\\frac{1}{3}\\\\pi r^2 h
  • Lateral surface area: pirell\\\\pi r \\\\ell
  • Base area: pir2\\\\pi r^2

Common use cases

  • Conical tent and hat manufacturing
  • Traffic cone calculations
  • Rocket and missile design
  • Architecture and design

FAQ

What if I only know the diameter? Divide by 2 to get the radius.

How is this different from a pyramid? A cone has a circular base; a pyramid has a polygonal base.

What about an open cone? Use only the lateral surface area: pirell\\\\pi r \\\\ell.

Can I calculate from volume? No, you need radius and either height or slant height.

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