The Surface Area Of A Cone Calculator
The surface area of a cone is the flat circular base plus the curved side that tapers to the point. The only extra quantity you need beyond radius and height is the slant height, the distance down the outside of the cone.
Total surface area
282.7433
- Slant height
- 13
- Lateral (curved) area
- 204.2035
- Base area
- 78.5398
- Curved side as a share of the total
- 72.22%
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
total surface area = pi x r x l + pi x r^2, where l = sqrt(r^2 + h^2)
- r
- The radius of the circular base
- h
- The perpendicular height from base to point
- l
- The slant height, measured down the side
- total
- Base area plus lateral area
How to check the result by hand
- 1
Find the slant height
Square the radius, square the height, add them and take the square root. For a radius of 5 and a height of 12 the slant height is sqrt(25 + 144), which is exactly 13.
- 2
Compute the base area
Pi times the radius squared. For a radius of 5 that is 78.53981633974483. Skip this if you only need the lateral area.
- 3
Compute the lateral area
Pi times the radius times the slant height. For a radius of 5 and a slant height of 13 that is 204.20352248333654.
- 4
Add the two together
204.20352248333654 plus 78.53981633974483 gives a total surface area of 282.7433388230814.
- 5
Sanity check the shape
The lateral area must be larger than the base for any cone taller than it is wide, and the total must exceed both parts. For these numbers the side is the dominant term.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate The Surface Area Of A Cone page.