Cone Surface Area Calculator
Find the total and lateral surface area of a right circular cone, plus its slant height, from the radius and vertical height.
How it works
Slant height l = √(r² + h²) · Lateral = πrl · Total = πr² + πrl
The surface of a cone is a curved lateral part plus one circular base. The lateral area depends on the slant height l — the distance from the base rim up to the apex — which forms a right triangle with the radius and the vertical height, so l = √(r² + h²). The lateral area is πrl, and adding the base πr² gives the total surface area.
Worked example
For radius 4 and height 9: slant height = √(4² + 9²) = √97 = 9.849. Lateral area = π·4·9.849 = 123.77, base = π·4² = 50.27, so total = 174.04 square units.
Sources: Cone — Wikipedia
Frequently asked questions
What is slant height and why does it matter?
Slant height is the straight distance along the cone’s surface from the base edge to the tip, l = √(r² + h²). The curved surface area uses the slant height, not the vertical height, because the surface itself slopes.
How do I find the area of just the curved surface?
Use the lateral area, πrl. That is the right figure for something like an open party hat or a cone with no bottom.
Is the vertical height the same as the slant height?
No. The vertical height h goes straight up the axis; the slant height l runs along the sloped surface and is always longer. They differ unless the radius is zero.
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This calculator is for educational purposes. Double-check important results before acting on them.