Cone Surface Area Calculator
Enter a base radius and a slant height to get the total surface area of a cone in square units — plus the lateral (curved side) area on its own.
Total and lateral area at once
Enter the radius and slant height and the calculator returns the total surface area (πr(r + l)) and the lateral area (πrl) together.
Use the slant height
The second input is the slant height l, not the vertical height — if you only know the height h, the slant height is √(r² + h²).
What is cone surface area?
The skin of a cone
A cone surface area calculator turns two measurements — the base radius and the slant height — into the area of the cone's outer skin. A right circular cone has two parts to its surface: the flat circular base and the curved side that wraps up to the apex. The total surface area covers both, while the lateral surface area is just the curved side on its own. Both come back in square units: enter the radius and slant height in centimetres and you get square centimetres, enter them in inches and you get square inches. It is the number behind how much paper wraps an ice-cream cone, how much sheet metal a funnel needs, or how much paint coats a conical roof.
Enter a base radius and a slant height in the same length unit to get the total and lateral surface area of the cone instantly.
The total surface area is pi times the radius times the radius plus the slant height; the lateral area drops the base.
A = π × r × (r + l)The base is a circle of area πr², and the curved side has area πrl; adding them and factoring out πr gives the compact form πr(r + l). The lateral surface area is just πrl, so for the same cone it is π × 3 × 5 = 47.12389 square units. Keep both inputs in the same length unit and the answer comes back in that unit squared.
Suppose a cone has a base radius of 3 and a slant height of 5 (in the same unit).
Find the lateral area
π × 3 × 5 = 47.12389 — the curved side on its own.
Add the base radius inside the bracket
r + l = 3 + 5 = 8 — radius plus slant height.
Multiply by π and the radius
π × 3 × 8 = 75.398224 square units — the total surface area, base included.
The two outputs answer two different questions. The total surface area (75.398224 for the cone above) is the whole outer skin — the curved side plus the circular base — and is what you want when the cone is closed, like a solid sculpture or a sealed tank. The lateral surface area (47.12389) is only the curved side, which is the right figure for an open cone such as a paper drinking cup, an ice-cream cone, or a funnel where there is no lid to cover. Because both formulas share the πrl term, the gap between them is exactly the area of the base, πr² — here π × 3² = 28.274334. As the radius grows relative to the slant height, the base takes up a larger share of the total; for a tall, narrow cone the curved side dominates instead.
The formula is exact, but one input is easy to confuse.
Slant height, not vertical height
The l in πr(r + l) is the slant height — the diagonal distance along the curved side from the base rim to the apex — not the vertical height h measured straight up the middle. If you only know the vertical height, convert first with the Pythagorean theorem: slant = √(r² + h²). This calculator covers a right circular cone with a circular base; it does not handle oblique cones or elliptical bases. Keep the radius and slant height in the same length unit or the square-unit result will be wrong.