Cone Surface Area Calculator
Total, lateral (curved) and base area of a right circular cone from radius and height or slant height.
A cone’s surface area covers a party hat, a waffle cone, a traffic cone, or a funnel — any shape that comes to a single point from a circular base. This calculator finds it from either the radius or the diameter, plus either the height or the slant height (whichever you know), and breaks the result into the base circle’s area, the curved lateral surface wrapping up to the point, and the total.
Enter your measurements in whichever form you have them, and the calculator handles the conversion automatically.
Cone Surface Area Formula
Base Area
Base Area = πr²
This is the area of the flat circular base.
Lateral (Curved) Surface Area
Lateral Area = πrl
Where l is the slant height — the distance from the base’s edge up to the apex, measured along the cone’s surface (not the same as the vertical height straight up the middle).
Total Surface Area
Total Surface Area = πr² + πrl
Finding Slant Height from Height (and Vice Versa)
Slant Height = √(Height² + Radius²)
The height, the radius, and the slant height form a right triangle, since the height runs straight up the cone’s center while the slant height runs along the outside. If you already know the slant height, you can enter it directly and skip this conversion — the calculator accepts either one.
By Radius vs. By Diameter
Since many real-world measurements (a cone’s opening width, a funnel’s rim) come as a diameter rather than a radius, this calculator offers both as direct inputs — the By Diameter mode simply divides by 2 first, then uses the exact same formulas.
Worked Example: By Radius
A cone with a 6-ft radius and an 8-ft height: Slant Height = √(8² + 6²) = √100 = 10 ft, Base Area = π × 6² ≈ 113.10 square feet, Lateral Area = π × 6 × 10 ≈ 188.50 square feet, Total SA = 113.10 + 188.50 ≈ 301.59 square feet.
Worked Example: By Diameter (Slant Height Already Known)
A cone with a 10-ft diameter and a 13-ft slant height already known: Radius = 10 ÷ 2 = 5 ft, Base Area = π × 5² ≈ 78.54 square feet, Lateral Area = π × 5 × 13 ≈ 204.20 square feet, Total SA = 78.54 + 204.20 ≈ 282.74 square feet.
When You Only Need Lateral Area
Not every project needs the full total surface area. If you’re calculating the paper or fabric for a party-hat or waffle-cone template, or wrapping only the outer surface of a cone-shaped shade, the lateral area alone — without the base circle — is the number you actually need.
Frequently Asked Questions
How do I find a cone’s surface area from its diameter instead of radius?
Use the By Diameter mode: enter the diameter along with the height or slant height, and the calculator divides the diameter by 2 to get the radius before applying the standard formulas.
What’s the difference between slant height and height?
Height is the straight vertical distance from the apex down to the center of the base. Slant height is the distance from the apex down to the base’s edge, measured along the cone’s outer surface. They’re related by Slant Height = √(Height² + Radius²).
What’s the difference between lateral and total surface area?
Lateral area (πrl) covers only the curved surface of the cone. Total surface area adds the base circle on top of that: Total SA = Base Area (πr²) + Lateral Area (πrl).