Cone Surface Area Calculator
The surface area of a cone consists of the curved lateral surface and the circular base. The slant height (distance along the slope from apex to base edge) is l = sqrt(r²+h²). The lateral surface area is π*r*l. The total surface area including the base is π*r*(r+l). This calculator computes both the lateral and total surface areas of a cone from its radius and height.
Cone surface area formulas
Slant Height = √(r² + h²)
Lateral Surface Area = π * r * l
Total Surface Area = π * r * (r + l)
Reference values
| Radius | Height | Slant Height | Total Surface |
|---|---|---|---|
| 2 cm | 5 cm | 5.39 cm | 47.12 cm² |
| 5 cm | 10 cm | 11.18 cm | 253.96 cm² |
| 3 m | 4 m | 5.00 m | 73.90 m² |
Cone surface area calculator: frequently asked questions
What is slant height?
Slant height l is the distance along the sloped surface from apex to base edge. Calculated as l = sqrt(r²+h²).
What is lateral surface area?
Lateral surface (just the curved side): A = π*r*l, where r is radius and l is slant height.
What is total surface area?
Total (curved side + circular base): A = π*r*(r+l).
How do I find slant height?
Use Pythagorean theorem: l = sqrt(r² + h²), where r is base radius and h is height.
Where is this useful?
Calculating cone surface area helps with material estimates, paint coverage, and cone-shaped structure design.
Official sources
- Khan Academy: Volume and surface area.
- NIST: National Institute of Standards.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.