Cone Surface Area Calculator
Find the surface area of a cone.
Results update as you type.
How it works
A cone has a circular base that tapers smoothly to a point, and this calculator finds its surface area from the base radius and the vertical height. You enter the radius and height, and it returns both the total surface area and the lateral surface area. The lateral surface is the curved side of the cone, and its area is pi times the radius times the slant height, where the slant height is the straight-line distance from the edge of the base to the tip. Because the slant height is not given directly, the calculator computes it from the radius and vertical height using the Pythagorean theorem, since the radius, height, and slant height form a right triangle. The total surface area adds the circular base, pi times the radius squared, to the lateral area. Whether you need the total or just the lateral area depends on the object: a solid cone or ice cream cone with a closed base uses the total, while an open cone like a funnel or a party hat uses only the lateral area. These formulas are used in manufacturing to find material for cone-shaped objects, in packaging, construction of roofs and funnels, and geometry education. A key point is to use the vertical height, not the slant height, as your input, since the calculator derives the slant height itself. Enter the radius and height to compute the cone's surface area.
Total = π·r² + π·r·√(r² + h²)
A cone's total surface area is the circular base, pi times the radius squared, plus the curved lateral surface, pi times the radius times the slant height. The slant height is found from the radius and vertical height using the Pythagorean theorem. The lateral area alone excludes the base, useful for open cones.
Source:Solid geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter base radius and height.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Total surface area updates instantly as you type — no button to press.
Frequently asked questions
How do you find the surface area of a cone?
Add the base area, pi times the radius squared, to the lateral area, pi times the radius times the slant height. The slant height comes from the radius and vertical height via the Pythagorean theorem. The calculator computes the slant height and both areas from the radius and height you enter.
What is the slant height?
The slant height is the straight-line distance from a point on the edge of the cone's base to its apex, along the curved surface's steepest line. It differs from the vertical height, which goes straight up the center. The slant height equals the square root of the radius squared plus the height squared.
What is the difference between total and lateral surface area?
The total surface area includes both the curved side and the circular base of the cone, while the lateral surface area is only the curved side, excluding the base. Use the total for a closed cone like a solid or an ice cream cone, and the lateral area for an open cone like a funnel or party hat.
Should I enter the vertical height or slant height?
Enter the vertical height, the perpendicular distance from the base to the apex through the center. The calculator derives the slant height from the radius and vertical height automatically. If you accidentally enter the slant height as the height, the result will be wrong, so make sure you use the true vertical height.
Where are cone surface area formulas used?
They are used to calculate the material needed to make cone-shaped objects like funnels, party hats, ice cream cones, and traffic cones, to design conical roofs and hoppers, in packaging, and in geometry education. Knowing the surface area tells you how much material covers or forms the cone.