A focused calculator for the surface area of a cone — the base circle plus the curved (lateral) surface combined.
How it works
The radius is multiplied by π and by the sum of the radius and slant height, combining the base area and lateral surface area in one expression.
What this does not include
This does not include other 3D shapes — for cubes, spheres, cylinders, and rectangular prisms, use this site’s general surface area calculator instead.
How to use this calculator
- Enter the cone’s radius and slant height.
A worked example
A cone with radius 3 and slant height 5: surface area = πr(r + slant) = 75.3982.
Radius 4, slant height 6: surface area = 125.6637.
What the variables mean
| Variable | Meaning |
|---|---|
| Radius | Radius of the circular base |
| Slant height | Distance from the base edge to the apex, along the cone’s surface |
Edge cases worth knowing
Slant height is different from vertical height. Slant height measures along the cone’s sloped surface, while vertical height measures straight up to the apex — using the wrong one here gives an incorrect result.
A radius of zero collapses the cone to a line, leaving no surface, so the calculator declines to show a result.
Frequently asked questions
What’s the difference between slant height and vertical height?
Slant height runs along the cone’s curved surface from the tip to the base edge; vertical height runs straight down the center — they’re only equal for a cone with zero radius.
What if I only know the vertical height, not the slant height?
The slant height can be found using the Pythagorean theorem from the radius and vertical height, then entered here.
What’s a real-world example of a cone?
A traffic cone, an ice cream cone, or a party hat — this formula finds the material needed to cover any of them.
