Instant cone volume and surface area from radius and height
Cone Dimensions
Results
√(r² + h²)
⅓ × π × r² × h
π × r²
π × r × l
π × r × (l + r)
Formulas
A cone calculator lets you find the volume, total surface area, lateral surface area, and slant height of any right circular cone in seconds. Enter the base radius and height, pick your unit (mm, cm, m, in, ft, and more), and all values are computed instantly using the standard geometry formulas — no algebra required. Perfect for students, engineers, and anyone working with cone-shaped objects.
The volume of a cone is V = (1/3) × π × r² × h, where r is the base radius and h is the perpendicular height. It equals exactly one-third of the volume of a cylinder with the same base and height.
Slant height (l) is the distance from the apex to any point on the base edge, measured along the surface. It is found using the Pythagorean theorem: l = √(r² + h²), where r is the radius and h is the vertical height.
Lateral surface area (π × r × l) covers only the curved side of the cone, excluding the base. Total surface area adds the circular base (π × r²), giving π × r × (l + r) for the full outer surface.
No — the formulas used here apply to right circular cones, where the apex sits directly above the center of the base. Oblique cones require more complex integration-based calculations.