ToolBark
Math

Cone Calculator

Instant cone volume and surface area from radius and height

Cone Dimensions

Results

Volume314.1593cm³
Radius
5 cm
Height
12 cm
Slant Height

√(r² + h²)

13 cm
Volume

⅓ × π × r² × h

314.1593 cm³
Base Area

π × r²

78.5398 cm²
Lateral Surface Area

π × r × l

204.2035 cm²
Total Surface Area

π × r × (l + r)

282.7433 cm²

Formulas

Slant Height (l)
l = √(r² + h²)
Distance from the apex to the edge of the base along the surface.
Volume (V)
V = ⅓ × π × r² × h
Space enclosed inside the cone.
Base Area (A_base)
A = π × r²
Area of the circular base.
Lateral Surface Area
A_lat = π × r × l
Area of the curved side, excluding the base.
Total Surface Area
A_total = π × r × (l + r)
Full outer area including the base and the lateral surface.
About

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.

FAQ
What is the formula for the volume of a cone?+

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.

How is the slant height of a cone calculated?+

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.

What is the difference between lateral and total surface area?+

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.

Does the calculator work for oblique (tilted) cones?+

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.

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