WorldCalcs

Cone Calculator

Enter the radius and height to get a cone's volume, slant height, and lateral and total surface area.

Reviewed by the WorldCalcs team · Methodology · Last reviewed: June 2026

Volume

37.69911184

V = (1/3)πr²h

Slant height

5

l = √(r² + h²)

Lateral surface area

47.1238898

A_lat = πrl

Total surface area

75.39822369

A = πr(r + l)

What is a cone calculator?

A cone is a 3-D shape with a circular base that narrows to a single point (the apex). This calculator works out a right circular cone's volume and surface area from its base radius and height — handy for everything from ice-cream cones to traffic cones and funnels.

How it's calculated

Volume is a third of the matching cylinder: V = (1/3) × π × r² × h. The slant height (the distance from the base edge to the apex) comes from the Pythagorean theorem: l = √(r² + h²). The lateral (side) surface area is π × r × l, and the total surface area adds the circular base: π × r × (r + l), where r is the radius, h the height, and l the slant height.

Example

A cone with radius 3 and height 4: slant height = √(3² + 4²) = √25 = 5. Volume = (1/3) × π × 3² × 4 = 12π ≈ 37.70. Lateral surface = π × 3 × 5 = 15π ≈ 47.12. Total surface = π × 3 × (3 + 5) = 24π ≈ 75.40.

All calculations happen in your browser. Nothing is sent, stored, or tracked.

Results are estimates and may contain errors — for general information only, not professional advice. Always verify before relying on them. Disclaimer

How to use

Type positive values for the base radius (r) and the perpendicular height (h). The calculator returns the volume, slant height, lateral surface and total surface instantly.

Values are rounded to about 6 significant digits using π ≈ 3.14159.

Frequently asked questions

How do I find the volume of a cone?+

Multiply π by the radius squared by the height, then divide by 3: V = (1/3) × π × r² × h.

What is the slant height of a cone?+

The straight-line distance from the edge of the base to the apex: l = √(r² + h²).

What's the difference between lateral and total surface area?+

Lateral surface is just the curved side (π × r × l). Total surface adds the circular base, giving π × r × (r + l).

Why is a cone's volume one-third of a cylinder's?+

A cone and a cylinder with the same base and height relate exactly 1:3 — three identical cones fill one cylinder.

What units does this use?+

Whatever unit you enter for radius and height — volume comes out in cubic units and surface area in square units.

Does this work for an oblique cone?+

No, these formulas are for a right cone (apex centred over the base). Oblique cones need different methods.

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