Cone Calculator (Volume, Slant Height, Surface Area)

How to use this calculator

Enter the base radius and height to get the slant height, volume and surface areas. You can also solve for the height from a volume, or the radius from the slant height.

Formulas

s = √(r² + h²) V = ⅓πr²h
Lateral area = πrs Total = πrs + πr²

Worked example

A cone with a 3 cm radius and 4 cm height:

• Slant height = √(9 + 16) = 5 cm
• Volume = ⅓ × π × 9 × 4 = 37.7 cm³
• Lateral area = π × 3 × 5 = 47.1 cm²
• Total surface = 47.1 + 28.3 = 75.4 cm²

Practical uses

• Silos and hoppers have conical bottoms — add the cone volume to the cylinder above.
• Piles of sand or gravel form cones. Measure the base circumference and height to estimate the volume.
• Funnels and paper cups use the lateral area to work out how much material is needed.

Frequently asked questions

What is the formula for the volume of a cone?

V = ⅓ × π × r² × h — exactly one third of a cylinder with the same base and height.

What is the slant height?

The distance from the tip to the edge of the base along the side, s = √(r² + h²).

How do I calculate a hopper or funnel volume?

For a full cone, use this calculator. For a truncated cone (cut off at the bottom), subtract the small cone from the large one.

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