Math

Cone Volume Calculator

Enter the radius and height of a cone to find its volume, slant height and surface area.

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Your numbers

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Volume
Volume
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Slant height
—
Total surface area
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Cone Volume Calculator by TheCalcTools

How the Cone Volume Calculator works

Enter the base radius and the perpendicular height.

The slant height is the hypotenuse of the right triangle formed by the radius and height.

Volume is one third of a cylinder with the same base and height.

The formula

V = ⅓πr²hl = √(r² + h²)

Worked example

Using the default values shown in the calculator:

Radius (r)3
Height (h)4
  1. Slant height = √(3² + 4²) = 5.00.
  2. Volume = ⅓ × π × 9 × 4 = 37.6991.
  3. Total surface area = π × 3 × (3 + 5) = 75.3982.

Result:

Volume37.6991
Slant height5.0000
Total surface area75.3982

Frequently asked questions

Why is the cone one third of the cylinder?

Integrating the shrinking circular slices from base to tip gives exactly one third of the cylinder’s volume.

What is slant height?

The distance along the surface from the tip to the edge of the base.

Sources and further reading

Cylinder Volume CalculatorEnter the radius and height to find a cylinder's volume and surface area Sphere Volume and Surface Area CalculatorEnter the radius to find the volume and surface area of a sphere Triangle Calculator (Solve Any Triangle: SSS, SAS, ASA)Choose what you know and enter the values Circle CalculatorEnter the radius to get the diameter, circumference and area of a circle Triangle Area Calculator (Heron's Formula)Enter three side lengths to find the triangle's area, perimeter and angles Pythagorean Theorem CalculatorSolve for any side of a right triangle using a² + b² = c²

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