Cone Calculator

Calculate volume, base area and surface area of a right circular cone

Your result will appear here.

About the Cone Calculator

A cone combines a circular base with a point or apex, so its volume and surface area depend on radius and height in different ways. The calculator can solve common cone properties from the dimensions you know.

Slant height is not the same as vertical height. Volume uses the perpendicular height, while lateral surface area uses slant height.

How to Use the Cone Calculator

  1. Enter the cone radius or diameter.
  2. Enter the perpendicular vertical height.
  3. Calculate volume, slant height and surface area as needed.
  4. Use compatible units and distinguish lateral area from total surface area.

How the Calculation Works

A right circular cone has volume V = (1/3)πr²h, where r is base radius and h is the perpendicular vertical height from the base plane to the apex. The one-third factor distinguishes the cone from a cylinder with the same base and height.

Its slant height is l = √(r²+h²). Lateral surface area is πrl, while total surface area adds the circular base: πrl + πr². The calculator keeps perpendicular height and slant height separate because they are used in different formulas.

Worked example

Cone Calculator Worked Example

Cone with radius 3 and height 4

Slant height = √(3²+4²)=5. Volume = (1/3)π×9×4 = 12π ≈ 37.70 cubic units. Total surface area = π×3×5 + π×9 = 24π ≈ 75.40 square units.

Result guide

Understanding Your Cone Calculator Result

Volume uses cubic units, while surface area uses square units. Do not use slant height in place of perpendicular height in the volume formula.

Before you rely on the answer

Assumptions and Limitations

  • The solid is a right circular cone.
  • Radius and height are measured consistently.
  • Surface calculations include or exclude the base according to the selected result.

Practical tip

Using This Result in Practice

If only diameter is measured, divide by two before checking the formulas manually. Confusing diameter with radius makes area four times too large.

Related calculations

Useful Calculations to Continue With

If the object has parallel circular ends rather than tapering to a point, use the Cylinder Calculator.

If you want to compare total outside area across different solid shapes, use the Surface Area Calculator.

Common questions

Cone Calculator FAQ

Why does cone volume include one third?

A cone with the same base and height as a cylinder has one third of the cylinder’s volume.

What is slant height?

It is the distance along the cone’s side from the edge of the base to the apex.

Does cone surface area include the base?

Total surface area includes the base; lateral surface area includes only the curved side.