Geometry GlanceSources

Cone calculator

cm

Centre to the circular edge.

cm

From the apex straight down to the base centre.

Advanced

Changing a measurement unit keeps its number: 3 cm becomes 3 m. Unit for all measurements applies to every input and the result. Result unit converts only the answers.

Right circular cone. Slant height must exceed radius. Volume uses perpendicular height.

Number format

Use a decimal point or comma, without thousands separators. Up to 15 significant digits and 64 characters; no fractions or expressions.

Cone schematic. Right circular cone. Slant height must exceed radius. Volume uses perpendicular height.hrs

Not to scale

Enter your measurements to see the results.

No personal result is available. These are the right circular cone formulas and conditions.

Formulas and conditions

Right circular cone

A right circular cone whose apex is above the base center. Dashed perpendicular height h, base radius r, and slant height s form a right triangle. A square marks the right angle between r and h. The rear base rim is dashed.hrs
Volume
V=πr2h3
Lateral area
LA=πrs
Closed surface area
SA=πr2+πrs
Slant height
s2=r2+h2

r base radius · d diameter = 2r · h perpendicular height · s slant height · V volume · LA lateral area · SA closed surface area

Right circular cone only; s > r > 0, h > 0.

Volume uses h, not s. Closed area includes the base.

Diagrams are schematic, not to scale.

The apex of a right circular cone is directly above the base center. Radius r, perpendicular height h and slant height s form a right triangle.

Choose either height type. A given slant height must be longer than the radius; use h = √(s² − r²) for volume. Lateral area uses s and excludes the base. Closed surface area adds one circular base.

Height from slant height
h=s2−r2

Use the same length unit throughout a formula. Convert mixed measurements first. Length and perimeter use units such as cm; area uses cm²; volume uses cm³. Decimal examples below are rounded to at most six significant figures, with ≈ marking an approximation.

Worked example: Radius 5 cm and slant height 13 cm

  1. h = √(13² − 5²) = √144 = 12 cm.
  2. V = π × 5² × 12 ÷ 3 = 100π cm³ ≈ 314.159 cm³.
  3. LA = π × 5 × 13 = 65π cm² ≈ 204.204 cm².
  4. Closed SA = 65π + 25π = 90π cm² ≈ 282.743 cm².

The 5–12–13 right triangle confirms the height. The cone volume is one third of a cylinder with the same radius and perpendicular height. Using s = 13 in the volume formula would overstate it.

Formula sources

Formulas are checked against these references. The explanation, diagrams and worked calculations here are authored for Geometry Glance.