Cone Calculator

Enter the radius of the base and the perpendicular height of the cone.

Cone

Volume37.6991118431
Total surface area
75.3982236862
Lateral (curved) area
47.1238898038
Slant height
5
Base area
28.2743338823

Formulas

V = (1/3)πr²h

slant height l = √(r² + h²)

lateral area = πrl

total area = πr(r + l)

Worked example

Radius 3, height 4

  1. Slant: √(9 + 16) = 5
  2. Volume: (1/3) × π × 9 × 4 = 12π ≈ 37.70
  3. Total area: π × 3 × (3 + 5) = 24π ≈ 75.40

Volume ≈ 37.7, surface ≈ 75.4 square units.

Piles of material

Loose gravel, sand or grain settles into a roughly conical pile. Measuring the base circumference and height lets you estimate the volume with the same formula.