Right Circular Cone Calculator: Find A, V, A_L, A_B

Your details

Choose which two measurements you know. The calculator derives everything else from those two values.
Radius of the circular base.
cm
Perpendicular distance from the base centre to the apex.
cm
Distance from the base edge to the apex along the surface.
cm
Known interior volume of the cone.
cm³
Known lateral (side) surface area of the cone.
cm²
Known total surface area (lateral + base) of the cone.
cm²
Volume (V)
314.1593cm³

Space enclosed by the cone

Total Surface Area (A)282.7433cm²
Lateral Area (A_L)204.2035cm²
Base Area (A_B)78.5398cm²
Slant Height (l)13cm
Radius (r)5cm
Height (h)12cm
Half-angle (θ)22.62deg
Aperture angle (2θ)45.24deg
Base angle (β)67.38deg

Volume: 314.1593 cm³ - Total surface area: 282.7433 cm².

  • Volume is 314.1593 cm³: the cone holds 0.3142 litres (metric) worth of space.
  • Total surface area is 282.7433 cm², of which 72.2% is the lateral curved side.
  • Slant height is 13.0000 cm (2.60 times the base radius).
  • Height-to-radius ratio is 2.40:1, giving a tall and narrow cone.

Next stepTo minimise surface area for a given volume, choose r equal to h times the cube root of 2 (approximately 1.26 x h). That aspect ratio gives the most material-efficient right circular cone.

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