Truncated Cone Volume Calculator
Compute volume and lateral area of a truncated cone: V = (π·h/3)·(R²+r²+R·r). For containers and construction.
Volume of a frustum of a cone
A frustum (truncated cone) is a cone with its top cut off by a plane parallel to the base. The volume is V = (πh/3)·(R² + r² + R·r), where R is the larger radius, r the smaller and h the height between the two circular faces. It generalises to any frustum as V = (h/3)·(A₁ + A₂ + √(A₁·A₂)). Example: R = 10 cm, r = 5 cm, h = 12 cm → V = (12π/3)·(100 + 25 + 50) = 700π ≈ 2,199 cm³. When r = 0 the formula collapses to the regular cone (πR²h/3).
Applications
Buckets, conical cups, lampshades, paint cans, margarine tubs and many supermarket packages have a frustum shape. Used in engineering for cooling towers of power plants, hoppers and silos, and in marketing for calculating product volume in non-cylindrical packaging.
FAQ
What if r = 0? It becomes a regular cone with volume V = πR²h/3.
And if R = r? The result is a cylinder, V = πR²h.
Does the formula work in litres? Yes — use cm for the dimensions and divide cm³ by 1,000 to get litres.
Related Tools
Cone Frustum (Volume + Lateral)
Compute cone frustum volume V = πh(R² + r² + R·r)/3 and lateral area A_lat = π(R+r)·g (g = slant).
Truncated Cone Area Calculator
Compute the total surface area of a truncated cone (R, r, h): A = πR² + πr² + π(R+r)·g, where g is the slant.
Volume Calculator
Calculate the volume of geometric solids: cube, sphere, cylinder, cone, pyramid and rectangular prism. Instant result with the formula used.
Pyramid Volume Calculator
Compute volume of a regular pyramid (square base): V = (base area × height) / 3. Also shows lateral and total area.
Hexagonal Prism Volume Calculator
Compute volume and area of a regular hexagonal prism: V = (3√3/2)·a²·h. For 3D geometry, packaging, crystallography.
Amihud Illiquidity (ILLIQ)
Computes the Amihud (2002) illiquidity measure: the average of the ratio of the absolute daily return to the dollar trading volume, scaled by one million as is convention. The intuition is that, in illiquid assets, a small volume already moves the price a lot — so the higher the ratio, the more illiquid the asset. It's one of the most used liquidity measures in research, since it needs only daily price and volume data. Enter the lists of returns in percent and dollar volumes.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.