Volume Tronco de Cone
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
V = πh(R²+r²+Rr)/3
About this calculator
This calculator determines the volume of a frustum of a cone (truncated cone), which is the portion of a cone remaining after its tip is cut off by a plane parallel to the base. The frustum has two parallel circular bases: a larger base (radius R) and a smaller base (radius r), and a height h (distance between bases). The formula used is V = (πh/3) * (R² + r² + R·r), where π is approximately 3.14159. This expression derives from the difference between the volume of the original cone and the volume of the removed smaller cone.
This calculation is useful in various practical situations, such as civil engineering to determine the volume of concrete in frustum-shaped pillars, in mechanical manufacturing of parts (shafts, gears), in the packaging industry (cups, buckets), and even in agriculture to estimate the volume of silos or reservoirs with this geometry. The calculator accepts positive values for radii and height, and the result is given in cubic units consistent with the input units.
When using the tool, ensure all measurements are in the same unit (e.g., centimeters or meters). If radii or height are given in different units, convert them first. Remember that a frustum is a common three-dimensional shape, and the calculated volume represents the space occupied by the solid. For applications requiring precision, such as engineering projects, it is recommended to use values with at least three decimal places.
Frequently asked questions
What is the difference between a frustum and a truncated cone?
They are the same solid. 'Frustum of a cone' is the standard term in English for the shape formed by cutting a cone with a plane parallel to its base.
Can I use this calculator for a full cone?
Yes, just set the smaller radius r to zero. The formula then reduces to V = (πR²h)/3, which is the volume of a complete cone.
What if my measurements are in different units?
Convert all measurements to the same unit before entering. For example, if the larger radius is in meters and the height in centimeters, convert the height to meters (divide by 100) or the radii to centimeters.
Does the calculator work with decimal values?
Yes, it accepts decimal numbers. Use a dot as the decimal separator (e.g., 2.5).
Can I calculate the volume of an inverted frustum?
Yes, the formula is independent of orientation. Just correctly identify the radii of the bases and the height between them.