Truncated Cone Volume Calculator
Calculate truncated cone volume based on larger radius, smaller radius, and perpendicular height. Truncated Cone Volume Calculator helps students, engineers, architects, and manufacturers determine frustum capacity and material requirements.
Highlights
- Calculate truncated cone volume using larger radius, smaller radius, and height.
- Supports multiple units, including mm, cm, m, km, inches, feet, and yards.
- Provides accurate volume results in cubic units, liters, milliliters, and gallons.
- Useful for students, engineers, architects, and manufacturing professionals.
- Ideal for estimating frustum capacity and material requirements.
Table of Contents
How Truncated Cone Volume Calculator Works?
A truncated cone, also called a frustum, is formed when the top portion of a cone is removed by a cut parallel to its circular base. This calculator determines the enclosed volume from the larger radius R, smaller radius r, and perpendicular height h. Both radii describe the circular bases, while the height is the straight-line distance between those parallel bases.
The expression inside the parentheses combines the areas represented by the two circular radii and their intermediate product. The calculator applies this formula using the entered larger radius, smaller radius, and height, then reports the volume in the selected cubic or liquid-volume output unit.
For example, using R = 5, r = 3, and h = 10:
| Symbol | Meaning | Required condition |
|---|---|---|
| R | Larger radius | Positive value |
| r | Smaller radius | Positive value, no greater than R |
| h | Perpendicular height | Positive distance between the bases |
| V | Truncated cone volume | Reported in a supported volume unit |
The calculator accepts radius and height inputs in mm, cm, m, km, in, ft, or yd. The available volume outputs include mm³, cm³, m³, km³, in³, ft³, yd³, mL, L, US gal, and Imp gal.
Practical Use Cases
Students can use the calculator to check geometry exercises involving frustums, verify substitutions into the truncated-cone volume formula, and compare results with manually calculated answers.
Engineers can estimate the internal capacity of tapered vessels, hoppers, tanks, and other components with two circular, parallel ends before completing detailed design work.
Architects can calculate the volume of tapered architectural features such as planters, roof elements, columns, and decorative structures when the larger radius, smaller radius, and perpendicular height are known.
Manufacturers can estimate material volume for molded, machined, or cast frustum-shaped parts, helping with preliminary material planning and production estimates.
Construction and landscaping professionals can estimate the capacity of tapered containers, aggregate forms, and other circular structures to support quantity planning.
Accuracy and Limitations
The calculator uses the exact truncated-cone formula V = πh(R² + Rr + r²)/3 and accepts positive floating-point values from 0.000001 through 1,000,000 for each input, with a stated step of 0.01. It assumes both bases are circular and parallel, the supplied height is perpendicular to the bases, and the larger radius is not smaller than the smaller radius. It does not model slanted or irregular shapes, wall thickness, openings, material compression, or manufacturing tolerances; the result represents the ideal enclosed geometric volume.
Quick Examples
Example #1: Small Metal Frustum
Estimate the volume of a small truncated cone component using millimeter measurements.
Example #2: Architectural Planter
Calculate the capacity of a tapered planter using centimeter dimensions.
Example #3: Industrial Storage Hopper
Determine the volume of a large truncated cone hopper using meter measurements.
