Truncated Cone Volume
Calculate truncated cone (frustum) volume using V = (πh/3)(R² + Rr + r²). Free online 3D geometry calculator for buckets, cups, and tapered containers.
About This Calculator
A truncated cone, also known as a conical frustum, is a three-dimensional geometric shape formed by cutting off the top portion of a right circular cone with a plane parallel to its base. This shape appears frequently in everyday objects such as drinking cups, buckets, planters, funnels, and decorative columns. Our truncated cone volume calculator helps students, engineers, contractors, and DIY enthusiasts compute the volume of such shapes quickly and accurately.
The calculator uses the standard frustum volume formula: V = (\u03c0h/3)(R\u00b2 + Rr + r\u00b2), where h is the vertical height, R is the bottom (larger) radius, and r is the top (smaller) radius. This formula is derived by subtracting the volume of the removed top cone from the volume of the original full cone. The result is given in cubic units matching your input linear units.
All three input dimensions must use the same unit of measurement. Whether you work in centimeters, inches, feet, or meters, the calculator delivers the volume in corresponding cubic units. The tool also supports shareable URL parameters, allowing you to bookmark or share specific calculation results with colleagues, students, or clients.
Truncated cone volume calculations are essential in manufacturing for determining material quantities in cups, buckets, and funnels. In construction and landscaping, the formula helps estimate fill volumes for tapered planters, hoppers, and decorative columns. The formula is derived from the full cone volume by subtracting the portion removed by the parallel cut, making it one of the fundamental mensuration formulas in 3D geometry.
Frequently Asked Questions
What is the formula for truncated cone volume?
The volume of a truncated cone is calculated using the formula V = (\u03c0h/3)(R\u00b2 + Rr + r\u00b2) where h is the vertical height, R is the bottom radius, and r is the top radius. This formula derives from subtracting the volume of the smaller cone (removed top) from the larger full cone.
What units does the truncated cone volume calculator use?
The calculator uses consistent input units. If you enter radii and height in centimeters, the volume will be in cubic centimeters. For inches, you get cubic inches. The result is a cubic unit based on your input linear units, suitable for any measurement system including US customary and metric.
What is the difference between a truncated cone and a frustum?
A truncated cone and a conical frustum refer to the same geometric shape: a cone with its top portion cut off by a plane parallel to its base. The result is a 3D shape with two circular faces of different radii (top and bottom) connected by a sloping lateral surface. The terms are used interchangeably in geometry.
How is truncated cone volume used in real-world applications?
Truncated cone volume calculations are used extensively in manufacturing for designing buckets, cups, planters, funnels, tapered containers, and architectural columns. The food and beverage industry uses it for cup and container sizing. In construction, it is used for calculating concrete volumes in tapered structures and hoppers.
Can I calculate truncated cone volume with different units for each dimension?
For accurate results, ensure all three dimensions (top radius, bottom radius, and height) use the same unit of measurement. Mixing units (e.g., inches for radius and feet for height) will produce incorrect volume results. Convert all measurements to the same unit before entering them into the calculator.
Is this truncated cone volume calculator free to use?
Yes, this calculator is completely free to use with no registration, subscription, or hidden charges required. You can make unlimited calculations and share results via URL for educational, professional, and personal projects.
How do I calculate the volume of a truncated cone by hand?
To manually compute the volume, use the formula V = (pih/3)(R^2 + Rr + r^2). First square the bottom radius (R), then multiply R by r, then square the top radius (r). Add these three values, multiply by the height (h), multiply by pi (3.14159), and divide by 3. The result is in cubic units matching your input units.
What is the difference between this calculator and the general truncated cone calculator?
This Truncated Cone Volume Calculator focuses exclusively on computing the volume of a conical frustum. The general Truncated Cone Calculator on Calculy provides additional computed properties including total surface area, lateral surface area, top and base areas, and slant height from the same three inputs. Choose this tool if you only need the volume result with a simple interface.