Calculate the volume of a truncated cone (frustum) with multiple input methods. Convert between cubic inches, cubic feet, liters, and gallons.
The Truncated Cone Volume Calculator focuses on computing the capacity of a frustum with flexible input methods and instant unit conversions. A truncated cone (frustum) is created when a cone is cut by a plane parallel to its base, leaving two circular faces of different sizes. This calculator lets you enter dimensions as radii and height, diameters and height, or slant height with radii — whichever measurements you have on hand. The volume formula V = (πh/3)(R² + Rr + r²) is applied after deriving the perpendicular height from slant height when necessary. Results are displayed simultaneously in cubic inches, cubic feet, liters, and US gallons, making this tool ideal for practical applications like determining the capacity of tapered tanks, calculating concrete volume for column footings, or sizing bucket-shaped containers. The unit conversion table provides reference factors between all supported units. Use the preset buttons to explore real-world frustum sizes — from small drinking cups to large industrial hoppers. Visual bars show the relative proportions of each dimension, helping you verify inputs at a glance before reading the volume output.
Truncated cones show up in buckets, cups, flower pots, hoppers, silos, and tapered concrete forms, so volume is often the quantity you actually need rather than just the shape dimensions. This calculator saves time when you must switch between radius, diameter, and slant-height measurements, and it immediately converts the result into practical units like liters and gallons for estimating fill capacity, material volume, or shipping space.
V = (πh/3)(R² + Rr + r²). If slant height l is given: h = √(l² − (R − r)²). Unit conversions: 1 cu ft = 1728 cu in, 1 cu ft ≈ 28.3168 L, 1 gallon ≈ 231 cu in.
Result: 795.8701 cu in, 0.4606 cu ft, 13.042 L, 3.445 gal
Using the radii + height mode with R = 6 in, r = 4 in, and h = 10 in gives V = (πh/3)(R² + Rr + r²) = (10π/3)(36 + 24 + 16) = (10π/3)(76) ≈ 795.8701 cubic inches. The calculator then converts that to about 0.4606 cubic feet, 13.042 liters, and 3.445 US gallons.
For a frustum, the most important distinction is whether you know the two radii, the two diameters, or a slant height instead of the true vertical height. The volume formula always uses the perpendicular height, so if your measurement comes from the side of the object you must convert that slant height first. That is why this calculator offers separate input modes rather than forcing every problem into a single format.
Many real containers are close to truncated cones rather than perfect cylinders. Buckets, planters, cups, and feed hoppers all taper from one circular opening to another. In those cases, a small change in the top or bottom radius can noticeably change the final capacity because the formula depends on three radius terms: $R^2$, $Rr$, and $r^2$. Seeing the result in cubic inches, cubic feet, liters, and gallons makes it easier to move from classroom geometry to real fill-volume estimates.
The most common mistakes are mixing up radius and diameter, entering the smaller radius as the larger one, and using slant height as though it were vertical height. A quick reasonableness check helps: if the top and bottom radii are close, the frustum should behave a lot like a cylinder, while a very small top radius should push the result closer to cone volume. Use the dimension bars and multi-unit outputs to confirm that the geometry and scale both make sense before relying on the answer.
V = (πh/3)(R² + Rr + r²), where R and r are the two radii and h is the perpendicular height. Use this as a practical reminder before finalizing the result.
Divide by 231. One US gallon equals 231 cubic inches.
Yes — select the "Diameters + Height" input method and the calculator will halve them internally. Keep this note short and outcome-focused for reuse.
Choose the "Slant Height + Radii" mode. The calculator derives the perpendicular height using h = √(l² − (R − r)²).
Conversions use standard factors (1 cu ft = 1728 cu in, 1 L = 61.0237 cu in) and are accurate to several decimal places.
This calculator is volume-focused with multi-unit output and flexible input methods. The full truncated-cone calculator also computes lateral and total surface areas.