Cone Bottom Tank Volume Calculator — Frustum, Hopper & Sloped Bottom

Cone Tank Volume Calculation: The Frustum Formula in Plain Numbers

A cone bottom tank is never one shape — it is a vertical cylinder sitting on a truncated cone. That is why a cone tank volume calculation needs two formulas and four measurements: the cylinder inside diameter D, the cylinder height H, the vertical cone height h, and the outlet diameter at the drain (whose radius we call r). The top radius of the cone is simply R = D ÷ 2. The truncated cone — a frustum — is the piece people get wrong, because the pointed-cone formula they remember from school does not fit a tank that stops at a 2-in drain.

The frustum formula in plain numbers: multiply π × h ÷ 3 by the sum of R², R×r and r². In symbols, V = πh/3 (R² + Rr + r²). Everything is in inches and cubic inches; divide by 231 to get US gallons, because 1 gallon = 231 cubic inches exactly. The cylinder above it is the familiar πR²H.

The three-term sum looks strange until you see what it averages. A frustum is a cone with its tip sliced off, so its cross-section sweeps from the big area πR² at the top to the small area πr² at the outlet. The middle term R×r is the geometric mean of the two end areas, and averaging the three gives the exact mean cross-section for a linear taper — no calculus required, and no approximation error either. That is also why the outlet diameter belongs in the inputs: forgetting the 2-in outlet and treating r as zero silently converts your frustum into a pointed cone and shifts the cone section by up to 8%.

🔻Cone-bottom process tanks — cylinder plus frustum

Cone-bottom process tanks — cylinder plus frustumPhoto: Unsplash

Calculate Volume in a Sloped Bottom Tank: The Prism Formula

Rectangular tanks and basins with one sloping side — hopper-style floors under a fixed roof, tanks set on graded pads, fermentation trays — use a much friendlier formula than the frustum. When the floor slopes linearly from depth h1 at one end to depth h2 at the other, the cross-section is a trapezoid and the tank is a prism: V = L × W × (h1 + h2) ÷ 2. In words: footprint times average depth.

Two cautions keep the prism formula honest. First, it assumes the slope runs across the entire length; if only half the floor slopes, split the tank into a flat box plus a wedge and add the two volumes — the wedge alone is L × W × (h2 − h1) ÷ 2. Second, average depth only works for a single straight slope; a V-shaped double slope has two wedges and no flat box. For tanks that mix cylindrical and rectangular sections, the water tank capacity calculator covers the common storage geometries side by side.

Here is the split method with numbers. Take the same 48 × 24 in footprint, but suppose only the last 24 in of length slopes, rising from 12 in to 18 in. The flat section is 24 × 24 × 12 = 6,912 in³ = 29.9 gal. The sloped section is a wedge: 24 × 24 × (18 − 12) ÷ 2 = 1,728 in³ = 7.5 gal. Total 8,640 in³ = 37.4 gal — barely half of the 74.8 gal full-slope answer, which shows how quickly the wrong assumption about where the slope lives distorts a sloped-bottom estimate. When the slope runs across the width instead of the length, the formula is identical with L and W swapped, because the prism formula only cares about footprint area and the two end depths.

Frustum Gallon Tank Calculator: Gallon Conversions and Standard Sizes

Any frustum gallon tank calculator lives or dies by three conversion constants: 1 US gallon = 231 cubic inches exactly, 1 gallon = 3.78541 liters, and 1 cubic inch = 0.004329 gallons. Convert after you compute volume in cubic inches — not before — because rounding early on a 100-gal tank drifts the answer by most of a gallon. The cone section of a standard poly tank is a bigger share of capacity than most buyers expect: roughly 11–15% of nameplate, which is exactly the volume you are trading away in exchange for drainability.

Typical rotationally molded cone-bottom poly tanks with 45° cones and 2-in outlets, sized with the frustum formula (a 55-gal tank computes to 55.0 gal with these dimensions).

Notice the pattern in the table: as diameter grows, the 45° cone deepens proportionally, so the cone share of capacity stays near 15%. Switch the same shells to 60° cones and the cone share drops to 9–11% while total height shrinks by 3–5 in per size — the trade-off the angle FAQ below quantifies.

One conversion trap deserves its own paragraph: imperial gallons. A UK imperial gallon is 277.42 cubic inches against the US 231 — about 20% larger — so a 55-gal cone-bottom tank quoted by a British supplier is not the same vessel as an American one. The 75-gal reference tank on this page holds 284 liters; expressed in imperial gallons that is only 62.5. Chemical dosing rates printed in liters per hectare or per 1,000 liters sidestep the whole mess, which is why the calculator shows liters next to every gallon figure — 15 gal = 56.8 L, 55 gal = 208.2 L, 100 gal = 378.5 L — and why you should confirm which gallon a spec sheet means before ordering liners, heaters or treatment.

Conical Fermenter and Brewing Case Studies

Brewing is where cone-bottom geometry earns its keep, and where the frustum math gets checked against real hardware every batch. Case one: the classic 7-gallon homebrew conical. Shells in this class measure about 13.7 in inside diameter with a 13.5 in straight wall, plus a 60° cone dropping to a 2-in dump valve. Run the numbers: cylinder π × 6.85² × 13.5 = 1,990 in³; cone height (6.85 − 1) ÷ 1.7321 = 3.38 in, so cone volume = π × 3.38 ÷ 3 × (46.9 + 6.85 + 1) = 194 in³. Brimful total: 2,184 in³ = 9.45 gal. A 7-gal batch fills it to 74%, leaving 2.45 gal of krausen headspace — which is exactly why a “7-gallon” fermenter is never 7 gallons brimful.

The cone itself holds 0.84 gal. That is the working zone: during fermentation, trub and dead yeast compact against the 60° wall and slide to the dump valve, so the first gallon you draw from the bottom is solids, not beer. Pull it, and the beer above the cone stays on clean yeast. A flat-bottom fermenter of the same capacity traps that sediment across the whole floor, where racking picks it back up.

🍺Conical fermenters — the cone is the yeast harvest zone

Conical fermenters — the cone is the yeast harvest zonePhoto: Unsplash

Case two scales the same logic to commercial units, where volumes are quoted in barrels: 1 bbl = 31 US gal = 117 liters. A 1-bbl unitank built around a 20-in inside diameter with a 20.9 in straight wall and a 60° cone to a 1.5-in tri-clamp outlet (r = 0.75 in) computes as follows: cone height = (10 − 0.75) ÷ 1.7321 = 5.34 in; cone volume = π × 5.34 ÷ 3 × (100 + 7.5 + 0.56) = 604 in³ = 2.62 gal; cylinder 6,566 in³ = 28.4 gal. Total 31.05 gal — a 1-bbl tank within rounding of its nameplate, with a wetted height near 26 in. A 7-bbl system follows the same recipe at roughly 42 in diameter, and its cone section holds about 7.5 gal of yeast worth harvesting every generation.

Hopper and Settling Zone: Why the Cone Is Working Volume

In a water or process tank, the cone volume is not dead space — it is working volume for solids. Everything denser than the liquid migrates down the walls and concentrates in the frustum, so the cone acts as a settling zone and drawdown hopper at the same time. The design question is whether the solids leave on their own. At a 60° wall angle, most slurries, yeast and grit slide cleanly to the outlet — this is the self-cleaning threshold behind the brewing, wastewater and silo standards. At 45°, free-flowing material still moves, but sticky or fibrous sludge can bridge and hold, which is why 45° dominates cheap poly tanks (fewer inches of height to mold) while 60° dominates stainless process vessels.

Treat the cone as working volume when you plan capacity, too. A 55-gal cone-bottom tank with 2–3 gal of accumulated sediment effectively stores 52 gal of water above the solids blanket — and each drawdown flush through the 2-in outlet resets it. Sizing the outlet matters here as well: a 2-in drain passes about 4× the solids cross-section of a 1-in stub, which is why hopper bottoms on slurry service step up to 3–4 in even when the liquid flow rate would not need it.

The cone’s gallon figure also sets your drawdown schedule. If the same 55-gal tank collects roughly half a gallon of silt per week, its 7.8-gal cone reaches a full blanket in about 15 weeks — but you should flush long before that, because a blanket deeper than a few inches starts re- entraining solids every time inflow stirs the tank. A quarterly drawdown keeps the settling zone working; an annual one lets the cone become a plugged mass of compacted sediment that no outlet passes. Cheap insurance: mark the calculated dip depth that corresponds to 2 gal of cone contents on the gauge, and flush whenever the reading climbs past it.

Liquid Level to Volume at Any Depth: The Partial Frustum Method

A dip stick reading in a cone-bottom tank translates to volume in two regimes, and the switch happens at the cone height. Here is the method step by step, using the 24-in reference tank (2-in outlet, 6.35-in cone, 36-in cylinder, 75.0 gal total).

For a usable dip chart, run the method at 1-in increments and tabulate the pairs. The cone portion of the chart is curved and dense with detail — 10% of depth is only 0.6% of volume down there — while the cylinder portion is perfectly linear. If you then need to know how long the tank takes to empty through the drain, the tank drain time calculator pairs the level-volume curve with the outlet flow — and the cone segment dominates drain time precisely because the volume per inch collapses toward the tip.

Conical Bottom Tank Volume In Excel

You do not need this page open to run a conical bottom tank volume calculation — a five-cell spreadsheet reproduces it. Lay the inputs down column B with labels in column A, then enter the formulas as chips below. Everything uses ordinary Excel functions: PI(), ^ for powers and IF for the level test.