Tank Geometry Volumes
Volume formulas for vertical cylindrical, horizontal cylindrical, cone-bottom, and rectangular tanks — and which calculator to reach for, plus the partial-fill and calibration caveats.
Definition
Tank geometry volume is the internal capacity of a vessel computed from its shape and dimensions. Four geometries cover most process tanks: the vertical cylinder (V = πD²/4·H), the horizontal cylinder (full V = πD²/4·L, with a circular-segment formula for partial fill), the cone-bottom vessel (a cylinder plus a conical bottom), and the rectangular tank or basin (V = L×W×H). The right formula — and the right calculator — depends on the shape and on whether you need full or partial volume.
Why it matters
Volume is the first number in almost every tank calculation: residence time, turnover, batch size, and inventory all start from it. The geometry matters because the same nominal capacity behaves very differently — a horizontal cylinder does not fill linearly with depth, a cone bottom changes the drain and the low-level volume, and a rectangular basin fills linearly but wastes corners on agitation. Using the wrong geometry formula is one of the easiest ways to put a large, silent error into every downstream result.
Formula
Units involved
- •V — volume in m³, litres, ft³, or gallons
- •D — diameter in m, mm, ft, or inches
- •H, H_cyl, H_cone — heights in m, mm, ft, or inches
- •L — length in m, mm, ft, or inches (cylinder length or rectangular length)
- •h — liquid depth for partial fill, in m, mm, ft, or inches
Concept diagram
Worked example
Compare a half-full horizontal cylinder and the same diameter as a vertical cylinder. The cylinder is 2 m inside diameter and 5 m long; liquid depth in the horizontal case is 1 m (half full).
- 01Horizontal full volume: V = π·D²/4·L = π × 2²/4 × 5 = 15.708 m³
- 02Half full → exactly half: V_liquid = 7.854 m³
- 03Check with the segment formula: r = 1, h = 1 → A = r²·arccos(0) = π/2 = 1.5708 m²; V = 1.5708 × 5 = 7.854 m³
- 04Same cylinder stood vertical, filled to 1 m: V = π·D²/4·H = π × 1 × 1 = 3.14 m³
Half a horizontal cylinder holds 7.854 m³; the same cylinder vertical at a 1 m level holds only 3.14 m³ — geometry and orientation change the volume at a given level.
Common mistakes
- •Using a depth proportion for a horizontal cylinder — it only fills linearly at the exact half-full point; everywhere else you need the segment formula.
- •Forgetting the cone on a cone-bottom tank — the conical bottom adds one-third of a same-size cylinder and changes the low-level volume.
- •Mixing diameter and radius — the cylinder formula uses (D/2)² or r²; using D directly overstates volume four-fold.
- •Inconsistent units — diameter in mm with height in m gives a nonsense volume. Convert everything to one unit first.
- •Treating geometric volume as usable volume — heads, internals, freeboard, and dead zones all reduce what is actually available.
When to use the calculator
Use the tank-volume or tank-diameter-height calculator for vertical cylinders, the horizontal-tank-partial-volume calculator for partly filled horizontal cylinders, the cone-bottom-volume calculator for cylinder-plus-cone vessels, and the rectangular-tank-volume calculator for basins, sumps, and launders.