Frustum / Tapered Tank Volume calculator

Volume of tapered vessels, buckets and hoppers. Exact geometry, instant results, nothing leaves your browser.

FIG. 1 — TANK CROSS-SECTION · LIVE

SCALE AUTO · REV A

01 · Tank shape

02 · Dimensions

Dim. unit

Liquid

03 · Fill depth (dipstick)50%

Wetted depth—

Surface width—

Ullage—

Liquid volume at fill depth

—US gal

Total capacity—

Filled · liters—

Filled · ft³—

Percent full—

Liquid weight—

Remaining to full—

Exact segment geometry — see methodology. Dished-head propane math is documented there too.

Buckets, vats and hoppers taper between two diameters. This calculator solves the frustum volume at any fill level by interpolating the radius linearly with height — the same math whether the wide end is up (bucket) or down (hopper, by swapping the diameters).

How this is calculated

Total volume

V = πH(R²+Rr+r²)/3

Filled volume at liquid depth h

V(h) = πh(ρ²+ρr+r²)/3, ρ = r+(R−r)·h/H

The standard frustum identity, evaluated at the wetted radius interpolated between the bottom and top radii. See the full derivation, a worked example and a fill-ratio table on the frustum (tapered) tank formula page.

FAQ

TVC-109/FAQ

How many gallons is a standard 5-gallon bucket really?

Most are ~11.9 in bottom diameter, ~10.3 in top... actually rated capacity varies by maker — measure both diameters and the height, enter them above, and read the brim-full number directly.