Sphere Tank Volume calculator

Spherical vessel volume and partial fill (spherical cap). 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.

Spheres hold the most volume per unit of surface area, which is why large gas storage uses them. Partial fill is the classic spherical-cap formula V = πh²(3r − h)/3 — enter the diameter and drag the level to see it.

How this is calculated

Total volume

V = (4/3)πr³

Filled volume at liquid depth h

V(h) = πh²(3r−h)/3

The spherical-cap formula — strongly nonlinear, exactly half the sphere at half depth. See the full derivation, a worked example and a fill-ratio table on the spherical tank formula page.

FAQ

TVC-108/FAQ

At half depth, is a sphere half full?

Yes — exactly 50%, by symmetry. At 25% depth it holds only ~15.6%.