Ellipsoid Volume (Oblong / Oval Solid)
The volume of a general ellipsoid - an oval or elliptical tank, a stretched dome, or an ellipsoidal float.
Example
You enter
- Length L (ft) 10
- Width W (ft) 6
- Height H (ft) 4
You get
- Ellipsoid volume 125.664
- Volume (gal) 940
- Half-ellipsoid (dome / head) 62.832 ft^3
Details, formula, and sources
V = (4/3) pi a b c = pi L W H/6 from the three full axes L (long), W (wide), H (tall). A 10 x 6 x 4 oval tank holds 125.7 ft^3 (940 gal); the half-ellipsoid (62.8 ft^3) is a matching 2:1 dished head or dome. Make the three axes equal (8 x 8 x 8) and it is a sphere, 268 ft^3 = (4/3) pi 4^3. Volume in ft^3 and gallons. A partial fill to a depth and the surface area (no elementary closed form) are separate. A takeoff aid; verify against the drawing.
a=L/2, b=W/2, c=H/2; V = (4/3) pi a b c = pi L W H/6; half-ellipsoid = V/2. Equal axes -> sphere (4/3) pi r^3.
The ellipsoid volume V = (4/3) pi a b c - standard solid geometry as in Machinery's Handbook (Industrial Press), by name; public domain.
Pure solid geometry, public; the three axis lengths are user-supplied measurements.
Estimate. AHJ and licensed professional govern.
Field names used by the API: length_ft, width_ft, height_ft, volume_ft3, volume_gal, half_volume_ft3
- Ellipsoid volume V = (4/3) pi a b c = pi L W H/6, a/b/c the semi-axessolid geometry
- Limits equal axes give a sphere; half-ellipsoid is a dished head/domesolid geometry
- Scope full/half volume; partial fill, surface area, and truncated shapes are separatescope of this tile