Tank and vessel volume
Liquid volume at any level for horizontal and vertical vessels — flat, 2:1 ellipsoidal, hemispherical, torispherical and conical heads — with a level-to-volume table.
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The Vessel Volume and Level Excel tool does everything here and more: volume, mass and level for horizontal and vertical vessels with any common head — plus transmitter %, alarm volumes, fill and drain time and a strapping table. Print-ready report, any units, visible formulas, no macros.
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How this calculator works
Horizontal vessels: the liquid in the straight shell is the circular-segment area × length (Perry's Eq. 10-109). Each head holds its full volume × x²(3 − 2x), where x = level/diameter (Eq. 10-110) — exact for 2:1 ellipsoidal and hemispherical heads and close for torispherical heads.
Vertical vessels: bottom head, straight shell and top head are added in turn. Ellipsoidal and hemispherical heads use the exact cap formula; torispherical heads are integrated exactly through the crown and the knuckle; a cone uses the frustum formula. Full head volumes: 2:1 ellipsoidal πD³/24, hemispherical πD³/12, ASME flanged and dished (crown radius D, knuckle 6 % of D) 0.0810 D³ with depth 0.169 D (Perry Table 10-65 gives 0.0809 D³).
The example is a 3 m horizontal vessel with 10 m straight length and 2:1 heads: capacity 77.75 m³ (70.69 m³ shell + 7.07 m³ heads), exactly half at 1.5 m. Checks: Perry Tables 10-64 and 10-66 are reproduced to the printed digits.
Limits: ideal shapes, inside dimensions; nozzles, internals, coils and bottom slope are not counted. Conical heads are for the bottom of a vertical vessel only. References: Perry's Chemical Engineers' Handbook §10 (partial volumes, Tables 10-64 to 10-66); ASME Section VIII head geometry; API MPMS Ch. 2 for strapping.