How deep is a 2:1 elliptical or hemispherical bottom head?

A 2:1 elliptical head is a quarter of the inside diameter deep; a hemispherical head is half. A 96 in tank's 2:1 head is 24 in deep and holds 501 gal.

Why is working volume lower than the tank's full capacity?

It stops at your high-level setpoint, leaving freeboard for foam, vortexing and a late stop. At the defaults that is 4,449 gal, 88.75% of the 5,013 gal to the top of the straight side.

How do I turn a level reading into gallons?

Enter the reading as the high-level setpoint and read the working volume. Above the head each inch adds 31.33 gal on a 96 in tank; inside the head each inch holds less.

Does a cone bottom hold less than a dished bottom of the same depth?

Yes, half as much: a cone holds a third of the cylinder with its diameter and depth, a dished head two thirds. A 24 in cone under a 96 in tank holds 251 gal.

Process Manufacturing calculator

Tank Working Volume Calculator

Find the gallons below the high-level setpoint of a vertical tank with a flat, cone or dished bottom. You need the vessel drawing, the setpoint and your batch volume.

What this calculator does

Gallons below a vertical tank's high-level setpoint, bottom head included, and whether your batch fits.

Formula used

A = π × inside diameter² ÷ 4; gallons = in³ ÷ 231
Head volume = A × head depth × 1/3 for a cone, 2/3 for a dished head, 0 for flat
Working volume = head volume + A × (high level − head depth), level capped at the top of the straight side
Level L inside the head: cone A × L³ ÷ (3 × depth²); dished A × L² × (3 × depth − L) ÷ (3 × depth²)
Batch level = head depth + (batch − head volume) ÷ A; spare = working volume − batch

Inputs explained

Inside Diameter: Shell inside diameter from the vessel drawing or nameplate.
Straight Side Height: Bottom tangent line to the top of the shell, from the drawing.
Bottom Head Type: Dished covers 2:1 elliptical and hemispherical heads.
Bottom Head Depth: Depth below the bottom tangent line; ID ÷ 4 for 2:1 elliptical.
High-Level Setpoint: Liquid height at your high-level switch, from the tank's lowest point.
Batch Volume: Recipe volume you plan to charge, all ingredients included.

How to use the result

Best suited to checking a scaled-up batch fits a vessel, converting a level reading to gallons.
ASME F&D heads hold about 9% less than the dished formula at their depth; use the vendor's head table. Does not deduct coils, baffles or agitators, or count liquid in a top head.

Current U.S. benchmarks

The producer price index for industrial chemicals stands at 336.006 (BLS, Aug 2026), up 13.3% from a year earlier. Quotes priced off last quarter's material cost miss this move.
The U.S. has 14,543 chemical manufacturing establishments employing about 911,245 workers (Census County Business Patterns, 2023).

Common questions

How deep is a 2:1 elliptical or hemispherical bottom head? A 2:1 elliptical head is a quarter of the inside diameter deep; a hemispherical head is half. A 96 in tank's 2:1 head is 24 in deep and holds 501 gal.
Why is working volume lower than the tank's full capacity? It stops at your high-level setpoint, leaving freeboard for foam, vortexing and a late stop. At the defaults that is 4,449 gal, 88.75% of the 5,013 gal to the top of the straight side.
How do I turn a level reading into gallons? Enter the reading as the high-level setpoint and read the working volume. Above the head each inch adds 31.33 gal on a 96 in tank; inside the head each inch holds less.
Does a cone bottom hold less than a dished bottom of the same depth? Yes, half as much: a cone holds a third of the cylinder with its diameter and depth, a dished head two thirds. A 24 in cone under a 96 in tank holds 251 gal.

Last reviewed 2026-10-01.