Engineering calculator reviewed for preliminary design use · Last updated: March 2026
Calculate internal volume of pressure vessels and storage tanks. Supports combinations of cylindrical and spherical shells with various head types: semi-elliptical, torispherical, hemispherical, and flat. Apply to hold-up and liquid inventory calculations.
What this calculator is used for
This calculator determines the internal volume of tanks and pressure vessels
by accounting for both cylindrical shells and head geometry.
Typical engineering use cases
Storage capacity determination
Process hold-up calculations
Governing equation and methodology
Total volume is calculated as the sum of shell and head volumes using standard
geometric formulas.
Engineering assumptions and limitations
Geometric full volume only
Practical design notes
Operating volume is usually lower than calculated full volume.
Worked Example
Given:
Vertical cylindrical vessel, inside diameter D = 2.0 m
Tangent-to-tangent shell length L = 4.0 m
Two 2:1 semi-elliptical heads
Method: Shell volume = πD²/4·L = π·1²·4 ≈ 12.57 m³. Each 2:1 ellipsoidal head = πD³/24; two heads = πD³/12 = π·2³/12 ≈ 2.09 m³. Total = shell + heads.
Result: Total geometric volume ≈ 14.7 m³.
Interpretation: This is the geometric (full) volume, not the working volume. Subtract space for vapour disengagement, level instrument margins, and minimum liquid heel. For tall, slim vessels the heads matter less; for short, fat vessels they are a large fraction of the total.
Common Mistakes & Misuse
Treating geometric (full) volume as usable working volume — vapour space and level margins reduce it.
Omitting the head volumes, which are a large fraction of total volume for short, large-diameter vessels.
Confusing tangent-to-tangent length with overall length (which includes the heads).
Applying the wrong head factor — 2:1 elliptical, hemispherical, and torispherical heads have different volumes.
Frequently Asked Questions
What head types are supported?
Semi-ellipsoidal (2:1), torispherical (ASME F&D), hemispherical, and flat heads are supported. Each head type has a different volume formula and different structural efficiency.
Is the calculated volume the liquid hold-up volume?
The result is the total internal geometric volume. Actual liquid hold-up depends on normal liquid level (NLL), high liquid level (HLL), and internals. Apply appropriate design margin.
For preliminary estimation and educational use only. Results may depend strongly on assumptions, input data, fluid or material properties, and the range of validity of the underlying equation. Verify critical calculations independently and follow the applicable code, specification, and formal engineering review process before using any result for design, procurement, fabrication, operation, or safety decisions.