The vessel volume calculator gives the total and partial (liquid-level) volume of horizontal and vertical pressure vessels with 2:1 elliptical, hemispherical, torispherical (ASME F&D, standard F&D, 80:10), flat, conical or toriconical heads. It produces a level-to-volume calibration (strapping) table, fill percentage, wetted area for API 521 fire cases, and working and dead volumes.
How vessel volume is calculated
A vessel is treated as a cylindrical shell plus two heads. The calculator works out each part separately at the chosen liquid level and adds them.
Full volume
- Cylindrical shell: V = (π/4) D² L, where L is the straight (tangent-to-tangent) length.
- 2:1 elliptical head (depth D/4): V = πD³/24 per head.
- Hemispherical head (depth D/2): V = πD³/12 per head.
- Torispherical heads (ASME F&D, standard F&D, 80:10): calculated from the crown radius and knuckle radius ratio.
- Conical head: V = (π/12) D² h, with h set by the cone half-angle.
Partial volume of a horizontal vessel
At liquid height h, the wetted circular segment area is A = R² cos−1[(R − h)/R] − (R − h)√(2Rh − h²), so the shell holds A × L. Two identical elliptical heads together form an ellipsoid, so their combined partial volume is (a/R) × πh²(3R − h)/3, where a is the head depth.
Partial volume of a vertical vessel
The bottom head fills first, using its own depth-volume relationship; above the tangent line the volume rises linearly with (π/4) D² per unit height.
Worked example: horizontal drum with 2:1 elliptical heads
Illustrative inputs: D = 2.0 m, straight length L = 6.0 m, 2:1 elliptical heads (depth a = 0.5 m).
- Shell = (π/4) × 2.0² × 6.0 ≈ 18.85 m³.
- Two heads = 2 × π × 2.0³ / 24 ≈ 2.09 m³.
- Total ≈ 20.94 m³ (about 5,530 US gallons or 131.7 bbl).
- At a 0.5 m liquid level: segment area = 1.0472 − 0.5 × 0.866 ≈ 0.614 m², so the shell holds 0.614 × 6.0 ≈ 3.69 m³; the heads add (0.5/1.0) × π × 0.5² × 2.5 / 3 ≈ 0.33 m³.
- Liquid volume ≈ 4.01 m³, about 19% full at 25% of diameter – showing why level and volume are not proportional in a horizontal vessel.
Strapping tables and wetted area
The calculator generates a level-to-volume table in 1, 2, 5 or 10% steps, and solves the reverse problem (volume to level) for setting LLL, NLL and HLL. It also reports the wetted area up to the liquid level, which is used with the API 521 environmental factor F for pool-fire relief load on unwetted and wetted surfaces.
Assumptions and limitations
- Dimensions are internal; enter the inside diameter, or the outside diameter less twice the wall thickness.
- Internals, nozzles, boots, baffles and demisters are not deducted unless entered as dead volume.
- Results are geometric values for preliminary design, level setting and estimating; custody-transfer tank calibration requires the applicable API MPMS procedures.
Related tools
- Tank volume calculator – all tank shapes and geometries
- Two-phase separator sizing calculator
- ASME VIII pressure vessel calculator
- PSV relief load calculator – fire case using wetted area
Frequently asked questions
How do you calculate the volume of a horizontal vessel?
Add the volume of the cylindrical shell, (pi/4) x D squared x L, to the volume of the two heads. For 2:1 elliptical heads each head holds pi x D cubed / 24; for hemispherical heads each holds pi x D cubed / 12. For a partial fill, use the circular segment area at the liquid height for the shell and the matching partial-head formula.
Why is the volume not proportional to the liquid level?
In a horizontal cylinder the liquid width changes with height: it is narrow near the bottom and top and widest at the centreline. So the first and last 10 percent of the level hold much less volume than the middle 10 percent. A strapping table converts level to volume accurately.
What is the volume of a 2:1 elliptical head?
A 2:1 semi-elliptical head has a depth of one quarter of the diameter, and its volume is pi x D cubed / 24, or about 0.1309 D cubed. Two such heads together hold the same volume as a cylinder of the same diameter that is D/3 long.
What is the difference between ASME F&D and standard F&D heads?
Both are torispherical. An ASME flanged and dished head has a crown radius equal to the diameter and a knuckle radius of 6 percent of the diameter. Standard F&D variants use different crown and knuckle ratios, such as a crown of 0.9D with a 10 percent knuckle, and 80:10 heads use 0.8D with a 10 percent knuckle, which changes depth and volume.
What is a strapping or calibration table?
It is a table of liquid level against volume for a specific vessel, used to convert a level transmitter or dip reading into stored volume and to set alarm and trip levels. The calculator generates it in fixed level steps and can export it.
Can I use this for custody-transfer tank calibration?
No. The tool gives geometric volumes for design, level setting and estimating. Custody-transfer and fiscal calibration require physical measurement and the applicable API MPMS calibration procedures.
Written by Muhammad Raza
Founder of Aienginear. Engineering and digital solutions professional with 26+ years managing projects, plant shutdowns and turnarounds in oil & gas, petrochemical and power generation.
