Fabrication Math

How to Calculate Vessel Volume, Shell Thickness, and Weld Length for Pressure Vessel Fabrication

Work through the five core fabrication calculations, volume, shell thickness, weld length, plate yield, and hydrotest fill, with real units and solved examples.

Start with vessel volume because it drives fill, weight, and hydrotest planning. For a vertical cylinder with 2:1 elliptical heads, total volume equals the shell (pi/4 x D^2 x L) plus both heads (pi/24 x D^3). Take a vessel with inside diameter D = 84 in (7 ft) and tangent-to-tangent length L = 240 in. Shell volume is 0.7854 x 84^2 x 240 = 1,330,000 in^3. Two elliptical heads add 0.1309 x 84^3 = 77,600 in^3. Total 1,407,600 in^3, divided by 231 = 6,094 gallons. The Vessel Volume calculator handles hemispherical and flat heads by swapping the head coefficient.

Shell thickness comes from ASME Section VIII Div 1, UG-27 circumferential stress: t = P x R / (S x E - 0.6 x P). Here P is design pressure (psig), R is inside radius (in), S is allowable stress (psi), and E is joint efficiency. For P = 150 psi, R = 42 in, SA-516-70 plate at S = 20,000 psi, and full radiography E = 1.0, t = (150 x 42) / (20,000 x 1.0 - 0.6 x 150) = 6,300 / 19,910 = 0.316 in. Round up to the next stock plate, 0.375 in, then add corrosion allowance.

Corrosion and mill tolerance are where thickness errors hide. Add a corrosion allowance, commonly 0.0625 to 0.125 in for carbon steel process vessels, on top of the calculated 0.316 in. Plate is also supplied to a mill under-tolerance of about 0.01 in for hot-rolled. So 0.316 + 0.125 corrosion = 0.441 in, ordered as 0.500 in nominal to clear tolerance. The Shell Thickness Allowance calculator stacks pressure thickness, corrosion, and mill tolerance so you do not specify 0.375 in and fail MDMT or UG-27 after machining.

Weld length feeds consumables, labor hours, and NDE footage, so calculate it explicitly. A single longitudinal seam equals shell length, 240 in. Each circumferential seam equals pi x mean diameter; for D = 84 in shell that is 3.1416 x 84 = 264 in per seam. A three-course shell has two girth seams (528 in) plus one long seam per course (720 in) plus two head-to-shell seams (528 in), totaling roughly 1,776 in, or 148 ft. The Weld Length Estimate calculator multiplies seam counts by geometry so you do not undercount head joints.

Convert weld length to deposited weld metal to size filler. Cross-sectional area of a 60-degree single-V groove on 0.5 in plate with a 1/8 in root is about 0.15 in^2. Volume = 0.15 in^2 x 1,776 in = 266 in^3. Steel weighs 0.284 lb/in^3, so deposited metal is roughly 75 lb. Apply a deposition efficiency of 0.85 for FCAW to get about 88 lb of electrode purchased. That figure drives both the Weld Consumable Cost input and your wire order.

Plate yield tells you how much stock to buy after nesting losses. A 84 in ID x 0.5 in shell course 240 in long unrolls to a blank of circumference 3.1416 x 84.5 (mean) = 265 in wide by 240 in tall. From a 96 in x 240 in plate you use 265 of 288 in^2 of width across two plates, leaving drop. Typical nesting yield on vessel plate runs 78 to 88 percent. The Plate Yield calculator converts finished part area to purchased plate weight at 20.4 lb/ft^2 for 0.5 in steel so you order the right tonnage.

Hydrotest fill volume is not the same as product volume because you fill to the top head and include nozzle necks. ASME UG-99 sets the test pressure at 1.3 times MAWP times the stress ratio for Div 1. For the 6,094 gallon vessel above, add nozzle and dome volume, roughly 3 to 5 percent, giving about 6,340 gallons of test water weighing 8.34 lb/gal, or 52,900 lb. That load plus vessel dead weight sizes your test-stand foundation. The Hydrotest Capacity calculator returns fill volume, water weight, and fill time at a given pump rate.

Tie the sequence together so inputs flow cleanly: diameter and length feed Vessel Volume; pressure, radius, and allowable stress feed Shell Thickness Allowance; the resulting geometry feeds Weld Length Estimate and Plate Yield; weld length feeds deposited-metal weight; and final volume feeds Hydrotest Capacity. Keep units consistent, inches and psi for ASME, then convert to gallons and pounds only at the end. A single diameter error of 2 in propagates through volume (5 percent), plate width (2.4 in), and weld length (6 in per girth seam), so lock the ID first and verify it against the approved drawing.

Published 2026-07-01.