Plate rolling calculator: the blank length of a rolled shell, with the formula, a chart and a worked example

Rolling a shell starts with one number: how long to cut the plate. Cut it to the outside circumference and the shell will not close; cut it to the inside and it gaps. The right length is the circumference at mid-thickness, and this page gives it for any diameter and plate, with the shell weight, the number of stock plates it takes, a chart and the formula.

The cylinder calculator draws the blank, with the 1:1 template and the DXF for the cutting table.

Plate rolling calculator

Pick which diameter your drawing gives, type it and the plate thickness. The shell height and the stock plate length are optional: with them come the weight and how many plates go round.

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The formula

When plate is rolled, the outside of the wall stretches and the inside is squeezed. In the middle there is a fibre that does neither, the neutral axis, and its length is the length of the flat blank. For rolling, where the diameter is many times the thickness, the neutral axis sits at mid-thickness.

Blank length

L = π × (D − t) = π × (d + t) = π × Dm D is the outside diameter, d the inside diameter, Dm the mean diameter and t the plate thickness. All three forms give the same length.

What the outside diameter gets wrong

π × D − L = π × t Worked on the outside diameter, the blank comes out π × t too long, whatever the diameter: 19.95 mm on 1/4 in plate, 0.785 in.

Shell weight

kg = L (m) × h (m) × t (mm) × 7.85 h is the shell height, the width of the plate; 7.85 kg/dm³ is carbon steel. In pounds: L (in) × h (in) / 144 × the weight per square foot of the plate.

The neutral axis and thickness guide explains why the middle of the wall, and when it moves.

Worked example

A shell of 1000 mm outside diameter, 1500 mm high, in 6.35 mm (1/4 in) carbon steel plate, from 3000 mm stock plates:

1. Mean diameter: 1000 − 6.35 = 993.65 mm.
2. Blank length: π × 993.65 = 3121.64 mm. Worked on the outside diameter it would be 3141.59 mm, 19.95 mm too long.
3. Weight: 3.12164 × 1.5 × 6.35 × 7.85 = 233.4 kg.
4. Stock plates: 3121.64 mm does not fit in one 3000 mm plate, so the shell takes 2 plates and 2 longitudinal seams; from a 6000 mm plate, 1 plate and 1 seam.

The same in inches: a 48 in outside diameter tank shell, 60 in high, in 1/4 in plate. Mean diameter 47.75 in, blank length π × 47.75 = 150.01 in (12 ft 6 in), 0.785 in shorter than the outside circumference, and 638 lb of plate.

Blank length chart

Blank length for common shells, from the outside diameter, on the neutral axis. Metric, in millimetres:

In inches:

What the formula does not tell

1. The weld gap. If the seam needs a root gap, cut the blank that much shorter: for a 2 mm gap on the example shell, 3119.64 mm.
2. The flat ends. A roll cannot bend the plate right to its edge. On a three-roll pyramid machine the ends stay flat for roughly half the distance between the bottom rolls; on initial-pinch and four-roll machines much less. Pre-bend the ends on a press brake or with a bending plate, or leave the blank long and trim the flats after rolling. Your roll's manual gives the flat for its geometry.
3. Thick plate on a small diameter. When the diameter is only a few times the thickness, the neutral axis moves a little towards the inside and the plate thins on the outside. Roll a trial piece and measure before cutting the whole batch.
4. Cones are not shells. A rolled cone is a sector, not a rectangle; the cone development guide gives its radii and angle.

Frequently asked questions

How do you calculate the length of plate to roll a cylinder?

Multiply the mean diameter by π: L = π × (outside diameter − thickness), or π × (inside diameter + thickness). A 1000 mm outside diameter shell in 6.35 mm plate needs a 3121.64 mm blank.

Do I use the inside or the outside diameter?

Neither: the mean one, at mid-thickness. Using the outside diameter makes the blank π × t too long and the seam overlaps; using the inside diameter makes it π × t too short and the seam gaps.

How much plate do I need to roll a 48 inch tank?

For a 48 in outside diameter in 1/4 in plate, the blank is 150.01 in long, 12 ft 6 in: π × 47.75. A 120 in plate is not long enough, so the shell takes two plates and two seams, or one 240 in plate.

Why does my rolled shell overlap?

Almost always because the blank was worked on the outside diameter: it is π × t too long, 0.39 in on 1/8 in plate. Work the length on the mean diameter.