Cylinder Development

Unrolling a cylinder

The lateral surface of a right circular cylinder develops into a rectangle. Its length is the circumference at the neutral surface and its width is the cylinder height. A neutral diameter of 100 mm gives a circumference of 314.159265 mm. Adding a 10 mm seam allowance gives a cut length of 324.159265 mm.

Choosing dimensions

Use the neutral surface diameter rather than an inside or outside diameter. Neutral surface position can vary when forming thick plate and is not predicted here. The allowance is added once along the length. End caps and trimming allowances are outside the rectangular blank calculation.

Check the cutting dimensions step by step

Consider a shell with a neutral diameter of 250 mm, height of 400 mm and seam allowance of 15 mm. Its circumference is π × 250 ≈ 785.398 mm. Adding the allowance gives a length of 800.398 mm. The rectangle covers 800.398 × 400 ≈ 320159.265 mm², approximately 0.320159 m². Divide by one million to convert square millimetres to square metres. Using the factor of one thousand for lengths would overstate the area.

The cutting length runs around the circumference, while the height runs along the cylinder axis. Mark these directions when laying out the blank on a sheet. Doubling height at the same diameter leaves the circumference unchanged and doubles only the area. This provides a useful check for swapped dimensions.

The seam allowance is an example input, not a recommended workshop value. Obtain the required allowance from the joint design and manufacturing plan. The result describes the rectangular blank. It is not the sheet purchasing quantity unless edge margins and nesting are also considered. Check the formed diameter on a trial piece before cutting a production batch.

Frequently asked questions

How do you calculate cylinder blank length from diameter?

For an example cylinder with neutral surface diameter 100 mm and seam allowance 10 mm, the developed cutting length is 324.2 mm. Seam allowance is added once to the neutral circumference, and the calculation does not locate the neutral surface or include end caps and edge trimming allowances.

Calculate with these values