Enter the inside hole diameter, the thickness of the material, and the length of the material into the calculator to determine the outside roll diameter.

Roll Outside Diameter Calculator

Enter your core size, material thickness, and length to get the finished roll diameter.

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Outside Diameter Formula

The following formula is used to calculate the outside diameter of a roll of material (idealized roll with no air gaps or compression). 

OD = \sqrt{ID^2 + \frac{4Lt}{\pi}}
  • Where OD is the outside diameter of the roll
  • L is the length of material wound on the roll
  • t is the thickness of the material
  • ID is the inside diameter (core diameter)

In this case, convert your inputs so they are consistent before using the formula (for example, use inches for ID, OD, L, and t so that L·t is in square inches).

Roll Diameter Definition

Roll diameter is a measure of the diameter of the circle created when a material of a certain thickness is rolled into a cylindrical shape.

The thicker and longer the material, the greater the roll diameter will be.

Example Problem

How to calculate outside roll diameter?

First, determine the length of the material being rolled. For this example, the material is found to be 1500 inches long.

Next, determine the thickness of the material. The sheet of material is measured to be 0.5 inches thick.

Next, determine the inner diameter. In this case, the inner diameter, also known as the core diameter, is 3 inches.

Finally, using the formula above, calculate the outside diameter:

OD = √( ID² + (4·L·t)/π )

OD = √( 3² + (4·1500·0.5)/3.14159 )

OD ≈ 31.05 inches

FAQ

What factors affect the roll diameter?

The roll diameter is affected by the length of the material being rolled, the thickness of the material, and the inside diameter (core diameter). Changes in any of these parameters can result in a different roll diameter.

Can the formula be used for any type of material?

The formula is a geometric approximation that works best for thin, flexible materials where compression and air gaps are negligible. For compressible materials, or when winding tension/air entrainment is significant, the actual outside diameter can differ from the calculated value.

How do you ensure accuracy when measuring for roll diameter calculations?

To ensure accuracy when measuring for roll diameter calculations, use precise measuring tools, convert measurements so they are consistent (ID, OD, L, and t in the same length unit), and double-check your measurements. Additionally, understanding the material properties and how they might affect the roll (such as material stretch or compression) can help in making more accurate calculations.