Roll Diameter Calculator: Finished OD from Length & Thickness
Enter core diameter, material thickness, and length to estimate the finished outside diameter of a wound roll — for carton sizing, unwind-stand capacity, and slitting plans.
Built for: checking whether a rewind fits the box, the machine, or the truck before you commit.
Roll Diameter Calculator
How it works — formula, worked example & reference
Formula: OD = √(ID² + 4tL/π) — the inverse of the roll-length formula: total wound cross-section back-solved for outside diameter.
Worked example: Core = 3 in, t = 62 mils, L = 150 ft (1,800 in): OD = √(9 + 4 × 0.062 × 1800 / π) = √151.1 = 12.3 in.
| Length on 3″ core, 62-mil material | Approx. roll OD |
|---|---|
| 50 ft | 7.4″ |
| 100 ft | 10.2″ |
| 150 ft | 12.3″ |
| 250 ft | 15.7″ |
| 500 ft | 21.9″ |
Same formula; verify against carton and unwind limits with margin.
These results are engineering estimates for preliminary material selection; final validation is the responsibility of your engineering team.
Common questions
How do I calculate the diameter of a finished roll?
Use OD = √(ID² + 4tL/π), where ID is the core outside diameter, t is material thickness, and L is length. Enter the values above and the tool returns the outside diameter.
Why do I need roll diameter?
Shipping cartons, converting equipment, and unwind stands all have maximum roll capacities. Knowing the finished OD before slitting or rewinding prevents rolls that do not fit the box or the machine.
Does liner thickness count?
Yes. If the material winds with a release liner, add liner thickness to material thickness — the roll builds at the combined caliper.