Roll Diameter Calculator
Solve outer diameter, core diameter, thickness, or turn count for a wound roll — choose what to find and get results instantly with a live diagram.
Worked examples
Stretch wrap roll before it ships
A packaging line wants to know how large a finished roll of stretch film will be before it's boxed, without waiting for it to come off the winder.
- L
- 1,500 m
- ID
- 76 mm
- t
- 25 µm
≈ 231.4 mm outer diameter, about 3,107 turns
Cable reel read off a turn counter
A winding machine operator has a revolution counter but no way to measure the roll directly, and needs both its outer diameter and the length of cable spooled so far.
- N
- 300 turns
- ID
- 50 mm
- t
- 0.6 mm
≈ 410.0 mm outer diameter, 216.8 m of cable
Wire spool sized before winding
An electrician wants to check whether 100 m of wire will fit within a spool's flange before feeding it onto the arbor, using only the wire gauge and the spool's empty core diameter.
- L
- 100 m
- ID
- 63.5 mm
- t
- 1.5 mm
≈ 441.6 mm outer diameter, about 126 turns
How the formula works
Every wound roll obeys one geometric identity, no matter which quantity you're solving for. Slice the roll straight across and its cross-section is an annulus — an outer circle of diameter OD with a smaller core circle of diameter ID cut out of the middle. Peel that ring apart at one point and pull it flat, and it becomes a long, thin rectangle: one side is the unwound length L, the other is the material's thickness t.
Peeling doesn't create or destroy material, so the annulus's area and the flattened rectangle's area must match. This calculator just rearranges that one equation for whichever variable you've told it to solve, and derives the turn count from the radial buildup divided by twice the thickness.
Frequently asked questions
How is this different from the Roll Length Calculator?
The Roll Length Calculator always solves for length from a fixed set of inputs. This calculator flips that around: pick outer diameter, core diameter, thickness, or turn count as the unknown, and the other quantities become your inputs. It's the same underlying geometry — an annulus that unrolls into a flat strip — just solved in whichever direction matches the number you're actually missing.
When is the core too small for a 'Core Ø' solve?
Given a fixed length and thickness, there's a minimum outer diameter below which no valid, non-negative core diameter exists — physically, that much material simply wouldn't fit onto a roll that small. The calculator works out this minimum outer diameter live as you type and flags an error if your entered outer diameter falls at or below it, so you always know how much room you actually have.
Why isn't the turn count a whole number?
Turn count comes from dividing the total radial buildup — outer radius minus core radius — by the material thickness, which models winding as a smooth, continuous spiral rather than counting discrete wraps. A result like 1,650.4 turns just means the outer layer ends partway through its final revolution; the fractional part reflects that last partial wrap, not a rounding error.
Can I compute outer diameter from a turn counter instead of a measured length?
Yes — switch to "From turns" mode. Many winding machines track revolutions rather than length directly, so if you know the turn count, material thickness, and core diameter, this mode gives you both the outer diameter and the equivalent unwound length without needing to measure the finished roll by hand.
If I switch what I'm solving for, do I lose the numbers I already entered?
No — whichever field was just calculated carries its value forward as an input the moment you switch modes, and every other field keeps whatever you typed. That lets you chain solves: find an outer diameter from a length, then immediately reuse that outer diameter to solve for thickness, without re-entering any shared values.
How big will a cable or wire spool get once I wind on a known length?
Use "Outer Ø" mode with the cable's insulated diameter as the thickness (t), the spool's empty arbor diameter as the core (ID), and the length of cable you plan to wind as L. The result is the finished outer diameter, so you can check it against the spool's flange size before you start winding and avoid overfilling it. The same setup works for any wire, rope, or hose spooled onto a reel.