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.
As on the roll length calculator, this area-based identity is mathematically identical to summing an Archimedean spiral's arc length turn by turn, for any roll with a realistic turn count — the two only diverge in the extreme case of a handful of turns on a near-degenerate core, a regime no real spool, reel, or roll good actually runs in, so the annular-area identity above is what this calculator solves.
Solving forward and solving backward don't distort a thickness error by the same amount, though — which mode you're in changes how forgiving the result is of an imprecise caliper. In "Outer Ø" and "Core Ø" mode, outer diameter comes from a square root: OD = √(ID² + 4Lt/π). A square root compresses whatever's inside it, so a given percentage error in thickness comes out roughly halved in the resulting OD — the exact damping factor is (1 − (ID/OD)²)/2, which sits at 0.5 for a hairline core and falls toward zero as the core takes up most of the roll's diameter. Run the numbers on the stretch-wrap example below (L 1,500 m, ID 76 mm, t 25 µm): a thickness reading that's 5% too high only shifts its 231.3 mm result to about 236.5 mm — a 2.2% change, not 5%.
In "From turns" mode, outer diameter is linear instead: OD = ID + 2Nt. There's no square root to damp anything, so a thickness error passes through close to full strength, scaled by how much of the final diameter is wound material rather than core — the factor is (1 − ID/OD), and unlike the square-root case above it holds exactly, not just approximately. Run the same 5%-high thickness reading through the cable-reel example below (N 300, ID 50 mm, t 0.6 mm): its 410.0 mm result becomes about 428 mm — a 4.4% change, roughly double the length-based case. If your thickness figure is a nominal spec rather than a measured value, a length-based solve is the more forgiving direction to trust it in.
Sensitivity, by length ≈ (1 − (ID/OD)²) / 2
Sensitivity, by turns = 1 − ID/OD
Predicting the finished roll before you wind it
The most common reason to solve for outer diameter ahead of time is interference: will the finished roll clear the winder's guarding, fit the flange on a spool, or leave enough clearance in the rack it's stored in? "Outer Ø" mode answers that directly from the length you plan to wind, the core you're starting from, and the material's thickness — check the result against the hard clearance number before the machine starts, not after.
Shaft and bearing loading is the other common check, and it needs one more step: weight, not just size. Once you know the finished outer diameter, the material occupies the same annulus shape as the diagram above, extruded across the roll's width — a cylinder with a smaller cylinder removed from its center. Multiply that volume by the material's density and you have the wound material's weight, on top of the core itself; the cylinder volume calculator handles that annulus-times-width volume directly if you plug in the same outer and core diameters this page just solved for.
"From turns" mode covers machines that count revolutions rather than measuring length — many winders and slitters do — so if a job ran 1,650 turns of 10 mil stock onto a 3 in core, this mode reads off both the equivalent length and the resulting outer diameter without anyone walking over to measure the roll by hand.
Whichever direction you're solving, the roll length calculator is the complementary tool: once a real roll exists, it goes back from a measured OD, ID, and thickness to length and turn count — the check worth running once the roll is actually sitting in the winder, to confirm the prediction held. For the full spread of roll and reel tools this site covers, see roll & reel calculators.
Getting the inputs right in reverse mode
Core OD, not core ID. Same trap as on the roll length calculator: "Core Ø" here means the diameter the wound material sits against — the outside of the tube or chuck — not the tube's own inner bore where a spindle passes through. Check a supplier's spec sheet carefully if it lists both.
What "core too small" actually means. In "Core Ø" mode, the calculator first works out the minimum outer diameter that a given length and thickness could possibly wind down to — physically, that much material simply won't compress onto a smaller core than that. An error here isn't a bug in your numbers so much as a sign that one of length, thickness, or the assumed outer diameter is off; the minimum-OD chip shows exactly how much room you're short.
Matching units to the mode you're in. Switching between the "By length" modes and "From turns" mode changes which fields are inputs, but not the units they're stored in — length stays in whatever unit you last set (mil through meters), thickness stays in mil through cm. Mixing gauge-rated film (100 gauge = 1 mil = 25.4 µm) into a field expecting microns without converting first is the most common way to get an outer diameter that's off by roughly the unit-mismatch factor, not a subtle rounding error.
Thickness is still measured flat. As with the length calculator, a caliper reading taken per TAPPI T411 or ISO 534 (paper and board) or ASTM D374 / ISO 4593 (film and sheeting) is a flat, evenly loaded measurement — a tightly wound roll compresses slightly under its own wind tension, and a loose one traps air between layers. If a predicted outer diameter consistently misses a measured one on the same material and winder, back-solve an effective thickness from one completed roll (outer diameter, core, and either length or turns are all it takes) and use that instead of the nominal spec.
Sources: Caliper/thickness measurement conventions referenced above — TAPPI T411 (paper and paperboard caliper, North America), ISO 534 (paper and board thickness, international, lighter measuring load than T411), and ASTM D374 / ISO 4593 (plastic film and sheeting thickness) — describe how a material's published thickness is measured, not a specific numeric value used in this calculator's math. Unit relationships (1 mil = 25.4 µm = 100 gauge for US polyethylene film) are exact unit-conversion definitions, not measured data. The sensitivity formulas above follow directly from this page's own OD = √(ID² + 4Lt/π) and OD = ID + 2Nt equations by calculus, not from an external source.
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.
Does a thickness error matter more in 'Outer Ø' mode or 'From turns' mode?
More in 'From turns' mode. Outer diameter solved from length and thickness comes from a square root, which compresses a percentage thickness error to roughly half (or less) of its size in the result. Outer diameter solved from a turn count is a straight linear relationship instead, so the same percentage thickness error shows up close to full-strength in the answer. If your thickness number is a nominal spec rather than something measured on this batch, solving from length rather than from turns is the more forgiving direction to trust it in.
What's the difference between 'core diameter' here and a spool or reel's flange diameter?
Core diameter is the small circle in the middle of the diagram — where the wound material starts, whether that's a cardboard tube, a chuck, or a bare arbor. Flange diameter is the outer disc on a reel or spool that keeps the wound material from sliding off the sides; it caps how big a finished roll can get, but it isn't an input to this calculator's geometry. Solve for outer diameter first, then compare that number against the flange diameter on the spool's spec sheet to confirm the roll will actually fit.