THE METHOD, MADE CLEAR
From two diameters
to an ideal length.
Rollremain estimates the linear length of a uniformly thick sheet wound around a circular core. It uses an area balance, so the answer is only as useful as the thickness measurement and winding assumptions.
The model in one equation
Imagine looking straight at the end of a roll. The wound material occupies a ring, also called an annulus. Its outside circle has the measured roll diameter; its inside circle has the core’s outside diameter. The area of this ring is π × (outside diameter² − core diameter²) ÷ 4.
Now imagine that same material laid flat as a long narrow rectangle seen from its edge. Its edge area is length × thickness. Equating the two areas gives the ideal length:
L = π × (D² − d²) ÷ (4 × t)
D = roll outside diameter
d = core outside diameter
t = single-layer material thickness
Every quantity must use one common length unit before calculation. When D, d and t are in millimetres, the answer is in millimetres. Divide by 1,000 for metres. The app evaluates the equivalent factored expression π × (D − d) × (D + d) ÷ (4 × t), which avoids subtracting two large, nearly equal squared numbers near an empty roll.
Worked example: 200 mm outside, 76 mm core
A nominal thickness of 0.1 mm
The squared diameter difference is 200² − 76² = 40,000 − 5,776 = 34,224 mm². The annular area is 8,556π mm². Dividing by the 0.1 mm layer thickness gives 85,560π mm of material.
That is 85.56π m, approximately 268.795 m. The radial build is (200 − 76) ÷ 2 = 62 mm. Dividing that build by 0.1 mm gives 620 ideal radial layers. This build ratio is not a count of complete turns; circumferences change through the roll.
Why roll width is not an input
For a constant-width roll, multiplying the annular area by roll width gives the ideal material volume. A flat strip’s volume is length × thickness × that same width. The widths cancel when solving for length. A wider roll with the same diameters and thickness therefore has the same modelled linear length, while containing more material by area or volume.
This cancellation assumes the width is uniform through the roll. Telescoped edges, a partial-width backing, changing widths or unevenly wound layers make the simple model less representative. Rollremain does not use material density, mass or a supplier’s length-to-weight conversion.
Measuring the right diameters
Outside diameter means the full distance across the currently wound material through the centre. It is not the radius, circumference or original full-roll diameter. Core diameter means the diameter across the outside surface that supports the first wound layer. Using the hole inside a thick cardboard core would overstate the area occupied by material and therefore overstate the length.
A real roll may not be perfectly round. Check whether measurements taken in different directions differ materially before treating one diameter as representative. The tool does not automatically average measurements or infer the shape. A core diameter of zero is allowed as an ideal coreless-coil model; it does not mean every real coreless coil is tightly packed at its centre.
Thickness: small number, large influence
Enter the full thickness of one layer as it remains wound. If a film stays attached to a release liner, both contribute to the layer build. If a compressible sheet changes thickness under winding pressure, a loose single-sheet measurement may differ from its effective thickness on the roll. The calculator cannot infer that difference or identify a material from its name.
Thickness sensitivity is deliberately separate from measurement accuracy. You enter a thinnest and thickest plausible layer; the app evaluates both assumptions with the same diameters. The nominal thickness must sit within that range. No probability, confidence level or guarantee is attached to the resulting length range.
Trying 0.09–0.11 mm for the first roll
At 0.11 mm, the estimate is approximately 244.359 m. At 0.09 mm, it is approximately 298.661 m. The nominal 0.1 mm estimate stays approximately 268.795 m.
The range is asymmetric around the nominal length because thickness is in the denominator. Making thickness 10% smaller increases the modelled length by about 11.11%; making thickness 10% larger reduces it by about 9.09%. These are arithmetic effects of the entered assumptions.
A second example and a useful cross-check
A 100 mm outside diameter, 50 mm core and 0.2 mm layer give π × (10,000 − 2,500) ÷ 0.8 = 9,375π mm, or approximately 29.4524 m. Doubling only the thickness to 0.4 mm halves that estimate to approximately 14.7262 m. Keeping thickness fixed while doubling both diameters multiplies the annular area, and therefore the ideal length, by four.
If the outside equals the core, the ring area is zero and the answer is zero. This includes the mathematical empty case where both diameters are zero. If the outside is smaller than the core, the inputs cannot describe this model and the result is cleared. Zero or negative thickness is invalid even for an empty roll.
Millimetres, centimetres and inches
One centimetre is exactly 10 mm and one inch is exactly 25.4 mm. The measurement selector applies to all five dimension and thickness fields. Changing it converts the displayed values while retaining the underlying physical measurements, rather than rounding each new display back into the next calculation. The metre/feet selector changes the presentation of the resulting length independently; one foot is exactly 304.8 mm.
For example, 200 mm outside, 76 mm core and 0.1 mm thickness can be written as 20 cm, 7.6 cm and 0.01 cm. Both describe the same physical roll. Do not enter a thickness in millimetres while the other fields are set to inches. If a supplier uses an unfamiliar thickness notation, establish its actual length-unit meaning before using it.
Where the ideal model falls short
The annular-area calculation assumes a circular, tightly filled cross-section, constant thickness and no air spaces between layers. Loose winding can increase the diameter without adding the material implied by this model. Compression, trapped air, uneven tension, folded edges, splices, coatings and variable thickness can all change the relationship between measured diameter and usable length.
The beginning and end of a real spiral also do not form a perfectly filled annulus. This matters particularly for very few layers. The app flags a positive radial build smaller than one nominal layer; it still shows the continuous-area arithmetic, rather than inventing a whole-turn count. It does not deduct damaged material, required leader length, unusable end sections, planned cuts or process waste.
Use the result as a planning estimate under stated assumptions. A product label, direct length measurement or appropriate calibrated production measurement may supply information that diameters alone cannot. This tool does not replace such information or promise a purchasable, usable or guaranteed remaining amount.
Saving a clear record
Copy estimate includes the entered measurements, thickness assumptions and model warning. CSV preserves numeric values in millimetres, metres and feet rather than just the rounded screen text. Diagram SVG saves a diameter-proportional cross-section; it is illustrative and is not a true-size print template or a picture of individual windings. These exports are created on your device, and this release does not upload or retain the inputs.