If you know a roll’s finished outside diameter, the outside diameter of its core, and the material’s caliper, you can estimate the linear footage wound on the roll. This is a geometric estimate based on the roll’s shape and the material’s thickness — not a direct measurement, and not a guarantee of exactly how much material is actually there.
What Is Linear Footage?
Linear footage is the total length of material on a roll, measured along the machine direction — how far the roll would stretch out if you unwound it in a straight line. It is typically expressed in linear feet.
Linear footage is a different number from roll width, basis weight, and roll weight. Width is how wide the web is; basis weight and roll weight describe how much the material weighs. Footage describes how long it is — none of the others tell you that on their own.
What Measurements You Need
Three inputs are required to estimate linear footage:
- Finished roll outside diameter (OD). The roll’s total diameter, core and wound material included, measured across the end face.
- Core outside diameter (OD). The outside diameter of the bare core — not the core’s inside diameter. The section below explains why this distinction matters here.
- Material caliper (thickness). The thickness of a single layer of the material, usually given in mils (thousandths of an inch) or points.
For how to physically take roll diameter measurements, our guide to measuring a paper roll covers the technique and the common mistakes. Our guide to paper roll core sizes covers core sizing in more depth — but that article is written around core inside diameter, which equipment compatibility depends on. This calculation needs the core’s outside diameter instead, which is the subject of the next section.
Why Core ID and Core OD Are Different Here
Core inside diameter (ID) and core outside diameter (OD) answer two different questions, and this calculation depends on getting the right one:
- Core ID matters for equipment compatibility — it’s the opening that fits over a shaft or accepts chucks.
- Core OD determines where the wound material physically begins, radially outward from the center of the roll. Because the footage formula is built from the roll’s geometry — how much of its total diameter is core versus wound material — it needs the core’s outside diameter, not its inside diameter.
Do not plug a core ID into this formula, even if it looks like a reasonable stand-in. A 3″ core ID does not mean the core OD is also 3″ — the core has a wall thickness, so its outside diameter is always a larger number. Exactly how much larger depends on that specific core’s construction, and this guide does not publish a typical or assumed wall thickness for that reason: using an assumed value here would silently corrupt the result. If you know the core ID but not the wall thickness or core OD, you need one of those two additional pieces of information before this formula can be used accurately — measure the core OD directly, or get it from the core’s specification.
The Linear Footage Formula
The formula comes from the annular (ring-shaped) cross-section of the wound material, viewed from the roll’s end face. That area, unrolled, forms a long rectangle whose thickness is the material’s caliper and whose length is what you’re solving for — the roll’s width cancels out of the calculation entirely, because both sides of that relationship scale with it equally.
Length (inches) = π × (Roll OD² − Core OD²) ÷ (4 × Caliper)
Then convert the result to feet:
Length (feet) = Length (inches) ÷ 12
All three inputs — Roll OD, Core OD, and Caliper — must be in the same linear unit (inches, in this version of the formula) before you calculate. Caliper is often given in mils; divide a mil figure by 1,000 to convert it to inches first.
Worked Example
This is an illustrative calculation, not a Paper Dimensions capability specification. The values below are chosen only to make the arithmetic easy to follow.
Given:
- Roll outside diameter: 40″
- Core outside diameter: 3.5″
- Caliper: 4 mils (0.004″)
- Square the diameters: 40² = 1,600; 3.5² = 12.25
- Subtract: 1,600 − 12.25 = 1,587.75
- Multiply by π: 1,587.75 × π ≈ 4,988.06 in²
- Multiply caliper by 4: 4 × 0.004 = 0.016
- Divide: 4,988.06 ÷ 0.016 ≈ 311,753.98″
- Convert to feet: 311,753.98 ÷ 12 ≈ 25,979.5 feet — roughly 26,000 feet
A 40″ OD roll on a 3.5″ core OD, in a 4-mil material, works out to roughly 26,000 feet of material by this formula. Actual roll footage may vary from this theoretical estimate — see the next section for why.
Why Actual Footage Can Differ
This formula is a theoretical geometric estimate. It assumes perfectly uniform caliper and no air between layers, and real rolls rarely match that assumption exactly. Factors that can make actual footage differ from the calculated value include:
- Caliper variation. Material thickness is rarely perfectly uniform across a web or down its length, and the formula only accepts a single caliper value.
- Winding density and air between layers. How tightly a roll is wound affects how much material actually fits within a given outside diameter.
- Uneven winding. A roll that isn’t wound consistently won’t match the uniform-cylinder assumption the formula is built on.
- Measurement error. Because the result depends on diameters squared, small errors in measuring roll OD or core OD have an outsized effect on the calculated footage.
- Core OD variation. Using an assumed or incorrect core OD, rather than the actual value, shifts the result in the same way any other mismeasurement would.
Treat the result as a theoretical estimate useful for planning, not as a substitute for a measured or counted footage where an exact number matters.
Linear Footage vs. Roll Weight
Footage and weight describe two different things: footage is length, and weight is mass. Basis weight or GSM can help estimate a roll’s weight once you already know its dimensions, but neither one tells you the roll’s footage directly — that still requires the roll OD, core OD, and caliper inputs above. Our guide to basis weight and our guide to basis weight vs. GSM cover how those weight figures work if you need that calculation separately.
Linear Footage vs. Finished Roll OD
The formula makes a few geometry relationships easy to see, holding the other variables constant:
- Same core and same caliper: a larger finished OD means more footage.
- Same finished OD and a thicker material: less footage, because each wrap takes up more radial space.
- Same finished OD and a larger core OD: less footage, because less of the roll’s radius is available for wound material.
These relationships explain why the numbers move the way they do, but the actual amount of change depends on the specific values involved — there is no fixed ratio that applies generally, so run the formula with your own numbers rather than estimating from the pattern alone.
What If I Don’t Know the Caliper?
A few reliable ways to find it:
- Check the mill or supplier’s material specification.
- Check the product’s data sheet, if one is available.
- Ask your supplier directly.
- Measure it yourself with appropriate equipment (such as a micrometer), if your process allows for that.
Don’t substitute basis weight for caliper as if the two are interchangeable — basis weight is a weight-per-ream figure, not a thickness measurement, and the two are not the same number even for the same material. Our basis weight guide covers that distinction in more depth if it’s useful.
What to Put on a Converting RFQ
Useful information for a converting request, alongside the rest of the job specification. Not every field applies to every job:
- Material or grade
- Basis weight or GSM, if known
- Caliper, if known
- Parent-roll width
- Parent-roll outside diameter
- Parent-roll core inside diameter
- Parent-roll core outside diameter, if known or relevant
- Desired finished width
- Desired finished outside diameter or length
- Desired finished core inside diameter
- Quantity
- Packaging requirements
Our RFQ preparation guide covers the complete specification a converter needs, including material, packaging, and scheduling details beyond footage alone.
Linear Footage at Paper Dimensions
When requesting rewinding from Paper Dimensions, provide the source-roll dimensions and your target finished diameter or length when known. The quote request form captures the specifications needed to evaluate the job, and any footage or length target can be discussed as part of your paper rewinding request.
Key Takeaways
- Linear footage is a geometric estimate calculated from roll OD, core OD, and material caliper — not a direct measurement.
- The formula is Length (inches) = π × (Roll OD² − Core OD²) ÷ (4 × Caliper), then divide by 12 for feet.
- Use core outside diameter, not core inside diameter — the wound material begins at the core’s outer surface, and substituting core ID will silently produce a wrong result.
- The worked example (roughly 26,000 feet) is illustrative only, built from hypothetical inputs, not a Paper Dimensions capability specification.
- Actual footage can differ from the calculated value because of caliper variation, winding density, uneven winding, or measurement error — treat the result as an estimate.
- Basis weight and GSM help estimate roll weight, not footage — footage still requires roll OD, core OD, and caliper.