Calculate a roll’s outside diameter from core size, material length and thickness, or find the length (linear footage) or thickness of a finished roll.
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Roll Outside Diameter Formula
The estimate conserves the cross-sectional area of material wound around the core and normalizes dimensions to metres. Use the core outside diameter, not its bore. The formulas below describe ideal 100% fill. For entered fill fraction f, divide the added 4Lt/pi term by f, or multiply the inverse length and thickness formulas by f. Fill models annular material fraction; it is not a general compression correction.
Find outside diameter:
Find length on roll:
- OD = outside diameter of the finished roll
- ID = outside diameter of the bare core (the inner boundary of the wound material, not the core bore)
- L = length of material on the roll
- t = material thickness
- pi = 3.14159…
Use the diameter mode with core outside diameter, total caliper and material length. Use length mode with measured roll/core outside diameters and caliper. Thickness mode infers total caliper from positive length and a nonempty roll. A comparison fill recalculates that same solve target with the other inputs fixed; it is an entered scenario, not a guaranteed tolerance.
Illustrative Thickness Conversions
These are illustrative thickness values assigned to example materials, not verified product specifications or typical ranges. Use the actual total measured caliper, including backing and other wound layers. The inch-to-mm conversions are rounded to three decimals.
| Material | Example thickness | Approx. mm |
|---|---|---|
| Aluminum foil | 0.0005 in | 0.013 mm |
| Plastic film / poly | 0.001 in | 0.025 mm |
| Masking tape | 0.002 in | 0.051 mm |
| Office paper | 0.003 in | 0.076 mm |
| Receipt paper / newsprint | 0.004 in | 0.102 mm |
| Cardstock | 0.007 in | 0.178 mm |
| Corrugated cardboard | 0.016 in | 0.406 mm |
Roll Diameter Reference
These size descriptions are informal illustrations, not industry classifications or machine-capacity limits.
| Outside diameter | General interpretation |
|---|---|
| Under 2 in | Small roll, similar to some tape or ribbon rolls |
| 2 to 5 in | Common small roll size, such as tape, labels, or small paper rolls |
| 5 to 10 in | Medium roll, often seen with receipt paper, labels, film, or craft material |
| 10 to 20 in | Large roll, common for shipping paper, sign vinyl, and production materials |
| Over 20 in | Industrial-size roll |
Example Calculations
Example 1: Find the outside diameter
You have a 3 in core, 500 ft of material, and the material is 0.004 in thick.
The finished roll outside diameter is about 6.29 in.
Example 2: Find the length on a roll
You measure an 8 in outside diameter roll with a 3 in core. The material thickness is 0.004 in.
The roll contains about 900 ft of material.
FAQ
Why does material thickness matter so much?
Roll diameter depends on the total cross-sectional area of material wound around the core. A small thickness error is repeated across many wraps, so the final diameter or length estimate can change noticeably. For the best result, measure the material thickness with calipers or use a verified product specification.
Should I use radius or diameter?
Use diameter. Enter the full distance across the core or finished roll, not the radius. The formula uses squared diameters, so entering a radius by mistake will give a result that is far too small.
Why is the result an estimate?
The ideal 100% fill model assumes even winding with no voids. An explicitly entered lower fill can represent calibrated air gaps; it does not automatically model compression, stretching, wrinkles or changing tension. Use total effective caliper under relevant conditions and compare against measured production rolls. Wrap count is a continuous-layer estimate, not an exact discrete spiral count.
