A wound roll is a spiral, but each layer adds one thickness to the radius, so the total length equals the cross-sectional area of the ring divided by the thickness. The result is accurate when the material is wound tightly; loosely wound rolls contain less length than calculated.
How to use the Roll Length Calculator
- Outer diameter
- Core (inner) diameter
- Material thickness
- Every result field is editable: type into Length on the roll and Outer diameter plus every other field update to match.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the outer diameter, core diameter and material thickness. Type a length into the result to find the outer diameter.
Tips
- Use the figures from your own bills and product labels – prices and appliance ratings vary widely.
- Look at yearly totals: small daily costs add up and make it easier to compare options.
- Round quantities up to whole packs, rolls or bulbs when you shop.
- Re-check the numbers when prices change; most results scale directly with the unit price.
Common mistakes to avoid
- Confusing watts (power) with watt-hours or kilowatt-hours (energy).
- Comparing prices without bringing them to the same unit first.
- Ignoring one-off costs such as installation, delivery or replacement parts.
Inputs explained
| Field | What to enter |
|---|---|
| Outer diameter | Units: mm, cm, in |
| Core (inner) diameter | Units: mm, cm, in |
| Material thickness | Units: mm, µm, mil, in |
What each result means
- Length on the roll = pi×([Outer diameter]^2 – [Core (inner) diameter]^2)÷(4×[Material thickness])
- Number of wraps = ([Outer diameter] – [Core (inner) diameter])÷(2×[Material thickness])
Example values
How the main result changes when Outer diameter changes and everything else stays at the example values above:
| Outer diameter (mm) | Length on the roll (m) |
|---|---|
| 100 | 33.2 |
| 150 | 131.3 |
| 200 | 268.8 |
| 250 | 445.5 |
| 300 | 661.5 |
| 400 | 1,211.3 |
Formula
Length = π × (D² − d²) ÷ (4 × t)Outer diameter = √(d² + 4 × t × L ÷ π)Worked example
Inputs — Outer diameter: 200 mm; Core (inner) diameter: 76 mm; Material thickness: 0.1 mm.
Results — Length on the roll = 268.8 m; Number of wraps = 620.
Frequently asked questions
How do I calculate how much paper is on a roll?
π × (outer diameter² − core diameter²) ÷ (4 × thickness).
Does tension matter?
Yes – the formula assumes a tight wind; loose rolls hold less material.
How do I measure thickness?
Measure a stack of 10 layers with a caliper and divide by 10.
What formula does the Roll Length Calculator use?
Length = π × (D² − d²) ÷ (4 × t).