# Roll Length Calculator

URL: https://speedycalculator.com/calculators/everyday-life/roll-length/
Last updated: 2026-10-25

> The roll length calculator works out the length of material on a roll – paper, tape, film, fabric, cable or steel strip – from the outer diameter, core diameter and material thickness, and finds the outer diameter for a given length.

## Inputs

- Outer diameter (mm, cm, in)
- Core (inner) diameter (mm, cm, in)
- Material thickness (mm, µm, mil, in)

## Results

- Length on the roll
- Number of wraps

## Formula

```
Length = π × (D² − d²) ÷ (4 × t)
Outer diameter = √(d² + 4 × t × L ÷ π)
```

## Explanation

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

FieldWhat to enterOuter diameterUnits: mm, cm, inCore (inner) diameterUnits: mm, cm, inMaterial thicknessUnits: 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)10033.2150131.3200268.8250445.5300661.54001,211.3

## 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.

## FAQ

**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).