# Label Roll Length and Outer Diameter Calculator

> Source: https://netray.co/tools/label-roll-length-and-outer-diameter-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Enter label size, gap, core and material thickness to get roll length in metres, the finished roll diameter, and the most labels that fit under a diameter limit.

## Category

manufacturing

## Industry

Packaging and Printing

## Audience

- Label converter
- Packaging plant manager
- Production planner
- Buyer

## Tool

**Kind:** calculator

**Inputs:**

#### Label length (feed direction)

**Key:** label_len

**Type:** number

**Default:** 100

**Min:** 5

**Step:** 1

**Unit:** mm

#### Gap between labels

**Key:** gap

**Type:** number

**Default:** 3

**Min:** 0

**Step:** 0.5

**Unit:** mm

**Help:** Die-cut gap or matrix gap in the feed direction.

#### Labels across the web

**Key:** across

**Type:** number

**Default:** 1

**Min:** 1

**Max:** 12

**Step:** 1

**Unit:** labels

#### Labels per roll

**Key:** labels_roll

**Type:** number

**Default:** 1000

**Min:** 1

**Step:** 100

**Unit:** labels

#### Core inside diameter

**Key:** core

**Type:** select

**Default:** 76

**Options:**

##### 25 mm (1 in)

**Value:** 25

##### 40 mm (1.5 in)

**Value:** 40

##### 76 mm (3 in)

**Value:** 76

#### Label plus liner thickness

**Key:** thickness

**Type:** number

**Default:** 160

**Min:** 40

**Max:** 500

**Step:** 5

**Unit:** microns

**Help:** Total caliper of face stock, adhesive and liner.

#### Maximum roll diameter allowed

**Key:** max_od

**Type:** number

**Default:** 200

**Min:** 50

**Step:** 5

**Unit:** mm

**Help:** Printer or applicator unwind limit.

**Outputs:**

#### Label pitch

**Key:** pitch

**Expr:** label_len + gap

**Format:** decimal

**Description:** Length plus gap, in millimetres.

#### Rows per roll

**Key:** rows

**Expr:** ceil(labels_roll / across)

**Format:** integer

#### Roll length

**Key:** roll_m

**Expr:** rows * pitch / 1000

**Format:** decimal

**Primary:** true

**Description:** Metres of web on the roll.

#### Outer diameter

**Key:** od

**Expr:** sqrt(core * core + 4 * rows * pitch * (thickness / 1000) / pi)

**Format:** decimal

**Primary:** true

**Description:** Millimetres, from the area of the wound spiral.

#### Max rows at diameter limit

**Key:** max_rows

**Expr:** floor(pi * (max_od * max_od - core * core) / (4 * (thickness / 1000)) / pitch)

**Format:** integer

#### Max labels per roll

**Key:** max_labels

**Expr:** max_rows * across

**Format:** integer

**Primary:** true

#### Within diameter limit (1 = yes)

**Key:** fits

**Expr:** if(lte(od, max_od), 1, 0)

**Format:** integer

**Chart:**

#### Roll outer diameter (mm) versus labels per roll

**Type:** line

**X:** labels_roll

**From:** 500

**To:** 5000

**Steps:** 30

**Series:**

- od

**Disclaimer:** Winding tension, backing paper compression and splice tape change real diameter by a few percent. Test one roll before committing a long run.

## Content

**Intro:** Label converters, packaging plants and warehouses need to know how long a roll is and how large it will be before they order labels or set a printer. This calculator uses the area of the wound spiral to give roll length, outer diameter and the most labels that will fit under a diameter limit.

**Sections:**

#### How to use the calculator

**Body:** Enter the label length in the feed direction and the gap between labels. Add the number across the web, the labels per roll you want and the core inside diameter. Enter the combined thickness of face stock, adhesive and liner in microns. The calculator gives pitch, rows per roll, roll length in metres, the outer diameter, and the maximum labels per roll that fit under your printer or applicator diameter limit. The chart shows how quickly diameter grows as you add labels.

**Bullets:**

- Pitch is label length plus gap
- Thickness is total laminate, not just face stock
- Use the printer's rated maximum roll diameter
- Common cores: 25, 40 and 76 mm

#### The formula behind roll diameter

**Body:** A wound roll is a spiral whose cross-sectional area equals the web length times its thickness. The area between core and outside is pi/4 x (OD squared minus core squared). Setting the two equal gives OD = sqrt(core squared + 4 x length x thickness / pi), with length and thickness in the same unit. Solving the other way gives the maximum length for a limit diameter. Because it ignores air between wraps and tension, treat the answer as accurate to a few percent. The calculator works in millimetres and converts microns for you.

#### Worked example and reading the result

**Body:** A 100 mm label with a 3 mm gap, one across, 1,000 labels on a 76 mm core and 160 micron laminate gives a 103 mm pitch, a 103 m roll and an outer diameter near 164 mm. With a 200 mm printer limit the same material fits about 1,630 labels. If the result exceeds your limit, reduce labels per roll or order a thinner liner. For high-speed applicators, also check weight and splice rules agreed with your label supplier.

#### Common mistakes

**Body:** People often use label length without the gap, quote thickness of face stock only, or forget that labels across the web share the same row. Another is ordering the wrong core size for a printer hub, which stops a roll loading at all. In an ERP, keep labels per roll, core and unit of measure on the item so purchase quantities convert correctly between rolls, labels and metres.

**Bullets:**

- Include the gap in the pitch
- Count rows, not labels, along the web
- Check core and hub fit
- Convert purchasing UoM between rolls and labels in the item master

**Cta:** If label rolls, UoM conversions and reorder points are painful in your ERP, we can build an agent that reads item masters and flags conversion mismatches. A short review is available on request.

**Faq:**

#### How do I calculate label roll length?

**Answer:** Multiply the number of rows per roll by the label pitch, which is label length plus gap, then divide by 1,000 for metres. If you have several labels across the web, rows are labels per roll divided by the number across.

#### How do I calculate the outside diameter of a label roll?

**Answer:** Use OD = square root of (core diameter squared plus 4 x web length x thickness divided by pi), with all values in millimetres. Thickness is the combined face stock, adhesive and liner caliper, expressed in millimetres.

#### What core size do I need?

**Answer:** It depends on the printer or applicator. Desktop and small thermal printers often use 25 mm or 40 mm cores, while industrial printers and many converters use 76 mm. Always check the printer's hub specification before ordering.

#### Why is my real roll bigger than calculated?

**Answer:** Winding tension, entrapped air, splices and liner variation add diameter. A small allowance of a few percent is normal. Measure a sample roll from your supplier and calibrate the thickness input to match.

## Search terms

label roll length calculator, label roll diameter calculator, labels per roll calculator, roll outer diameter formula, how many labels on a roll, label core size, thermal transfer label roll size, label metres per roll

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