# Paper Roll Length, Weight and Run Time Calculator

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

## Short answer

Estimate how many metres, square metres and kilograms are on a roll and how long it runs on your press.

## Category

manufacturing

## Industry

Packaging and Printing

## Audience

- Press operator
- Warehouse planner
- Converter

## Tool

**Kind:** calculator

**Inputs:**

#### Roll outer diameter

**Key:** od

**Type:** slider

**Default:** 1000

**Min:** 200

**Max:** 1600

**Step:** 10

**Unit:** mm

#### Core outer diameter

**Key:** core

**Type:** select

**Default:** 76

**Options:**

##### 76 mm (3 in)

**Value:** 76

##### 152 mm (6 in)

**Value:** 152

##### 200 mm

**Value:** 200

##### 254 mm (10 in)

**Value:** 254

#### Roll width

**Key:** width

**Type:** number

**Default:** 1000

**Min:** 10

**Step:** 10

**Unit:** mm

#### Basis weight

**Key:** gsm

**Type:** number

**Default:** 80

**Min:** 5

**Step:** 1

**Unit:** g/m2

#### Caliper (thickness)

**Key:** caliper

**Type:** number

**Default:** 100

**Min:** 5

**Step:** 1

**Unit:** microns

#### Air entrainment in wound roll

**Key:** air

**Type:** number

**Default:** 3

**Min:** 0

**Max:** 50

**Step:** 0.5

**Unit:** %

**Help:** Winding adds air between layers, which makes the effective layer thicker.

#### Press speed

**Key:** speed

**Type:** number

**Default:** 150

**Min:** 1

**Step:** 5

**Unit:** m/min

**Outputs:**

#### Effective layer thickness

**Key:** eff

**Expr:** caliper * (1 + air / 100)

**Format:** decimal

**Description:** Microns, including air.

#### Roll length

**Key:** length

**Expr:** pi * (od * od - core * core) / (4 * eff / 1000) / 1000

**Format:** number

**Description:** Metres. Spiral formula: area of the annulus divided by layer thickness.

**Primary:** true

#### Roll area

**Key:** area

**Expr:** length * width / 1000

**Format:** number

**Description:** Square metres.

#### Roll net weight

**Key:** weight

**Expr:** area * gsm / 1000

**Format:** decimal

**Description:** Kilograms of paper, excluding core.

**Primary:** true

#### Run time at press speed

**Key:** run_min

**Expr:** length / speed

**Format:** minutes

**Chart:**

#### Roll weight vs outer diameter

**Type:** line

**X:** od

**From:** 300

**To:** 1500

**Steps:** 30

**Series:**

- weight

**Disclaimer:** Results assume uniform caliper and tension. Real rolls vary. Confirm with scale weights or the mill roll tag.

## Content

**Intro:** Rolls are bought by weight, scheduled by length and run by time. This calculator links all three from the geometry of the roll, so you can check a mill tag, plan a changeover or estimate how long a roll will last on press.

**Sections:**

#### How to use it

**Body:** Enter outer diameter, core diameter, width, basis weight and caliper. Add an air entrainment allowance if you know it, then the press speed. Roll length comes from the annulus area divided by the effective thickness of one layer. Area is length times width, weight is area times basis weight, and run time is length divided by speed. Use the slider to see how weight grows with diameter.

#### The formulas

**Body:** The wound layers form a ring between the core and the outer diameter. Its area is pi x (OD squared minus core squared) / 4. Divide that by the effective layer thickness to get length. Because weight scales with the square of diameter, a roll that is 10 percent larger in diameter holds roughly 20 percent more material. Basis weight in grams per square metre multiplied by area in square metres gives grams.

**Bullets:**

- Length = pi x (OD^2 - core^2) / (4 x thickness)
- Area = length x width
- Weight = area x basis weight
- Run time = length / speed

#### Common mistakes

**Body:** Mixing millimetres and metres is the usual problem, followed by using the core inner diameter instead of the outer. Calipers also vary by grade and calender setting. For films the same formula works with thickness in microns; basis weight is then thickness times density. Always allow for splices, leaders and waste when scheduling a roll to a specific job quantity.

**Bullets:**

- Use core outer diameter
- Measure caliper on the actual grade
- Subtract leader, splice and start-up waste from usable length
- Compare to the mill tag and update the air factor

**Cta:** We can connect roll geometry and remaining footage to your ERP inventory and work orders, so planners see accurate run times.

**Faq:**

#### Does weight include the core?

**Answer:** No. The result is net paper or film weight. Add the core weight and any wrapping to get gross weight for shipping or receiving checks.

#### How do I find caliper?

**Answer:** Take it from the mill certificate, a micrometer reading on a sample, or compute it as basis weight divided by apparent density. Use the thickness measured at roll winding conditions.

#### Why include air entrainment?

**Answer:** Air is dragged between layers as the web winds, so a wound roll is slightly bulkier than the sum of the layer thicknesses. A small percentage keeps the length estimate closer to reality.

#### Can I use this for plastic film?

**Answer:** Yes. Enter thickness in microns and set basis weight as thickness times density, for example 20 microns of polyethylene at 0.92 g/cm3 is about 18.4 g/m2.

## Search terms

paper roll length calculator, roll weight calculator from diameter, web roll footage calculator, paper roll run time calculator, roll diameter to length, film roll length from diameter and thickness, reel weight formula, basis weight gsm roll weight

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