# Blog

## Printer Math: Untangling the Confusing World of Converting and Calculating

Math. Let’s face it, if printers don’t have enough to juggle…ink types, paper types, cylinder pressure, drying times, tension and alignments…they have the whole challenge of understanding exactly how paper math works. There’s grammage and sheet sizes, calculating costs and shipping weights, working backward into converting rolls to sheets. While many industries have a standard measurement, the printing industry seems to like to keep things interesting. To make matters worse different regions use completely different formulas (we’re looking at you, USA)!

Whether it’s metric or MSI, basis weight or grammage, today we’re going to help you sort out the confusion and make sense of the mysterious world of printer math.

**MSI, Square ****Metres, Feet and Sheets – the building blocks of converting by area!**

If you’ve ever been to a print shop there’s a good chance you’ve heard people talk about the number of sheets required for a job or the length of a roll of material needed to produce labels. Working with sheets and roll length makes it easy to quickly calculate how much material you need based on the size of your print and cost to do so.

It’s pretty straight forward to calculate your costs when you know your cost per 320mm x 460mm sheet is $.65 and you need 100 sheets to print your job. 100 x $.65 each = $65.00……easy! But what happens if you want to change your sheet size? What if you don’t know how much material you’ll need for your labels, only your label size and quantity?

**Enter Square Metres and MSI!**

Perhaps the easiest way to work with any material in printing, whether you need to figure out the price for different size sheets or rolls, or how much material you need, is to convert it into the basic units of Square Metres (for metric) or MSI (for US measurements). Both of these units determine the surface area of a sheet/roll size for any given material. With these two basic units you can quickly convert to different size sheets, know how much usable material is on a roll, or figure out pricing no matter the size.

**Square Metre**

The metric system makes it incredibly easy to convert and calculate the costs of material regardless of size. It’s not uncommon to see material priced by the square metre because it’s just so simple to convert everything else! For those who don’t use metric, here’s a quick rundown:

*10 mm = 1 cm*

*100 cm = 1 metre*

*1 square metre = 10,000 square cm (100cm x 100cm)*

*(length(cm) x width(cm) ) / 10000 = area in square metres*

Pretty easy! That means if I have a sheet that’s 320mm x 450mm, each sheet is .144 square metres:

32cm x 45cm = 1440 square cm

1440/10000 = .144 square metres

Let’s look at a real-world example:

The material we need for this print job costs $3.25/square metre

We know that the sheet size we need to print on is 210mm x 297mm (21cm x 29.7cm)

How much does each sheet cost?

21cm x 29.7 cm = 623.7 square cm

623.7/10000 = .06237 square metres per sheet

.06237 square metres x $3.25 = $.203 per sheet

Here’s another example:

The material we have is $.65 per sheet for a 330mm x 460mm sheet (33cm x 46cm)

We need to know how this compares to the competitor’s material that costs $4.43/square metre

33cm x 46cm = 1518 square cm

1518/10000 = .1518 square metres per sheet

$.65/.1518 square metres = $4.28/square metre

Our current material is cheaper than the competitions!

**MSI**

In the USA, one of the most common measurements used in printing converting (especially when dealing with rolls) is the MSI. The MSI measurement stands for one thousand square inches and is used to convert roll pricing, sheet pricing, and other calculations. While it’s a bit different than using the metric system, it’s still a fairly straight forward calculation once you understand it.

*1 MSI = 1000 square inches*

*For sheets:*

*(Length (in) x Width(in) ) / 1000 = MSI per sheet*

*For rolls:*

*((Length (ft) x Width(in) x 12) / 1000 = MSI per rolls*

Example 1:

The material we are purchasing costs $1.55 per MSI and cuts into a 13in x 19in sheet (with no waste)

How much does each sheet cost?

13in x 19in = 247 square inches per sheet

247/1000 = .247 MSI per sheet

$1.55 x .247MSI = $.383/sheet

Example 2:

We need to convert a master roll of material into sheets and determine approximately how much each sheet costs

Each Master roll is 54 inches wide and 10,000 feet long and will be cut to 18×12 sheets

It costs $11,534.00/roll

Approximately how much will each finished sheet cost?

54in x 10,000 ft x 12 = 6,480,000 square inches per master roll

6,480,000 / 1000 = *6480 MSI per master roll*

$11,534 / 6480 = $1.78/MSI cost of material

12in x 18in = 216 square inches per sheet

216 / 1000 = *.216 MSI per sheet*

.216 MSI x $1.78 = *$.384/sheet*

**Grammage, Basis Weight, and Caliper: Understanding the difference in GSM, Basis Weight, M Weight and Thickness**

Now that we understand the basics of converting using roll or sheet size, it’s time to understand density and thickness. You can tell a lot about a material from the grams per square metre (GSM) or Basis Weight (such as 80lbs text). These measurements help determine critical information such as the quality of a material, or how much the print job will weigh when shipped.

When discussing grammage and thickness, there is one point that is commonly confused. GSM and Basis Weight are NOT the same as caliper or thickness. GSM and Basis weight measure the density of a material…the amount of material in a given area. These measurements are a good indicator of the quality of paper and of the relative thickness of a material. For example, standard copy paper might have a 75gsm weight, but a high-quality paper used in a corporate presentation might be 100gsm.

However, the GSM or basis weight does not give a good indication of the actual thickness of a material and it’s a common mistake made. For instance, a paper board that is 270microns thick (10.7 mil for US measurements) has a standard density of around 271gsm. A denser material, such as synthetic polyester, that is the same 270microns thick would have the density of around 365gsm. For this reason, it’s important to understand both Weight and Caliper calculations!

** **

**Understanding GSM**

When talking about how heavy or dense a material is, there are two common references. Grams per square metre (GSM) measures the weight in grams for any given material in one square metre.

Calculating the GSM for a material is pretty straight forward:

*GSM = Weight in Grams / Area in square metres*

Example:

A 320mm x 450mm (32cm x 45cm) sheet of polyester materials weighs 52.56 grams

What is the GSM?

32cm x 45cm = 1440 square cm per sheet

1440 / 10000 = .144 square m per sheet

52.56 grams / .144 square m = 365gsm

**Understanding Basis Weight**

In the US, many paper and material sellers will measure materials based on the Basis Weight instead of the GSM. This is primarily due to the fact that many US paper sizes don’t convert evenly to square metres, and as a result, creates a less direct measurement. The basis weight of any material is the weight of 500 sheets of a given size of material and is typically expressed in pounds and paper type, such as 80lbs Text or 100lbs Cover. What makes basis weight tricky is that it’s not a measure of the actual cut size of the sheet, but instead the weight of the uncut master, or basis, sheet size.

To calculate Basis Weight, you must know what the uncut master, or basis, sheet size is. Here are some common basis sizes in inches:

Bond Paper – 17 x20

Coated Cover C2S – 20×26

Tag – 24 x 36

Offset Text Paper – 25 x 38

Example: 80lbs C2S Cover means that 500 sheets of 20×26 material weighs 80lbs, regardless of the actual size of material being used.

Given the non-standardized sheet sizes, calculating and working in basis weight can be extremely confusing for someone not familiar with it.

Fortunately, converting from basis weight to GSM is easy!

*(Basis Weight x 1406.5) / Area of the Basis Sheet = GSM*

Example:

What is the GSM of 80lbs Text Weight Paper?

We know that Text Weight paper typically uses a basis size of 25in x 38in

80lbs x 1406.5 = 112,520

25in x 38in = 950 square inches per sheet

112,520 / 950 = 118.4gsm

**A Note on Caliper**

While GSM and basis weight measure the density of a material, to determine the actual thickness the two most common measurements are microns (metric) and mils (US). Converting these is easy once you understand the terminology:

1 mil = .001 inches

1 mil = 25.4 microns

1 point (pt) = 1 mil

Example:

The customer wants their postcards printed on 10 pt card stock

What thickness in inches, mil, and microns should we set our machine for?

10 pt = 10 mil

10mil x .001 in = .010 inches

10 mil x 25.4 microns = 254 microns

While printer math can seem daunting at times, these basic formulas can help get your materials squared away and converting done in no time! By using these same calculations not only can you determine sizes, cost, and materials needed, but you expand further into calculating things like shipping weight, number of sheets needed for a job, and price per unit!

Need more help with printer math or come across something we didn’t cover in this lesson? Feel free to reach out to the Kernow Team at __sales@kernowcoatings.com__ so we can help guide you through any questions you may have!

**Quick Reference:**

*1 MSI = 1000 square inches*

*1 square metre = 1.55 MSI*

*12×18 sheet = .216 MSI*

*13×19 sheet = .247 MSI*

*1 mil = .001 inches*

*1 mil = 25.4 microns*

*( Length(cm) x width(cm) ) / 10000 = area in square metres per sheet*

*( Length (in) x Width(in) ) / 1000 = MSI per sheet*

*( (Length (ft) x Width(in) x 12 ) / 1000 = MSI per roll*

*Weight in Grams / Area in square metres = GSM*

*(Basis Weight x 1406.5) / Area of the Basis Sheet = GSM*

* *

– The Kernow Coatings Sales Team