# How is the paper weight measured

## Paper - mass and thickness

### Basis weight and sheet weight

The basis weight, also known as basis weight, square meter weight or grammage, is the mass of a square meter of paper in grams, i.e. it is specified in the unit g / m².

With the help of the area weight, the mass of each arch and each number of arches can be calculated: The area of the arch in square meters is multiplied by the area weight and, if necessary, the number of arches.

**Example:** What is the mass of 200 sheets in the format 50 cm × 70 cm, area mass 80 g / m²?

First the area of the arch is calculated in square meters. The easiest and safest way to do this is to convert the lengths of the sides of the sheet into the unit of meters in advance.

50 cm: 100 cm / m = 0.5 m

70 cm: 100 cm / m = 0.7 m

0.5m x 0.7m = 0.35 m²

Then the area of the arc is multiplied by the basis weight:

0.35 m² x 80 g / m² = 28 g

Finally, multiply by 200 (arcs):

28 g x 200 = 5600 g

All calculation steps summarized:

0.5m x 0.7m x 80 g / m² x 200 = 5600 g

If the mass is larger, the result can be converted into the unit kilogram (= 1000 g) or ton (= 1000 kg = 1 000 000 g).

### Standard formats

For standard formats of the A series according to DIN EN ISO 216, sheet or sheet dimensions can be calculated using a simpler method. While the results are not entirely accurate, they are usually reasonably accurate for practical purposes.

The A0 sheet has an area of almost exactly one square meter (841 mm × 1189 mm = 999 949 mm²). All smaller formats in series A are created by dividing format A0. To find out how many sheets or sheets of the smaller format correspond to an A0 sheet, a power is formed with the base number 2 and the format class number as an exponent.

**Example:** How many A4 sheets correspond to an A0 sheet?

24 = 16

To find the mass of a sheet or sheet, divide the mass of one square meter (A0-sheet) by this power. If there is more than one sheet or sheet, the number is then multiplied.

**Example:** What is the mass of 500 A4 sheets, 80 g / m² per unit area?

80 g: 24 500 = 80 g: 16 500 = 5 g 500 = 2500 g

The exact calculation with the edge lengths of the A4 format (210 mm × 297 mm) produces a slightly different result:

0.210 m ∙ 0.297 m ∙ 80 g / m² ∙ 500 = 2494.8 g

### Thickness and (specific) volume

The specific volume has the unit cm³ / g, so it indicates the volume in cubic centimeters of a gram of paper. In practice, the specific volume of the paper is usually called “volume” for short and is given without a unit, i.e. like a ratio.

The sheet thickness in micrometers (µm) is calculated by multiplying the basis weight in grams per square meter by the volume.

**Example:** What is the thickness in micrometers of a sheet of paper with a basis weight of 80 g / m² and a volume of 1.6?

(80 x 1.6) µm = 128 µm

To calculate the sheet thickness in millimeters, the product of the area weight and volume is divided by 1000.

**Example:** What is the thickness in millimeters of a sheet of paper with a basis weight of 80 g / m² and a volume of 1.6?

(80 x 1.6: 1000) mm = 0.128 mm

To calculate the height of a stack of paper, the sheet thickness is multiplied by the number of sheets or sheets.

**Example:** What is the height in millimeters of a stack of 2500 sheets of paper with a basis weight of 70 g / m² and a volume of 1.2?

(70 x 1.2: 1000 x 2500) mm = 210 mm

Volume is determined by dividing the thickness of the paper in micrometers (μm) by the basis weight in grams per square meter.

**Example:** A sheet of paper with a basis weight of 80 g / m² is 120 μm thick. Volume?

120 : 80 = 1,5

If the thickness is given in millimeters, it is multiplied by a factor of 1000 (1 mm = 1000 μm).

**Example:** A sheet of paper, basis weight 120 g / m², is 0.15 mm thick.

0,15 · 1000 : 120 = 1,25

### Exercises

**1** Please calculate the weight in grams in each case.

- One sheet, format 43 cm × 61 cm, weight per unit area 250 g / m²

- 100 sheets, format 70 cm × 100 cm, surface weight 60 g / m²

- 50 sheets A2, weight per unit area 130 g / m²

- 500 sheets of A5, weight 100 g / m²

**2** Please calculate the mass in each case in kilograms.

- 4000 sheets, format 64 cm × 90 cm, surface weight 90 g / m²

- 150 sheets, format 72 cm × 105 cm, surface weight 500 g / m²

- 7500 sheets A3, weight 80 g / m²

- 20,000 sheets of A6, weight per unit area 200 g / m²

**3** How thick is a sheet of paper?

Please state solutions in both micrometers and millimeters.

- Basis weight 70 g / m², volume 2

- Basis weight 240 g / m², volume 1.25

- Basis weight 110 g / m², volume 1.5

**4** Please calculate the volume of the paper in each case.

- Basis weight 100 g / m², sheet thickness 160 µm

- Basis weight 250 g / m², sheet thickness 300 µm

- Basis weight 90 g / m², sheet thickness 0.18 mm

- Basis weight 160 g / m², sheet thickness 0.2 mm

**5** A stack of cardboard contains 2000 sheets in the format 70 cm × 100 cm, surface weight 300 g / m², volume 1.25.

- What is the mass in kilograms of the pile?

- What is the height in centimeters of the stack?

**6** A book block has 360 pages in A5 format; Basis weight of the paper 80 g / m², volume 1.75.

- How thick (in millimeters) is the book block?

- What is its mass (in grams)? (Printing ink, glue and stitching thread are not to be taken into account)

**Solutions:** Please touch the gray area with the mouse pointer or your finger.

1 65.6 g 4200.0 g 1625.0 g (1621.6 g) 1562.5 g (1554.0 g)

2 207.36 kg 56.70 kg 75.00 kg (74.84 kg) 62.50 kg (62.16 kg)

3 140 µm 0.14 mm 300 µm 0.3 mm 165 µm 0.165 mm

4 1,60 1,20 2,00 1,25

5 420.00 kg 75.00 cm

6 25.2mm 450.0g (447.6g)

(The book block with 360 pages consists of 180 sheets of paper!)

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