Walden's Paper Catalog Online Directory Walden's Paper Catalog  - The Authority on Paper
Home

|

Search Paper Catalog

|

Industry Standards

|

Glossary

|

F.A.Q.

|

About Us

|

Advertise

|

Help

|

Subscribe!
 North America's #1 Resource for Paper Grade and Company InformationTuesday, October 21, 2014
Quick Sign InQuick Sign In
User Name
Password
Remember Me

Forget your password?

Subscribe Today!

Walden-Mott Corp. - Owner of Walden's Paper Catalog and related directories.
spacer
Back to Industry Standards

Formulas, Weights and Measures

This chapter sets forth formulas and tables that may be used to determine the relationship of various weights, sizes and thicknesses of paper. The text is divided into the following sections.

  • Basis Weights
  • Weight of Sheets of Various Dimensions
  • Bulk of Sheets of Various Weights and Calipers
  • Economical Use of Paper Sizes
  • Weight and Square Footage of Rolls

Basis Weights

The weight of a given square area of paper is called its basis weight. This measure could have been established as the weight of 1000 square feet, or some other convenient dimension. In countries using the metric system of measurement, it is shown in grams per square meter.

However, historically, the U.S. paper industry linked the weight to a ream (500 sheets) based on the most suitable size of the type paper involved. For example, the dimension of 17" x 22" (four sheets of 8 1/2 x 11") was established for writing papers. The dimensions used to state the basis weight for various types of paper are as follows:

Dimensions

Square Inches
in one sheet

Writing Paper 17" x 22" 374
Printing Paper 25" x 38" 950
Cover 20" x 26" 520
Printing Bristol 22 1/2" x 28 1/2" 641
Index Bristol 25 1/2" x 30 1/2" 778
Newsprint, Tag & Tissue 24" x 36" 864

The following table shows the equivalent weights of various types of paper based on the respective dimensions used.

 

    BOND  17" x 22"

  PRINTING  25" x 38"

COVER  20" x 26"

BRISTOL
22 1/2" x 28 1/2"

INDEX
25 1/2" x 30 1/2"

NEWSPRINT, TAG
& TISSUE

 24" x 36"


BOND
LEDGER
MIMEO
DUPLICATOR
WRITINGS

13
16
20

33
41
51

18
22
28

22
27
34

27
38
42

30
37
46

24
28
32

61
71
81

33
39
45

41
48
55

50
58
67

56
64
74

36
40
44

91
102
112

50
56
61

62
69
75

75
83
92

83
93
102




BOOK
OFFSET
TEXT

12
16
18

30
40
45

16
21
24

20
27
30

25
32
37

27
36
41

20
24
28

50
60
70

27
32
38

34
40
47

41
49
57

45
55
64

31
35
39

80
90
100

43
48
54

54
60
67

66
74
81

73
82
91

47
59

120
150

65
80

80
100

98
123

109
136



COVER

29
36
43

73
91
110

40
50
60

49
62
74

60
75
90

66
82
100

47
58
65
72

119
146
164
183

65
80
90
100

80
99
111
124

97
120
135
150

108
134
149
166


MILL
BRISTOL

58
70
82

148
176
207

81
97
114

100
120
140

121
146
170

135
162
189

93
105
117

237
267
296

130
146
162

160
180
200

194
218
243

216
242
269

PRINTING
BRISTOL

52
59
71
83
95

133
151
181
211
241

73
83
99
116
132

90
102
122
143
163

109
123
148
173
198

121
137
165
192
219

INDEX
BRISTOL

43
53
67

110
135
170

60
74
93

74
91
115

90
110
140

100
122
156

82
105

208
267

114
146

140
182

170
220

189
244



TAG

43
54
65

110
137
165

60
75
90

74
93
111

90
113
135

100
125
150

76
87
109
130

192
220
275
330

105
120
151
181

130
148
186
222

158
180
225
270

175
200
250
300

Weights of Sheets of Various Dimensions

The weight of any size sheet is equal to the ratio of its square area to the square area of the base size for that type paper.

For example:

Assume that the sheet of interest is 70 lb. printing paper in the size 42" x 58".

As noted previously, the size on which the 70 lb. basis weight is based is 25" x 38". The square area of the basic size is equal to 25" x 38" = 950 square inches.

Determine the square area of the sheet of interest
42" x 58" = 2436 square inches.

Divide the square area of the sheet of interest by the square area of the base —
2564 by 950 =2.564

Since the 42" x 58" sheet is 2.564 times bigger than the 25" x 38", it must weigh that much more. Therefore, multiply 70 lbs. by 2.564 to determine the weight of 500 sheets 42" x 58".

70 x 2.564 = 179 lbs.

If the weight for 1000 sheets is desired, multiply the 500 sheet weight by 2.

Tables showing the weight per thousand sheets of the various types of printing and writing papers are provided on the following three pages.

PRINTING PAPERS—Weights Per M Sheets
                                                                         
Basis 25" x 38"

BASIS

30

35

40

45

50

60

70

80

90

100

120

150

17-1/2 x 22-1/2

25

29

33

37

41

50

58

66

75

83

99

124

19 x 25

30

35

40

45

50

60

70

80

90

100

120

150

23 x 29

42

49

56

63

70

84

98

112

126

140

169

 

23 x 35

51

59

68

76

85

102

119

136

152

170

204

 

22-1/2 x 35

50

58

66

75

83

99

116

133

149

166

199

249

24 x 36

54

64

72

82

90

110

128

146

164

182

218

272

25 x 38

60

70

80

90

100

120

140

160

180

200

240

300

26 x 40

66

76

88

98

110

132

154

176

198

218

262

328

28 x 42

74

86

100

112

124

148

174

198

222

248

298

372

28 x 44

78

90

104

116

130

156

182

208

234

260

312

390

30-1/2 x 41

78

92

106

118

132

158

184

210

236

264

316

396

32 x 44

88

104

118

134

148

178

208

238

266

296

356

444

33 x 44

92

106

122

138

152

184

214

244

276

306

366

460

35 x 45

100

116

132

150

166

198

232

266

298

332

398

498

36 x 48

108

128

144

164

180

220

254

292

328

364

436

544

38 x 50

120

140

160

180

200

240

280

320

360

400

480

600

41 x 54

140

164

186

210

234

280

326

372

420

466

560

700

44 x 64

178

208

238

266

296

356

414

474

534

592

712

888

35 x 46

102

118

136

152

170

204

238

272

306

338

406

 

38 x 52

124

146

166

188

208

250

292

332

374

416

500

 

41 x 61

156

184

212

236

264

316

368

420

472

528

632

 

42 x 58

154

180

206

230

256

308

358

410

462

512

615

 

44 x 66

178

208

238

266

296

356

414

474

534

592

712

 

46 x 69

201

234

267

301

334

400

468

534

602

668

802

 

52 x 76

250

292

332

374

416

500

582

666

748

832

998

 

BONDS and WRITING PAPERS—Weights Per M Sheets
                                                                        
Basis 17" x  22"

BASIS

13

16

20

24

28

32

36

40

44

8-1/2 x 11

6.50

8.00

10.00

12.00

14.00

16.00

18.00

20.00

22.00

8-1/2 x 13

7.68

9.44

11.81

14.18

16.54

18.90

21.27

23.63

26.00

8-1/2 x 14

8.26

10.18

12.72

15.26

17.81

20.36

22.90

25.45

28.00

11 x 17

13.00

16.00

20.00

24.00

28.00

32.00

36.00

40.00

44.00

16 x 21

23-1/2

29

36

43

50-1/2

57-1/2

65

72

79

16 x 42

47

58

72

86

101

115

130

144

158

17 x 22

26

32

40

48

56

64

72

80

88

17-1/2 x 22-1/2

27

34

42

51

59

67

76

84

93

17 x 26

31

38

47

57

66

76

85

95

104

17 x 28

33

41

51

61

71-1/2

81-1/2

92

102

112

18 x 23

29

35-1/2

44-1/2

53

62

71

80

89

97-1/2

18 x 46

58

71

89

106

124

142

160

178

195

19 x 24

32

39

49

58-1/2

68-1/2

78

88

98

107

20 x 28

39

48

60

72

84

96

108

120

132

21 x 32

47

58

72

86

101

115

130

144

158

22 x 25-1/2

39

48

60

62

84

96

108

120

132

22 x 34

52

64

80

96

112

128

144

160

176

22-1/2 x 22-1/2

35

43

54

65

76

87

97

108

119

22-1/2 x 34-1/2

54

66

83

99

116

133

149

166

183

22-1/2 x 35

56

67

84

101

118

134

152

168

186

23 x 36

58

71

89

106

124

142

160

178

195

24 x 38

64

78

98

117

137

156

176

196

214

24-1/2 x 24-1/2

42

51-1/2

64

77

90

103

116

128-1/2

141

24-1/2 x 28-1/2

49

60

75

90

105

119-1/2

134-1/2

149-1/2

164-1/2

24-1/2 x 29

49-1/2

61

76

91

106-1/2

122

137

152

167

24-1/2 x 38-1/2

66

81

101

121

141-1/2

161-1/2

182

202

222

24-1/2 x 39

66

82

102

122

144

164

184

204

225

25-1/2 x 44

78

96

120

144

168

192

216

240

264

26 x 34

62

76

94

114

132

152

170

189

208

28 x 34

66

82

102

122

143

163

184

204

224

34 x 44

104

128

160

192

224

256

288

320

352

35 x 45

109

135

168

202

236

270

303

337

371

COVER PAPER—Weights Per M Sheets
                                                                          
Basis 20" x 26"

BASIS

50

60

65

80

90

100

130

20 x 26

100

120

130

160

180

200

260

22-1/2 x 28-1/2

123

148

160

197

222

246

320

23 x 29

128

154

167

205

231

256

334

23 x 35

155

186

201

248

279

310

402

26 x 40

200

240

260

320

360

400

520

35 x 46

310

372

402

496

558

620

804

INDEX BRISTOL—Weights Per M Sheets
                                                               
Basis 25-1/2" x 30-1/2"

BASIS

90

110

140

170

220

20-1/2 x 24-3/4

117

144

182

222

286

22-1/2 x 28-1/2

148

182

230

280

362

22-1/2 x 35

182

223

284

344

444

25-1/2 x 30-1/2

180

220

280

340

440

28-1/2 x 45

296

364

460

560

724

PRINTING BRISTOL—Weights Per M Sheets
                                                                        
Basis 23" x 35"

BASIS

47

80

100

120

22-1/2 x 28-1/2

134

160

200

240

23 x 35

168

201

252

302

26 x 40

216

260

TAG—Weights Per M Sheets
                                                                         
Basis 24" x 36"

BASIS

90

100

125

150

175

200

250

22-1/2 x 28-1/2

134

148

186

223

260

297

371

24 x 36

180

200

250

300

350

400

500

28-1/2 x 45

268

296

372

446

520

594

742

Bulk of Sheets of Various Weights and Calipers

The thickness of the sheet can be an important factor in the production, delivery and use of paper. This property influences the strength of the sheet and the height formed when a series of sheets are placed top of each other.

This section presents procedures and tables that may be used to determine the bulk of papers of interest to the reader.

Bulk Determination

Micrometer
Reading

Pages Per
Inch

Micrometer
Reading

Pages Per
Inch

Micrometer
Reading

Pages Per
Inch

.007

1142

.019

420

.031

258

.0075

1066

.0195

410

.0315

254

.008

1000

.020

400

.032

250

.0085

942

.0205

390

.0325

246

.009

888

.021

380

.033

242

.0095

842

.0215

372

.0335

238

.010

800

.022

364

.034

234

.0105

762

.0225

356

.0345

232

.011

726

.023

348

.035

228

.0115

696

.0235

340

.0355

224

.012

666

.024

332

.036

222

.0125

640

.0245

326

.0365

218

.013

614

.025

320

.037

216

.0135

592

.0255

314

.0375

212

.014

570

.026

308

.038

210

.0145

552

.0265

302

.0385

208

.015

532

.027

296

.039

204

.0155

516

.0275

290

.0395

202

.016

500

.028

286

.040

200

.0165

484

.0285

280

.0405

198

.017

470

.029

276

.041

194

.0175

456

.0295

272

.0415

192

.018

444

.030

266

.042

190

.0185

432

.0305

262

.0425

188

TABLE OF APPROXIMATE BULKS

The table below indicates the approximate thickness of various papers in thousandths of an inch.

 

Basis

Thick-
ness

 

Basis

Thick-
ness

BOND
     17 x 22


9
13
16
20


.002
.0025
.003
.004

ENGLISH FINISH
     25 x 38


45
50
60
70


.0025
.0035
.004
.0045

BRISTOL (Plate)
     22-1/2 x 28-1/2


100
120
140
160
180


.008
.010
.012
.014
.017

INDEX
     20-1/2 x 24-3/4


58-1/2
72
91
111
143


.007
.008
.0105
.0135
.0175

BRISTOL (Antique)
     22-1/2 x 28-1/2


100
120
140
160
180


.012
.014
.016
.018
.020

LEDGER
     17 x 22


24
28
32
36
40
44


.004
.005
.00525
.00575
.0065
.007

COATED (Book)
     25 x 38


60
70
80
100
120


.003
.0035
.004
.0055
.006

OFFSET
     25 x 38


50
60
70
80
100
120


.004
.0045
.005
.006
.0075
.009

     

SUPER
     25 x 38

50
60
70

.0025
.003
.004

COATED COVER
     20 x 26


50
60
65
80
100


.00475
.006
.0065
.0075
.0095

TAG
     24 x 36


80
100
125
150
175
200
250
300


.006
.0075
.009
.011
.0125
.015
.018
.0225

COVER
     20 x 26


50
65
80
100
130


.007
.009
.0105
.0135
.018

TEXT
     25 x 38


60
70
80


.0045
.0065
.007

EGGSHELL
     25 x 38


50
60
70
80


.0045
.005
.006
.0065

VELLUM
     17 x 22


20
24
28
32
36
40


.004
.005
.006
.0065
.0075
.0085

CALIPER THICKNESS AND APPROXIMATE
WEIGHT OF BLANKS—
Based on size 22" x 28"


Ply


Caliper

Approximate Wt.
per 1000 sheets

Plain Blanks

3

.015

280

4

.018

330

5

.021

360

6

.024

420

8

.030

520

10

.036

600

Coated Blanks

3

.015

340

4

.018

420

5

.021

460

6

.024

530

8

.030

650

10

.036

760

Railroad Board

4

.018

400

6

.024

530

8

.030

650

Tough Check

3

.012

310

4

.018

430

6

.024

550

8

.030

680

Thick China

 

.011

300

COMPARISON OF BULK-TO-WEIGHT RATIO BETWEEN LIGHTWEIGHT PAPERS AND OFFSET

Ream Weight
25 x 38

Pages
Per Inch

24

Lightweight Printing

1184

45

Offset-Smooth Finish

588

30

Lightweight Printing

1030

50

Offset-Smooth Finish

533

35

Lightweight Printing

888

60

Offset-Smooth Finish

444

Q. How do you determine how many sheets of 6-ply blank will reach a height of 4 feet?

A. Divide the total height desired by the thickness of a single blank.

Example: The single-sheet caliper of 6-ply blank is 0.024.

Formula: 48"   = 48,000 = 2000 sheets
              0.024         24

Q. Which basis weight will most closely meet the publisher’s requirement if body of a 450-page book is to measure about one inch in thickness. Paper to be used is regular finish offset with average thickness of:

Basis Caliper
50 0.00375
60 0.00450
70 0.0050
80 0.0055

A. Basis 60

Formula: 1 450 =0044

                       2

Q. The case binding of a book is limited to 1 5/8". The number of pages, 560. What is the average caliper of each sheet?

A. 1 5/8" = 1.625" (decimal)  560 pages = 280 sheets
Divide the total thickness of the book by the number of sheets:

Formula: 1.625   =0.0058 (Avg. caliper of each sheet)
                 280

Q. If 4 sheets of a 25 x 38 - 60 lb. paper calipers 16 points, (.016 inches) how thick in inches would 248 pages be?

A. 0.496" or 1/2"

Q. Your customer orders 35" x 45" Basis 60, regular finish offset paper to be packed on skids, each to contain 30 reams in a single tier. You are aware that the plant cannot accommodate skid-heights in excess of 6 feet. The heights of the normal skid-runner is 9". How would you estimate the overall heights of the skid and load?

A. Solution: Basis 60, regular finish offset calipers .0045
30 reams - 500 x 30 = 15,000 sheets
thickness of 15,000 sheets is:
15,000 x .0045 or 67.5"

Total heights of the skid and load is:

Paper                          67.5"

Runner                          9.0" (standard)

Skid Floor & Top         3.00 (standard)

                                   79.5

Obviously, the height of the skid and load would exceed the limitation by 7.5". To be safe, reduce the heights of the load to 57.5". The estimated number of sheets to yield 57.5" will be:

57.5 or 57.000  or 12.777 sheets

.0045      4.5

This figure can be rounded to 13,000 sheets or 26 reams to the skid.

Q. How do you determine the bulking index of the basis weight of a sheet of paper when you know the bulking index of another basis weight of the same kind of paper?

A. Bulking Index = Single Sheet Thickness in Thousands
                                                 Basis Weight

Example: If a paper bulks six points (.006") for basis weight 24 x 38—50, its bulk for basis weight 25 x 38—65 will be:

Bulking index for 50 lb. = .006" =
                                            50

.0012" per lb.; .00012 x 65 = .0078" thickness for 25 x 38—65 lb. paper.

Economical Use of Paper Sizes

Economical use of printing papers is achieved by planning cut outs of the regular sizes of printing papers. In this planning, it is necessary to allow for the fact that all printed booklets must be trimmed after folding, and that is is advisable to allow for a small trim when printed folders are cut from a large sheet.

The following tabulation shows the commonly used finished folder and booklet sizes and the standard flat sheets of paper from which they are cut. The finished units can be printed in the multiples listed on standard printing equipment. They will fit into standard envelopes.

All but two of the printed units in the tabulation plan economically in multiples of 2,4,8,16 and 32 pages. With few exceptions, multiples of 6, 12, 20, 24, 28 and 40 pages do not fit most equipment or standard paper sizes.

A sound planning procedure is to strive to plan books and booklets in multiples of 8, 16, and 32  for the sake of economy.  See below.

How to figure cutting of pieces from sheets.

How many pieces 6 x 9 cut from 25 x 38?

Formula: Divide Vertically   Divide Diagonally
                     25 x 38                    25 x 38
                       6     9                       6    9
                        4 x 4—16 out          6 x 2—12 out

6 x 9 and/or 9 x 12 cuts from — 19 x 24, 25 x 38, 38 x 50;
all standard paper sizes.

How many 5 x 8 pieces can be cut from a 25 1/2 x 30 1/2 sheet?

Formula: Divide Vertically     Divide Diagonally
                 25 1/2 x 30 1/2         25 1/2 x 30 1/2
                    5         8                        5           8
                    5          3—15 out          6           3—18 out

5 1/2 x 8 1/2 and/or 8 1/2 x 11 cut from:

17 x 22
22 x 34
22 1/2 x 35
25 1/2 x 30 1/2
34 x 44 or 35 x 45
all standard paper sizes

3 1/2 x 5 1/2, 4 x 6 and/or 5 x 8 cut from

22 1/2 x 28 1/2
25 1/2 x 30 1/2
all standard paper sizes

NOTE- When grain of the “piece” size is important, the grain of the standard sheet size must match—for instance 6 x 9 - grain 9;  25 x 38 - grain 38; 6 x 9 - grain 6; 25 x 38 - grain 25.

Weight and Square Footage Content of Rolls

This section explains how to determine the weight and number of square feet in a roll of paper. It also provides a table and formula concerning the weight lost when outer layers of the roll are removed (slabbed off).

Estimating the weight of a roll of paper.

The approximate weight of a roll of paper may be obtained from the following formula:

                                      a = (b2-c2) de

in which,

a — weight of the roll in pounds
b — diameter of the roll in inches
c — diameter of the core in inches
d — width of the roll in inches
e — factor given in the table below

FACTORS

Antique Finish  .018 Regular offset .022 Supercalendered .028
Vellum Offset .020 Machine Finish .026 Coated 1 Side .030
Bond Paper  .021 E.F. Book .027 Coated 2 Sides .033

Problem: To find the weight of a roll of antique paper, 40 inches in diameter, 50 inches wide, wound on a 3 inch core.

Answer: Weight of Roll = (402-32) x 50 x .018

                                        = (1600 - 9) x 50 x .018

                                        = 1591 x 50 x .018

                                        = 1432 lbs.

Determining the number of feet in a roll.

The approximate linear footage in a roll of paper may be obtained from the following formula:

Linear feet =Weight of roll (lbs.) x Basic size (L x  W) x 500
                         Width of roll (in.) x 12 in. x  basis weight

Example: A roll of Book paper, basis 25 x 38—55 lb., 40" wide weighs 2,000 lbs.  Therefore:

Linear feet = 2,000 lbs. x *25 x 38 x 500 = 950,000,000
                          40 in. x 12 in. x 55 lb.             26,400

Linear feet = 35,985

NOTE: The above footage is based on an exact basis weight of 55 lb. Under actual conditions the basis weight may vary slightly above or below the given weight. If the actual basis weight is slightly higher than 55 lb., the footage will be slightly under 35,985 feet and vice versa.

*Book paper 25 x 38 (950). Other Basic sizes:

Bond & Writing 17 X 22 (374)

Printing Bristol 22 1/2 x 35 (788)

Cover 20 x 26 (520)

Tag, Newsprint 24 x 36 (864)

Index 25 1/2 x 30 1/2 (778)

Vellum Bristol 22 1/2 x 28 1/2(641)

Calculating weight-loss of paper in rolls.

Percentage weight-loss for various thicknesses of paper slabbed from a roll can be calculated by using this equation:

Key: D original roll diameter in inches

        S thickness of slab removed in inches

        400 faction

% weight-loss = 400(DS - S2)

                                D2

Example: a 2-inch slab is removed from a 38" diameter roll weighing 2,100 pounds

% weight-loss = 400 (38 x 2-22) = 38

                           400 76-4 = 19.95%

                                 1,444

The weight-loss is 0.1995 x 2,100 or 419 pounds

Weight Loss Calculation Table

Percent of Roll Weight
Loss from Various Original
Roll Diameters (inches)

Slab Thickness
(inches)*


36"


37"


38"


39"


40"

1/8

1.38%

1.35%

1.31%

1.28%

1.25%

1/4

2.76

2.68

2.61

2.55

2.50

1/2

5.48

5.33

5.19

5.06

4.94

3/4

8.16

7.94

7.74

7.54

7.36

1

10.80

10.52

10.25

9.99

9.75

1 1/2

15.97

15.56

15.17

14.53

14.44

2

20.99

20.45

19.95

19.46

19.00

2 1/2

25.85

25.20

24.58

24.00

23.44

3

30.56

29.80

29.09

28.40

27.75

3 1/2

35.11

34.26

33.45

32.68

31.94

4

39.51

38.57

37.67

36.82

36.00

4 1/2

43.75

42.73

41.76

40.83

39.94

5

47.84

46.75

45.71

44.71

43.75

5 1/2

51.77

50.62

49.52

48.45

47.44

6

55.56

54.35

53.19

52.07

51.00

    * Starting from original diameter

 

Site Map | Contact UsCopyright 2008 Walden-Mott Corp. Terms Of Use | Privacy Policy