PaperCatalog.com - Formulas, Weights and Measures

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
COVER	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
MILL BRISTOL	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
INDEX BRISTOL	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
TAG	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 ÿ 450 =0044

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)

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