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23Pre-press
1Computer to Film
1Barco
(1998) MegaSetter Plus Optics 600 Q
22Computer to Plate
4Agfa
(1998) Avantra 44 XT
(2001) VS4
(2008) Avalon N8-50E
(2011) Avantra 44S
10Heidelberg
(1999) Trendsetter 3230
(2000) Trendsetter 3244
(2001) Topsetter 102
(2003) Trendsetter 400 Quantum
(2005) Prosetter 102 SCL
(2005) Trendsetter 800 II
(2006) Suprasetter S74
(2007) Suprasetter A 52 / A 74
(2007) Suprasetter E105
(2007) Trendsetter 800-III Quantum
1Fuji
(2001) P 9600 II
2Kodak
(2003) ThermoFlex Wide II 5280
(2010) Magnus 800
1Creo
(2000) Lotem 800 V
2ECRM
(2003) Mako 4
(2005) Mako 8
Kodak
1Linotype Hell
(1995) Linotronic 560
1Screen
(2002) B1 8000
Barco
Others
308Presses
5Digital Printing
Web Press
5Sheet-fed
3Heidelberg
(1997), Quickmaster DI 46/4
(2000), QM 46-4 DI Plus
(2001), QM DI 46-4 Pro
2KBA
(2006), Genius 52-5+L
(2011), Genius 52-5 L UV
29Flexo Print
1Arsoma
(1999) EM280
1Comco
(2005) Proglide FLX 16
1Flexotecnica
(1989) 804 CR
5Gallus
(1997) T-250
(2005) EM 280-8
(2007) EM 280-5
(2007) Gallus EM 510 S
200 Screen Press
5Mark Andy
(1985) MA 830
(1996) MA 4150 8C
(2000) MA 2200 6C
(2002) MA 4200 8C
(2004) LP 3000 8C
1Massenzana
(1993) SL 100 EV 5
9Nilpeter
(1991) F 2400 - 5
(1994) F 3000 - 6
(1995) F 2400 - 6
(1996) B 300 - 6
(1997) F 2400 - 9
(1999) MO 3300 - 8
(2000) FA 3000
(2000) FA 3300
(2004) FA 4200 - 8
1Schiavi
(2002) Alpha 8 C
Solflex
1Uteco
(1989) RR 608
3Windmoeller & Hoelscher
(1988) Olympia 1478
(2002) W &H Novoflex CI - gearless
(2005) Primaflex CM
1Stellaflex
(1996) CL 8
274Offset Sheetfed
81 Color
8Heidelberg
(1971, 1973), Kord Grey 64
(1974) GTO 46
(1974) Sork
(1980) Kord 64
(1983) GTO 52 - 1+
(1985) GTO 52+
(1994) 52-1 N
(1996) GTO 52
Ryobi
362 Colors
16Heidelberg
(1988) MOZP-S
(1988) SM 102ZP
(1991) GTOZP 52+
(1993) MOZ-S
(1996) QM 46-2+
(1996) SM 52-2P
(1996) SM 74-2-P-H
(1997) SM 102-2-P
(1997) SM 102-Z
(1997) SM 74-2P
(1998) SORMZ
(2001) SM 52-2 SE
(2002) SM 74 2
(2003) SM 52-2+
(2005) PM 74-2-P
(2007) PM 74-2
12MAN Roland
(1994-1995) R 302
(1995) R 702 3B + LV
(1996) PRZ00-E+NP
(1997) R702 SW
(1998) R202 T
(2000) R202E TOB
(2001) R 302 HOB
(2002) 202 E
(2002) 202 TOB
(2004) R 702 P
(2006) R 702 3B P
(2007) R902-6 BP
5Ryobi
(1983) 522 HX
(1993) 522 PFH
(1996) 3302 M
(2001) 522 HXX
(2007) 522 HE
1Shinohara
(1990) Fuji Shinohara 52-2P
1KBA
(1998) Planeta Rapida 142-2 SW
1Komori Lithrone
(1990) SPRINT 228 I
1014 Colors
33Heidelberg
(1986) MOV-S
(1991) CD 102 V+L
(1991) SM 102 VP
(1994) GTOV S 52+
(1995) SM 74-4P+L
(1997) SM 102-4+L
(1997) SM 74-4-P3-H
(2000) CD 102-4+L UV
(2000) SM 52-4
(2000) SM 74-4
(2000) SM 74-4 3PH+L
(2002) CD 102-4+LX
(2002) SM 52-4P
(2003) CD 102-4
(2003) CD 102-4+L
(2003) GTO 52-4
(2003) SM-102-4-P3
(2004) GTO 52 4+
(2004) PM74 4P
(2004) SM 102-4P
(2005) SM 102-4P+L
(2005) CD 102-4 SE
(2005) CD 74-4+LX (C)
(2005) PM 52-4
(2005) PM 52-4-P
(2005) SM 102-4 P3 L
(2005) SM 52-4+LX
(2005) SM 74 4H
(2005) SM CD 102-4+LX
(2007) PM74-4
(2008) Rapida 106-4
(2008) SM 74-4 PH
(2008) SM 74-4H+L
24MAN Roland
(1982) R 804 7
(1986) R 804 6
(1992) R 204
(1992) R 604+LE
(1995) R 704
(1995) R 704 +L
(1995) R 804 5
(1996) R 304
(1996) R 704 3B
(1996) R 704 3B LV
(1998) R 704 P
(1999) R 704P 3B
(1999) R 704 3B SW
(2000) R 204 E
(2001) R 304 P
(2002) R 304+LV
(2002) R 904 6
(2003) R 904 7B
(2003) R 204 TOB
(2004) R 304 HOB
(2006) R 204 EOB
(2006) R 704+LV
(2007) R 504 HOB+L
RVFOB
15Ryobi
(1993) 524 H
(1997) 3304 H
(1997) 524 HX
(2000) 3304 HA
(2001) 3304 HA PCSF
(2001) 524 HXX
(2002) 754 S
(2002) 754 S4 D
(2006) 754 L
(2007) 524 HE
(2007) 684 ES
(2007) 754 WIDE
(2007) 754-SW-A
(2007) 784 E
(2009) 524 GX
1Sakurai
(2004) Oliver 472 ED2 + C
14KBA
(1994) Planeta Varimat 162 V48a-2
(1997) RA 104-4
(2000) R 162 - 4SW2
(2002) R 162a-4 PWVA
(2003) RA 105-4 SW2 PWHA
(2004) RA 105-4 SW
(2004) RA 105u-4 SW2
(2005) Karat 46
(2006) 162A-4 SW2
(2006) RA 105-4+SW-2-P40
(2007) RA 142-4 SW
(2008) Planeta 105 4CX
(2008) R 142-4 SW2
(2008) RA 106-4
7Komori Lithrone
(1990) L 428 EM
(1997) L 428 EM + L
(2001) L 420 B
(2001) L 428
(2001) L 428 ES
(2002) L 440
(2003) L 428 H
2Miller
(1985) TP 104 4P
(1991) TP 104 4
3Mitsubishi
(1993) 3F 4
(2000) 3H 4+LX
(2004) Diamond 3000S 4
2Shinohara
(2005) 52 IV P
(2007) 75 IV MP
865 Colors
20Heidelberg
(2005) SM CD 74-5
(1986) SM 102 FP+L
(1990) SM 102 F+L
(1990) SM 102-F
(1994) SM 72 FP
(1995) SM 74-5+L
(1996) SM 74-5P
(1997) SM 102 5-P
(1997) SM 52-5-P
(1998) SM 52-5P2
(2000) SM CD 74-5+LX (F)
(2002) SM CD 102-5+LX
(2002) SM CD 74-5+L (C)
(2005) SM CD 74-5P (C)
(2006) XL 105-5+LX
(2007) SM 74-5+L
(2008) SM CD 102-5
(2008) SM XL 75-5P (C)
(2011) SM XL 75-5+L-C
(2011) SM XL 75-5+LX (C)
11Komori Lithrone
(1990) L528
(1990) L544 C
(1991) L540
(1994) L526 ESA
(1997) L540 LX
(2000) L528 CX
(2000) LS529 EM
(2003) L528 EM
(2003) L540 SP
(2006) LS529 M
(2008) LS529 H
17MAN Roland
(2002) R 305 N
(1990) R 605 3B L
(1990) R 805 7B
(1994) R 705 3B+LV
(1998) R 905 6 + L
(2000) R 305 P HOB
(2000) R 705 LTTLV
(2000) R 705+LV
(2001) R 305 HOB E
(2001) R 305 P
(2002) R 705 3B P+LV
(2004) R 205 E OB
(2005) R 705
(2007) R 205 E
(2007) R 705 3B Hi Print
(2007) R 705+LV HiPrint
(2008) R 205 E OB+L
6Ryobi
(2008) 755-XLW-E
(2007) 525 GX
(2007) 755 W
(2008) 755 LX–XLW
(2010) 755 G+LX
(2010) R 925 D
25KBA
(1996) RA 104-5 L ALV CX PWHA
(1991) Planeta Varimat
(1992) RA 104-5 LX
(1994) RA 104-5 + L
(1994) RA 72-5 + L
(1994) RA 72-5+L ALV
(1994) RA 72-5+LX
(1997) RA 104-5
(1998) RA 105-5
(2000) RA 105-5-LX-CX
(2001) RA 74-5+LALV2 PWHA
(2002) RA 105-5 SW
(2002) RA 105-5+L+CX+UV
(2002) RA 74-5+L ALV
(2003) RA 105-5 SW
(2003) RA 105-5+L CX ALV2 PWHA
(2004) RA 105-5+L PWVA HYBRID
(2004) RA 74-5
(2006) Performa 74-5
(2007) RA 162a-5L CX PWVA-UV
(2008) Performa 74-5 SW2
(2008) RA 105-5+L ALV2 CX
(2008) RA 106 SIS-5 PWVA
(2008) RA 162a-5L ALV2 PWVA
(2011) RA 75E-5+L
1Adast
(2005) Adast 757
1Miller
(1987) TP 104 5 C
4Mitsubishi
(2006) D 3000 5 LS + C LX
(2006) D 3000 LS-5+L
(2007) D 3000 LS + LX
(2008) D 3000 S-5+TC+ED+SPC
1Shinohara
(2000) 74V
256 Colors
17Heidelberg
(1995) SM 74-6-H+L
(1990) SM CD 102 S+L
(1990) SM CD 102-6+L
(1990) SM CD 102-6-S
(1996) SM 74-6P
(1997) CD 102 6 LX LV
(1998) SM 74-6P2+L
(1998) SM 74-6 PH
(2001) SM 74-6+LX
(2001) SM CD 102-6
(2002) CD 102-6+LX
(2004) SM 102-6P
(2004/08) SM CD 102-6+LX-UV
(2005) SM XL 105-6+LX
(2006) SM CD 102-6+L SE
(2007) XL 105-6+LX
(2007) XL 105-6+LYYLX
2MAN Roland
(1990) R 606 + LE
(1994) R 706+TLV
3Komori Lithrone
(1991) Lithrone L640+C
(1999) Lithrone L626P
(2007) Lithrone LS629+C
3KBA
(2003) R 105-6+L SW2PVA
(2004) RA105U-6 SW
(2012) R 105-6 CX PWHA
Mitsubishi
17 Colors
1KBA
(1998) RA 142 - 7 SW1
38 Colors
1Heidelberg
(1998) SM 74 8P5
2KBA
(2003) Rapida 105-8SW
(2005) Rapida 105-8SW4 PWVA
1210 Colors
5Heidelberg
(1999) SM 102-10P6
(2001) SM 102 12-P7S
(2002) SM102-10-P6-S
(2005) SM CD 74-10P
(2007) XL 105 10 P
3Komori Lithrone
(2002) Lithrone SP 540
(2006) Lithrone LS1029P
(2007) Lithrone LS 1029
2MAN Roland
(1999) R 710
(2006) R710 P
2KBA
(2002/2009) RA 105U-10 SAPC SW5
(2005) Rapida 105-10 SW5 CX PWVA
212 Colors
2Heidelberg
(2002) SM102-12PS
(2006) CD 74-12-P-C
Web Offset
Akzidenz
Newspaper
Packaging
25Post-press
5Binding & Gluing
4Kolbus
(1988/95) Ratiobinder KM 470/25
(1998) Perfect Binding Line
(2000) KM 472 A
(2005) KM473 Ratiobinder Perfect Binding Line
1Wohlenberg
(2001) Quickbinder
2Collators
1Duplo
(1997) DC 10000
1Horizon
(1999) VAC-100a / SPF-20A
10Folders
1Heidelberg
(2006) Diana ECO 80
2Jagenberg
(1974/79) Diana 350
(1999) Diana 104-1
2Bobst
(1978) Farma 36
(1980) Domino 100-M
1Mueller Martini
(1999) Monostar 3016/21
1Sigloch
(2008) BLSD 60
1Stahl
(1990) T36/4K
1Sutter
(1991) Aida 82
1Vega
(1998) 100S
Others
Varnishing, Laminating & Foiling
7Guillotines
5Polar
(1990) 155 EMC-Monitor Autotrim
(1990) Mohr 137 EMC Monitor
(2001) Line Cutter
(2003) Pile Lift LW-1000-6
(2004) 92 X
1Schneider-Senator
(1998) 115 E-Line
1Wohlenberg
(2003) Cutter CUT-TEC 115
Inserting
Saddle Stichers
Sewing
1Sheeters
(1984) CSS - 71 10
Slitter & Rewinder
Stitching, Trimming
Book Produktion
12Packing Machinery
1Die Cutters
1Heidelberg
Die Cutter SBB
2Folders & Gluers
2Bobst
(1999) Media 68 II-A2
(2004) Cartonpack II
8Bag Making
2Holweg
(1980) CPZ4S / 72
(2000) RS 26
4Newlong
(1984) 335 T
(1985) 327 T
(1990) 127 T + 506 / H
(1991) SOS 345 T
2Windmüller & Hölscher
(1965) Triumph III B
Extra EX Type DM 521
Box Making
1Case Making
1Crathern
(1989) Casemaker
Corrugated Cardboards
   

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Standard paper sizes like ISO A4 are widely (>90%) used all over the world today. This text explains the ISO 216 paper size system and the ideas behind its design.

 

History of the ISO paper formats

 

The practical and aesthetic advantages of the sqrt(2) aspect ratio for paper sizes were probably first noted by the physics professor Georg Christoph Lichtenberg (University of Göttingen, Germany, 1742-1799) in a letter that he wrote 1786-10-25 to Johann Beckmann. After introducing the meter measurement, the French government published 1794-11-03 the "Loi sur le timbre" (no. 2136), a law on the taxation of paper that defined several formats that already correspond exactly to the modern ISO paper sizes: "Grand registre" = ISO A2, "grand papier" = ISO B3, "moyen papier" = ISO A3, "petit papier" = ISO B4, "demi feuille" = ISO B5, "effets de commerce" = ISO 1/2 B5.

The French format series never became widely known and was quickly forgotten again. The A, B, and C series paper formats, which are based on the exact same design principles, were completely independently reinvented over a hundred years after the "Loi sur le timbre" in Germany by Dr. Walter Porstmann. They were adopted as the German standard DIN 476 in 1922 as a replacement for the vast variety of other paper formats that had been used before, in order to make paper stocking and document reproduction cheaper and more efficient.

The DIN paper formats were soon also introduced in many other countries, for example, Belgium (1924), Switzerland (1929), Soviet Union (1934), Japan (1951), India (1957), United Kingdom (1959), Mexico (1965), France (1967), Australia (1974), Columbia and Kuwait (1975). Porstmann's DIN paper format system finally became both an international standard (ISO 216) as well as the official United Nations document format in 1975 and it is today used in almost all countries on this planet.

Note: The Lichtenberg Ratio – used by the standard paper format series – is occasionally confused with the Golden Ratio (which Euclid referred to as the "extreme and mean ratio"). The Lichtenberg Ratio is defined by the equation a/b = 2b/a = sqrt(2), whereas the Golden Ratio is defined by a/b = (a+b)/a = b/(a-b) = (1 + sqrt(5))/2. While aesthetically pleasing properties have been attributed to both, the Lichtenberg Ratio has the advantage of preserving the aspect ratio when cutting a page into two. The Golden Ratio, on the other hand, preserves the aspect ratio when cutting a maximal square from the paper, a property that seems not particularly useful for office applications. The Golden Ratio was for a while a more fashionable topic in the antique and renaissance arts literature and it has a close connection to the Fibonacci sequence in mathematics.

The ISO Standrad

 

In the ISO paper size system, the height-to-width ratio of all pages is the square root of two (1.4142 : 1). This aspect ratio is especially convenient for a paper size. If you put two such pages next to each other, or equivalently cut one parallel to its shorter side into two equal pieces, then the resulting page will have again the same width/height ratio.

 
A diagram demonstrating the sqrt(2) width/height ratio
 

The ISO paper sizes are based on the metric system. The square-root-of-two ratio does not permit both the height and width of the pages to be nicely rounded metric lengths. Therefore, the area of the pages has been defined to have round metric values. As paper is usually specified in g/m², this simplifies calculation of the mass of a document if the format and number of pages are known.

ISO 216 defines the A series of paper sizes based on these simple principles:

  • The height divided by the width of all formats is the square root of two (1.4142).
  • Format A0 has an area of one square meter.
  • Format A1 is A0 cut into two equal pieces. In other words, the height of A1 is the width of A0 and the width of A1 is half the height of A0.
  • All smaller A series formats are defined in the same way. If you cut format An parallel to its shorter side into two equal pieces of paper, these will have format A(n+1).
  • The standardized height and width of the paper formats is a rounded number of millimeters.

For applications where the ISO A series does not provide an adequate format, the B series has been introduced to cover a wider range of paper sizes. The C series of formats has been defined for envelopes.

  • The width and height of a Bn format are the geometric mean between those of the An and the next larger A(n-1) format. For instance, B1 is the geometric mean between A1 and A0, that means the same magnification factor that scales A1 to B1 also scales B1 to A0.
  • Similarly, the formats of the C series are the geometric mean between the A and B series formats with the same number. For example, an A4 size letter fits nicely into a C4 envelope, which in turn fits as nicely into a B4 envelope. If you fold this letter once to A5 format, then it will fit nicely into a C5 envelope.
  • B and C formats naturally are also square-root-of-two formats.

Note: The geometric mean of two numbers x and y is the square root of their product, (xy)1/2, whereas theirarithmetic mean is half their sum, (x+y)/2. For example, the geometric mean of the numbers 2 and 8 is 4 (because 4/2=8/4), whereas their arithmetic mean is 5 (because 5-2=8-5). The arithmetic mean is half-way between two numbers by addition, whereas the geometric mean is half-way between two numbers by multiplication.

By the way: The Japanese JIS P 0138-61 standard defines the same A series as ISO 216, but a slightly different B series of paper sizes, sometimes called the JIS B or JB series. JIS B0 has an area of 1.5 m², such that the area of JIS B pages is the arithmetic mean of the area of the A series pages with the same and the next higher number, and not as in the ISO B series the geometric mean. For example, JB3 is 364 × 515, JB4 is 257 × 364, and JB5 is 182 × 257 mm. Using the JIS B series should be avoided. It introduces additional magnification factors and is not an international standard.

The following table shows the width and height of all ISO A and B paper formats, as well as the ISO C envelope formats.

 
A Series Formats       B Series Formats     C Series Formats
 
4A0 1682 x 2378   66 1/4 x 93 5/8    
2A0 1189 x 1682   46 3/4 x 66 1/4    
A0 841 x 1189   33 x 46 3/4 B0 1000 × 1414     C0 917 × 1297
A1 594 x 841   23 3/8 x 33 B1 707 × 1000     C1 648 × 917
A2 420 x 594   16 1/2 x 23 3/8 B2 500 × 707     C2 458 × 648
A3 297 x 420   11 3/4 x 16 1/2 B3 353 × 500     C3 324 × 458
A4 210 x 297   8 1/4 x 11 3/4 B4 250 × 353     C4 229 × 324
A5 148 x 210   5 7/8 x 8 1/4 B5 176 × 250     C5 162 × 229
A6 105 x 148   4 1/8 x 5 7/8 B6 125 × 176     C6 114 × 162
A7 74 x 105   2 7/8 x 4 1/8 B7 88 × 125     C7 81 × 114
A8 52 x 74   2 x 2 7/8 B8 62 × 88     C8 57 × 81
A9 37 x 52   1 1/2  x 2  B9 44 × 62   C9 40 × 57
A10 26 x 37   1 x 1 1/2  B10 31 × 44   C10 28 × 40
 

Due to popular demand, I have prepared an unofficial table with the ISO sizes in inch fractions. Each listed inch fraction has the smallest denominator that keeps the value within the ISO 216 tolerance limits. Product designers should use the official millimeter values instead.

 
A Series Formats B Series Formats C Series Formats
4A0 66 1/4 × 93 5/8
2A0 46 3/4 × 66 1/4
A0 33 × 46 3/4 B0 39 3/8 × 55 3/4 C0 36 × 51
A1 23 3/8 × 33 B1 27 3/4 × 39 3/8 C1 25 1/2 × 36
A2 16 1/2 × 23 3/8 B2 19 3/4 × 27 3/4 C2 18 × 25 1/2
A3 11 3/4 × 16 1/2 B3 13 7/8 × 19 3/4 C3 12 3/4 × 18
A4 8 1/4 × 11 3/4 B4 9 7/8 × 13 7/8 C4 9 × 12 3/4
A5 5 7/8 × 8 1/4 B5 7 × 9 7/8 C5 6 3/8 × 9
A6 4 1/8 × 5 7/8 B6 4 7/8 × 7 C6 4 1/2 × 6 3/8
A7 2 7/8 × 4 1/8 B7 3 1/2 × 4 7/8 C7 3 3/16 × 4 1/2
A8 2 × 2 7/8 B8 2 1/2 × 3 1/2 C8 2 1/4 × 3 3/16
A9 1 1/2 × 2 B9 1 3/4 × 2 1/2 C9 1 5/8 × 2 1/4
A10 1 × 1 1/2 B10 1 1/4 × 1 3/4 C10 1 1/8 × 1 5/8
 

The allowed tolerances are ±1.5 mm for dimensions up to 150 mm, ±2 mm for dimensions above 150 mm up to 600 mm, and ±3 mm for dimensions above 600 mm. Some national equivalents of ISO 216 specify tighter tolerances, for instance DIN 476 requires ±1 mm, ±1.5 mm, and ±2 mm respectively for the same ranges of dimensions.

   

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