Screen diagonal

The screen diagonal is a measure of the size of a screen . It describes the distance between two diagonally opposite corners.

The indication of the screen diagonal is only useful to a limited extent. The advantage of a single measure compared to the common specification of width and height can only be used if all devices in a class have the same aspect ratio , as was common for televisions for a long time. Compared to specifying the image area, the diagonal has the advantage that it can be determined by a single measurement and without a calculation.

In advertising, the screen diagonal is often given in inches , especially for computer monitors and liquid crystal displays . See also dpi .

Use according to technique

With tube monitors (CRT), the screen diagonals are usually specified in two parts as a physical and visible screen diagonal, as part of the tube is always covered for technical reasons. If only one value is given, it usually refers to the physical diagonal.

As the size of tube monitors was not determined by the visible diagonal but by the overall size of the (partly invisible) tube, the comparison value compared to flat screens should generally be reduced by about 5 cm (2 inches). A 48 cm (19-inch) tube monitor corresponds roughly to a 43 cm (17-inch) TFT monitor .

Use by device class

TV

Commercially available television sets are predominantly in the range from 30 cm to 127 cm, with the largest classic tube sets only having a visible screen diagonal of around 85 cm. The specification is also applied to projection screens with higher values. The classic aspect ratio was 4: 3, but today's standard is 16: 9 devices.

In some smaller models, the line between television and computer monitor is also blurred. These models can be used both as a computer monitor (these then also have the usual connections for this) and as a television with remote control and integrated tuner . As a rule, these models are at least HD ready , but mostly capable of Full HD .

Computer monitors

Most computer monitors have a screen size between 48 cm and 71 cm (19 in to 28 in), with the demand for larger devices steadily increasing. Portable 18 cm to 38 cm (7 in to 15 in) and old 36 cm to 43 cm (14 in to 17 in) models are sometimes also smaller, while larger devices are also used for professional, graphics-oriented applications ( DTP , CAD ). Traditionally, the television aspect ratio of 4: 3 was common, but in addition to the more square 5: 4, wider formats such as 16: 9, 16:10, 15:10 (3: 2) are becoming more and more common because they correspond more to the natural field of vision of humans.

Small appliances

There are also devices with screen diagonals below 30 cm (12 in), e.g. B. cell phones, PDAs , hi-fi systems, etc., which do not have or need large displays for energy, space or price reasons.

geometry

Side lengths and area

Screen width and height depending on the diagonal

Typical screen sizes and geometry parameters in comparison

If the aspect ratio ( a: b , e.g. 4: 3 or 16: 9 ) is known, the side lengths ( w , h ) and the image area ( A ) can be calculated according to the Pythagorean theorem with the diagonal ( d ) :

${\displaystyle {\begin{aligned}w&={\tfrac {a}{\sqrt {a^{2}+b^{2}}}}\cdot d\\h&={\tfrac {b}{\sqrt {a^{2}+b^{2}}}}\cdot d\\A&={\tfrac {a\cdot b}{a^{2}+b^{2}}}\cdot d^{2}\end{aligned}}}$

For example, a 4: 3 screen with a 50 cm diagonal has a horizontal side of 40 cm (= ⁴ ⁄ ₅ 50 cm) and a vertical side of 30 cm (= ³ ⁄ ₅ 50 cm), thus an area of ​​12 dm² (= ¹² ⁄ ₂₅ × 2500 cm² = 40 cm × 30 cm).

pixel

If the resolution ( W = x , H = y ) is known, the size of a screen point ( P ) can be determined accordingly:

square pixels

${\displaystyle {\frac {W}{H}}={\frac {a}{b}}}$

${\displaystyle P_{x}=P_{y}={\frac {1}{\sqrt {W^{2}+H^{2}}}}\cdot d}$

general

${\displaystyle P_{x}={\frac {a}{{\sqrt {a^{2}+b^{2}}}\cdot W}}\cdot d}$

${\displaystyle P_{y}={\frac {b}{{\sqrt {a^{2}+b^{2}}}\cdot H}}\cdot d}$

${\displaystyle N_{P}=P_{x}\cdot P_{y}}$

Said screen with 50 cm diagonal would therefore with a resolution of 1280 × 960 px px (= 1.23 MPX) square pixels having a theoretical edge length of ⁵ / ₁₆ millimeters or 312.5 microns, which corresponds to 81.3 px / in (DPI).

If the diagonal is given, the image resolution ( R ), i.e. the number of dots per unit of length (e.g. dots per inch , dpi ), is obtained by an inverse operation:

square pixels

${\displaystyle {\frac {W}{H}}={\frac {a}{b}}}$

${\displaystyle R_{x}=R_{y}={\frac {\sqrt {W^{2}+H^{2}}}{d}}}$

general

${\displaystyle R_{x}={\frac {{\sqrt {a^{2}+b^{2}}}\cdot W}{a\cdot d}}}$

${\displaystyle R_{y}={\frac {{\sqrt {a^{2}+b^{2}}}\cdot H}{b\cdot d}}}$

In the case of two devices with different aspect ratios ( a ₁ : b ₁ and a ₂ : b ₂ ), the diagonals ( d ₁ and d ₂ ) must differ in order to display an image with the same height ( h ) or width ( w ):

same height

${\displaystyle h_{2}=h_{1}}$

${\displaystyle d_{2}=d_{1}\cdot {\frac {b_{1}}{b_{2}}}\cdot {\sqrt {\frac {a_{2}^{2}+b_{2}^{2}}{a_{1}^{2}+b_{1}^{2}}}}}$

same width

${\displaystyle w_{2}=w_{1}}$

${\displaystyle d_{2}=d_{1}\cdot {\frac {a_{1}}{a_{2}}}\cdot {\sqrt {\frac {a_{2}^{2}+b_{2}^{2}}{a_{1}^{2}+b_{1}^{2}}}}}$

Comparison table

The table is calculated from the diagonal and the aspect ratio. The lengths are rounded to one, the surfaces to two places. B = width, H = height, A = area

diagonal			4: 3 = 12: 9				16: 9				8: 5 = 16:10				5: 4 = 15:12				21: 9 = 7: 3
(in)	(cm)		B (cm)	H (cm)	A (dm²)		B (cm)	H (cm)	A (dm²)		B (cm)	H (cm)	A (dm²)		B (cm)	H (cm)	A (dm²)		B (cm)	H (cm)	A (dm²)
1	2.5		2.0	1.5	0.03		2.2	1.3	0.03		2.2	1.4	0.03		2.0	1.6	0.03		2.3	1	0.02
2	5.1		4.1	3.0	0.12		4.4	2.5	0.11		4.3	2.7	0.12		4.0	3.2	0.13		4.7	2	0.09
3	7.6		6.1	4.6	0.28		6.6	3.7	0.25		6.5	4.0	0.26		6.0	4.8	0.28		7th	3	0.21
3.5	8.9		7.1	5.3	0.38		7.7	4.4	0.34		7.5	4.7	0.36		6.9	5.6	0.39		8.2	3.5	0.29
4th	10		8.1	6.1	0.50		8.9	5.0	0.44		8.6	5.4	0.46		7.9	6.3	0.50		9.2	3.9	0.36
5	13		10	7.6	0.77		11	6.2	0.69		11	6.7	0.73		10	7.9	0.79		11.9	5.1	0.61
6th	15th		12	9.1	1.11		13	7.5	0.99		13	8.1	1.04		12	10	1.13		13.8	5.9	0.81
7th	18th		14th	11	1.52		15th	8.7	1.35		15th	9.4	1.42		14th	11	1.54		16.5	7.1	1.17
8th	20th		16	12	1.98		18th	10	1.76		17th	11	1.86		16	13	2.01		18.4	7.9	1.45
9	23		18th	14th	2.51		20th	11	2.23		19th	12	2.35		18th	14th	2.55		21.1	9.1	1.92
10	25th		20th	15th	3.10		22nd	12	2.76		22nd	14th	2.90		20th	16	3.15		23	9.8	2.26
10.1	26th		21st	15th	3.16		22nd	13	2.81		22nd	14th	2.96		20th	16	3.21		24	10	2.45
11	28		22nd	17th	3.75		24	14th	3.34		24	15th	3.51		22nd	17th	3.81		26th	11	2.84
12	30th		24	18th	4.46		27	15th	3.97		26th	16	4.18		24	19th	4.53		28	12	3.26
13	33		26th	20th	5.23		29	16	4.66		28	18th	4.90		26th	21st	5.32		30th	13	3.94
13.3	34		27	20th	5.48		29	17th	4.88		29	18th	5.13		26th	21st	5.57		31	13	4.19
14th	36		28	21st	6.07		31	17th	5.40		30th	19th	5.68		28	22nd	6.17		33	14th	4.69
15th	38		30th	23	6.97		33	19th	6.20		32	20th	6.52		30th	24	7.08		35	15th	5.23
15.4	39		31	23	7.34		34	19th	6.54		33	21st	6.88		31	24	7.46		36	15th	5.51
16	41		33	24	7.93		35	20th	7.06		34	22nd	7.42		32	25th	8.06		38	16	6.09
17th	43		35	26th	8.95		38	21st	7.97		37	23	8.38		34	27	9.10		40	17th	6.7
18th	46		37	27	10.0		40	22nd	8.93		39	24	9.39		36	29	10.2		42	18th	7.7
19th	48		39	29	11.2		42	24	9.95		41	26th	10.5		38	30th	11.4		44	19th	8.3
20th	51		41	30th	12.4		44	25th	11.0		43	27	11.6		40	32	12.6		47	20th	9.4
21st	53		43	32	13.7		46	26th	12.2		45	28	12.8		42	33	13.9		49	21st	10.2
22nd	56		45	34	15.0		49	27	13.3		47	30th	14.0		44	35	15.2		51	22nd	11.4
23	58		47	35	16.4		51	29	14.6		50	31	15.3		46	36	16.6		53	23	12.2
24	61		49	37	17.8		53	30th	15.9		52	32	16.7		48	38	18.1		56	24	13.5
25th	64		51	38	19.4		55	31	17.2		54	34	18.1		50	40	19.7		59	25th	14.8
26th	66		53	40	20.9		58	32	18.6		56	35	19.6		52	41	21.3		61	26th	15.8
27	69		55	41	22.6		60	34	20.1		58	36	21.1		54	43	22.9		63	27	17.2
28	71		57	43	24.3		62	35	21.6		60	38	22.7		56	44	24.7		65	28	18.3
29	74		59	44	26.0		64	36	23.2		62	39	24.4		58	46	26.5		68	29	19.8
30th	76		61	46	27.9		66	37	24.8		65	40	26.1		60	48	28.3		70	30th	20.9
32	81		65	49	31.7		71	40	28.2		69	43	29.7		63	51	32.2		74	32	23.8
34	86		69	52	35.8		75	42	31.9		73	46	33.5		67	54	36.4		79	34	27.0
37	94		75	56	42.4		82	46	37.7		80	50	39.7		73	59	43.1		86	37	32
40	102		81	61	49.5		89	50	44.1		86	54	46.4		79	63	50.4		94	40	37.7
42	107		85	64	54.6		93	52	48.6		90	57	51.1		83	67	55.5		98	42	41.5
46	117		93	70	65.5		102	57	58.3		99	62	61.4		91	73	66.6		108	46	49.6
52	132		106	79	83.7		115	65	74.5		112	70	78.4		103	83	85.1		121	52	63.1
55	140		112	84	93.7		122	68	83.4		118	74	87.7		109	87	95.2		129	55	71
60	152		122	91	111		133	75	99.2		129	81	104		119	95	113		140	60	84
65	165		132	99	131		144	81	116		140	88	123		129	103	133		152	65	99
70	178		142	107	152		155	87	135		151	94	142		139	111	154		164	70	115
75	191		152	114	174		166	93	155		162	101	163		149	119	177		176	75	132
80	203		163	122	198		177	100	176		172	108	186		159	127	201		187	80	149
85	216		173	130	224		188	106	199		183	114	209		169	135	228		199	85	169
90	229		183	137	251		199	112	223		194	121	235		179	143	255		210	90	190
95	241		193	145	279		210	118	249		205	128	262		188	151	284		222	95	210
100	254		203	152	310		221	125	276		215	135	290		198	159	315		233	100	234
105	267		213	160	341		232	131	304		226	141	320		208	167	347		245	105	258
110	279		224	168	375		244	137	334		237	148	351		218	175	381		256	110	282
115	292		234	175	410		255	143	365		248	155	383		228	182	416		268	115	309
120	305		244	183	446		266	149	397		258	162	418		238	190	453		280	120	337

Comparison with paper

An A4 sheet of paper (297 mm × 210 mm) is 364 mm (14.3 in) diagonal with an aspect ratio of √2  ≈ 1.414. H. between 4: 3 and 16:10. An A3 page is twice as large (420 mm × 297 mm), A5 is half the size (210 mm × 148 mm). The American letter format is similar in size to A4: 11 in × 8.5 in = 279 mm × 216 mm, diagonal 13.9 in = 353 mm.

Smallest screen diagonals (in inches) on which common paper formats can be displayed in their original size

	across				high
paper	5: 4	4: 3	8: 5	16: 9	5: 4	4: 3	8: 5	16: 9
A5	11	11	11	12	14th	14th	16	17th
A4	15th	15th	16	17th	19th	20th	22nd	24
Letter	15th	15th	17th	18th	18th	19th	21st	23
2 letter					22nd	22nd	21st	23
A3	22nd	21st	22nd	24	27	28	32	37
A2		30th		37				52
A1				52				70
A0				70				100

Web links

Wiktionary: Screen diagonal  - explanations of meanings, word origins, synonyms, translations

• Overview of different screen diagonals in relation to A4 format