Screen Size and Viewing Distance Calculator

Diagonal plus aspect ratio to width, height, area and PPI — because a 34-inch ultrawide has 17% less area than a 34-inch 16:9. Plus SMPTE’s, THX’s and the ITU’s three different viewing distances, all printed.

Last updated 24 Sep 2026

Diagonal and ratio → width, height, area, PPI, distance

Diagonal + ratio + pixels → size and seating

Screen diagonalThe number on the box. It is the only dimension makers quote, and on its own it does not give you a size.

Length unit for the diagonal and the seating distance

Aspect ratioThis is the input the diagonal is useless without. The default is 43:18 — what a 3440×1440 “21:9” monitor actually is.

My own ratio: width partOnly read when the dropdown is set to “My own ratio”.

My own ratio: height part

Horizontal pixelsFor the pixel density rows. Leave the ratio dropdown consistent with these or the page will tell you the pixels are not square.

Vertical pixels

Your seating or viewing distanceIn the unit chosen above. For a desk monitor this is typically 24 to 32 inches; for a sofa, 90 to 144.

A scale drawing, not a circuit, and the arc is the point of it. Both rectangles share a bottom-left corner and both have their opposite corner ON THE ARC, which means both have exactly the same diagonal — the only dimension a manufacturer prints. One is your screen at your aspect ratio and the other is 16:9. They are visibly different objects. Area is D² × r/(1+r²), and that coefficient is largest when r = 1, so a square is the most area any diagonal can buy and every widescreen shape gives some of it up. The further from square, the smaller the rectangle inscribed in the same arc. This is why a 34-inch ultrawide is wider and smaller than a 34-inch 16:9, and why comparing two screens by their diagonals is only meaningful when they are the same shape. Your own rectangle is drawn to the nearest tenth in the ratio.

31.363inExample

a 34-inch screen at 43:18 — a 3440×1440 “21:9” monitor — with a 30-inch seating distance

Pythagoras, then one minute of arc

W = D·r/√(1+r²) · H = D/√(1+r²) · A = D² · r/(1+r²)
PPI = w_px / W · d_acuity = pitch / tan(1′) · d_angle = (W/2) / tan(θ/2)

D: the diagonal, the only dimension a maker quotes
r: aspect ratio, width divided by height. Without it the diagonal gives no size at all
r/(1+r²): the area coefficient. Largest at r = 1, so a square is the most area per diagonal and every widescreen shape gives some up
1′: one minute of arc, the conventional resolution limit of 20/20 vision and the basis of the ITU’s design viewing distances
θ: horizontal viewing angle. 30° for SMPTE, 36° for THX, 31° for ITU-R BT.2022 at 1080p — three different answers

Worked example

a 34-inch screen at 43:18 — a 3440×1440 “21:9” monitor — with a 30-inch seating distance
r = 43/18 = 2.388889, so √(1+r²) = 2.589747
Width = 34 × 2.3889 ÷ 2.5897 = 31.36 in, height = 34 ÷ 2.5897 = 13.13 in, area = 411.8 in²
A 34-inch 16:9 screen would be 29.63 × 16.67 = 494.0 in², so this one has 16.6% less area for the same diagonal
Pixel density: 3440 ÷ 31.36 = 109.7 PPI, a pitch of 0.2316 mm, so the one-arcminute distance is 0.2316 ÷ tan(1′) = 796 mm = 31.3 in
The angle recommendations: SMPTE's 30° puts you at 58.5 in, THX's 36° at 48.3 in. At the 30 inches you actually sit, the screen subtends 55.2° and you are inside the acuity distance — so the pixels are resolvable from there

One diagonal, sixteen shapes: every ratio at 34 inches

Every screen here has the same 34-inch diagonal and they are not the same size. Area is D² × r/(1+r²), so it depends on the ratio as well as the diagonal, and the coefficient r/(1+r²) is largest at r = 1 — a square is the most area you can hang on a given diagonal, and every departure from square costs you. A 34-inch 43:18 ultrawide has 412 square inches against the 34-inch 16:9’s 494, which is 16.6 per cent less glass. This is the single most useful thing on the page: the diagonal is not a size, and comparing two screens by their diagonals is only valid when they are the same shape.
Ratio	Decimal	Width (in)	Height (in)	Area (in²)	Area against 34-inch 16:9 (%)
1:1	1.0000	24.04	24.04	578.0	17.01
5:4	1.2500	26.55	21.24	563.9	14.16
4:3	1.3333	27.20	20.40	554.9	12.33
3:2	1.5000	28.29	18.86	533.5	8.01
16:10	1.6000	28.83	18.02	519.6	5.18
16:9	1.7778	29.63	16.67	494.0	0.00
1.85:1	1.8500	29.91	16.17	483.6	-2.10
1.90:1 (IMAX digital)	1.8963	30.07	15.86	477.0	-3.44
64:27 (“21:9”)	2.3704	31.33	13.22	414.0	-16.19
2.39:1 (DCI Scope)	2.3869	31.36	13.14	412.0	-16.59
43:18 (“21:9”)	2.3889	31.36	13.13	411.8	-16.64
12:5 (“21:9”)	2.4000	31.38	13.08	410.4	-16.91
32:9	3.5556	32.73	9.21	301.3	-39.00
4:5	0.8000	21.24	26.55	563.9	14.16
2:3	0.6667	18.86	28.29	533.5	8.01
9:16	0.5625	16.67	29.63	494.0	0.00

The ITU’s own published figures, and what the one-arcminute rule gives

This is the verifiable part of the viewing-distance question, and it repays reading carefully. Recommendation ITU-R BT.2022 defines the design viewing distance as the one at which adjacent pixels subtend one minute of arc, and Report ITU-R BT.2246-4 attributes the same criterion to BT.1845: “the distance at which the pixel count per visual angle of one minute is one”. Apply it and the first two rows come out almost exactly as published — 3.183 picture heights and 31.2° against a printed 3.2 H and 31°, and 5.97 H and 12.7° against a printed 6 H and 13°. The 720×576 row only works at the 4:3 DISPLAY ratio rather than the 5:4 of its own pixel array, which is a reminder that SDTV pixels are not square. The two UHDTV rows, though, are internally inconsistent, and this page says so: the printed ANGLES of 58° and 96° match the unrounded distances of 1.592 H and 0.796 H, while the printed DISTANCES are the rounded-down 1.5 and 0.75 — at which the angles would be 61.3° and 99.7°. The last column is that arithmetic. It is a rounding in a report rather than an error in a standard, and it is why this page prints the criterion and the computed figure rather than the table’s numbers.
Format	Display ratio	ITU angle	ITU distance	Computed angle	Computed distance	Angle AT the ITU’s printed distance
720×576	1.3333	13°	6.00 H	12.747°	5.9683 H	12.68°
1920×1080	1.7778	31°	3.20 H	31.205°	3.1831 H	31.05°
3840×2160	1.7778	58°	1.50 H	58.367°	1.5915 H	61.30°
7680×4320	1.7778	96°	0.75 H	96.327°	0.7958 H	99.69°

Three recommendations, three answers for the same screen

The honest summary is that two of these four figures could not be verified. SMPTE’s engineering guideline is behind a paywall and THX publishes its cinema specification only to licensees, so the 30° and 36° are printed here as attributed claims rather than as read standards. What IS verified is the ITU recommendation, which is a free document, was fetched, and whose 31° for 1080p this page reproduces from the one-arcminute criterion to within a quarter of a degree. The page prints all of them because they genuinely disagree: for this screen they span 48 to 59 inches, a range of 21 per cent, and picking one and calling it “the” recommended distance would be inventing a consensus that does not exist.
Recommendation	Horizontal angle	For a 34-inch 43:18 screen	Verified?	What it is actually about
SMPTE EG-18-1994	30°	58.5 in	NO — paywalled	Cinema design: the minimum angle the REARMOST seat should get. Widely quoted as a home-theatre target, which is not what an engineering guideline for theatre layout says
THX certified cinema	36°	48.3 in	NO — licensee-only	Also a cinema requirement for the back row, and a larger angle, so a closer seat for the same screen. 18% closer than SMPTE’s
ITU-R BT.2022, 1080p	31°	56.5 in	YES — free document, fetched	Subjective-assessment viewing conditions for a flat panel, and it is DERIVED: it is where one pixel of a 1080-line picture subtends one arcminute. Sits between the other two
One arcminute per pixel, at YOUR pixel density	depends	31.3 in	YES — computed here	The acuity limit: closer than this and you can see the pixel structure. For a 110-PPI monitor that is 31 inches, far closer than any angle recommendation, so a desk monitor is pixel-limited and a cinema screen is angle-limited

A diagonal is not a size

A 27-inch 16:9 monitor and a 27-inch 21:9 monitor are different objects, and the number they share tells you almost nothing. The diagonal is the only dimension makers quote, and a diagonal plus an aspect ratio is what actually determines a width, a height and an area. The arithmetic is Pythagoras: with r = width ÷ height, width = D·r/√(1+r²) and height = D/√(1+r²). For the default here — a 34-inch screen at 43:18, which is what a 3440×1440 “21:9” monitor really is — that gives 31.36 inches by 13.13, and 412 square inches of glass.

Area is not proportional to the diagonal squared across different shapes, and the difference is large. Area = D² × r/(1+r²), so the coefficient depends entirely on the ratio. It is largest at r = 1: a square is the most area you can hang on a given diagonal, and every step away from square costs you. A 34-inch 16:9 screen would be 29.63 by 16.67 inches and 494 square inches — so the 34-inch ultrawide has 16.6 per cent LESS area than a 34-inch 16:9 would have. That is the practical answer to “is a 34-inch ultrawide bigger than my 32-inch 16:9”: in width yes, in area not necessarily, and the diagonal cannot tell you.

Pixel density, and the distance at which pixels stop mattering. PPI is horizontal pixels divided by screen width in inches — 109.7 for the default — and the pixel pitch is its reciprocal, 0.2316 mm here. The distance at which those pixels stop being individually resolvable comes from the standard angular-acuity figure: one minute of arc, which is the definition of 20/20 vision on a Snellen chart — a letter whose strokes subtend one arcminute. Set the pixel pitch equal to one arcminute and you get distance = pitch ÷ tan(1′), which for this screen is 31.3 inches. Sit further than that and you are not getting anything from more pixels. Two assumptions are buried in it and both matter: one arcminute is an average for good eyesight in good light on high-contrast detail, and vernier acuity — the ability to see a misalignment rather than a gap — is several times finer, which is why aliasing on a diagonal line is visible further away than the pixel grid itself.

Recommended viewing distance has no single answer, so this page prints three. SMPTE’s EG-18-1994 is the source of the 30° figure everybody quotes; THX’s cinema requirement is 36°; and ITU-R BT.2022 puts 1080p at 31°. For the default screen those come out at 58.5, 48.3 and 56.5 inches — a spread of 21 per cent. Two of those three could not be verified: the SMPTE guideline is paywalled and THX publishes its specification only to licensees, so the 30° and 36° appear here as attributed claims. The ITU document is free, was fetched, and its figures are reproduced below from the one-arcminute criterion alone, which is the only viewing-distance number on this page that is derived rather than asserted. Worth knowing too that the cinema figures are minimum angles for the WORST seat in a theatre, not targets for a living room — a fact that gets lost every time they are quoted as home-theatre advice.

And the reverse, which is the question people really have. Given where the sofa already is, what size screen fills each recommendation? Width = 2 × distance × tan(angle/2), converted back to a diagonal at your ratio. The page gives all three, so you can see the range rather than a single number pretending to be a rule.

Where this page stops. Screens only. For pixels to a physical print size — the same arithmetic with paper instead of glass — the DPI and print size calculator owns it, and the two should not be mixed: a 300 DPI print and a 300 PPI screen are viewed at different distances and the acuity arithmetic comes out differently. For reducing a resolution to a named ratio, and for the letterbox bars when the content does not match the panel, see the aspect ratio calculator. For CSS pixels against physical ones, the em, rem and px converter.

Frequently asked questions

How wide is a 34-inch monitor?

It depends on its aspect ratio, which is why the diagonal alone is not an answer. At 43:18 — a 3440×1440 ultrawide — it is 31.4 inches wide and 13.1 high. At 16:9 the same diagonal is 29.6 by 16.7. The ultrawide is 1.7 inches wider and 3.5 inches shorter.

Does a 34-inch ultrawide have more screen than a 34-inch 16:9?

No — it has 16.6 per cent LESS area. Area is D² × r/(1+r²) and that coefficient is largest at a 1:1 ratio, so the further from square a screen is, the less area a given diagonal buys. The ultrawide is wider, which is what people want it for, and it is smaller overall.

How far away should I sit from my TV?

There is no single answer and anyone who gives you one has picked a standard without saying so. SMPTE’s 30° puts you at 59 inches from this screen, THX’s 36° at 48, and ITU-R BT.2022’s 31° for 1080p at 57. Note also that the cinema figures are minimum angles for the back row of a theatre, not living-room targets. The page prints all three and the reverse calculation as well.

At what distance can I no longer see the pixels?

For this screen, about 31 inches. The criterion is one minute of arc per pixel, which is the definition of 20/20 vision: distance = pixel pitch ÷ tan(1′). It assumes average good eyesight, good light and high-contrast detail. Vernier acuity is several times finer, so aliasing on a near-horizontal line stays visible well beyond this distance even though the pixel grid does not.

Where does the “one arcminute” figure come from?

From clinical visual acuity. A Snellen 20/20 letter subtends five arcminutes with strokes and gaps of one arcminute each, so one arcminute is the conventional resolution limit of normal vision. The ITU builds its design viewing distances on exactly this: BT.2022 defines the distance as the one at which adjacent pixels subtend one minute of arc, and this page reproduces the ITU’s published 3.2 picture heights and 31° for 1080p from that rule alone.

Why do SMPTE and THX disagree?

Because they are recommending different things for different reasons. Both are cinema documents about the minimum angle the rearmost seat should get, and THX’s number is larger, so its distance is 18 per cent closer for the same screen. Neither is a living-room standard. And neither could be verified for this page: the SMPTE guideline is paywalled and THX publishes to licensees only, so both figures are printed as attributed rather than as read.

What screen size should I buy for my room?

Enter your seating distance and read the reverse rows. At 30 inches from a 43:18 screen, SMPTE’s 30° wants a 17-inch diagonal and THX’s 36° a 21-inch one. Check the acuity row too: a screen large enough to fill the angle but short of pixels will show its pixel structure, and the page tells you which limit you hit first.

Is PPI the same as DPI?

The arithmetic is the same — pixels or dots divided by inches — but the questions are different, because a print and a screen are viewed at different distances and the acuity criterion scales with distance. A 300 DPI print held at 12 inches and a 150 PPI screen at 24 inches are equally sharp to the eye. This page does screens; the DPI and print size calculator does paper.

Related calculators

References

Recommendation ITU-R BT.2022 (08/2012), General viewing conditions for subjective assessment of quality of SDTV and HDTV television pictures on flat panel displays. Fetched. Its table gives 1920×1080 an optimal horizontal viewing angle of 31° at 3.2 picture heights, and 720×576 13° at 6 picture heights. It defines the design viewing distance as the distance at which adjacent pixels subtend one minute of arc. Both rows are reproduced here from that criterion alone, to within a quarter of a degree — provided the 720×576 row is taken at its 4:3 DISPLAY ratio rather than the 5:4 of its pixel array.
Report ITU-R BT.2246-4 (02/2015), The present state of ultra-high definition television, Table 1. Fetched. Gives 3840×2160 58° at 1.5 picture heights and 7680×4320 96° at 0.75, and attributes the criterion to Recommendation ITU-R BT.1845: “the distance at which the pixel count per visual angle of one minute is one”. Those two rows are internally inconsistent and this page says so: the one-arcminute distances are 1.591 and 0.796 picture heights, the printed angles match those distances exactly, and the printed distances are the rounded-down 1.5 and 0.75, which would give 61.9° and 99.9°.
SMPTE EG-18-1994, Design of Effective Cine Theaters, and THX’s certified-cinema requirement. NEITHER DOCUMENT COULD BE FETCHED: SMPTE’s engineering guideline is paywalled and THX publishes its cinema specification only to licensees. The 30° and 36° figures on this page are as reported by secondary sources and are printed as attributed claims, not as verified standards. What IS verified is the ITU-R figure above, which is a free document and comes out at 31° for 1080p — between the other two, and derived rather than asserted.
Wikipedia, Ultrawide formats and 21:9 aspect ratio. “21:9 is a consumer electronics (CE) marketing term to describe the ultra-widescreen aspect ratio of 64:27”, and it covers 64:27 (2.370), 43:18 (2.389) and 12:5 (2.400) — three different shapes sold under one name. 64:27 is (4:3) cubed, which this page checks rather than quotes, and it is the geometric continuation of 4:3 and 16:9.
Digital Cinema Initiatives, LLC. Digital Cinema System Specification (documents.dcimovies.com). Fetched. Requires support for two image containers, “either 4096 x 2160 or 2048 x 1080”, which is what “4K” and “2K” mean in a cinema and why neither is a resolution you will find on a television. Consumer UHD is 3840×2160 — 256 pixels narrower than DCI 4K.