tech calculator

Screen Resolution & PPI Calculator

Calculate pixel density, dot pitch, aspect ratio, and physical panel size from a resolution and diagonal.

PPI = √(width² + height²) ÷ diagonal inches. Example: a 27-inch 1920×1080 monitor has a 2,202.9-pixel diagonal, so 2,202.9 ÷ 27 = 81.59 PPI, a 0.3113 mm dot pitch, and a 23.53 × 13.24 inch panel.

Formula Verified by Dr. James Callahan, PhD

Quick actions: Save inputs, view saved runs, print, share, or export results

Saved Runs

Inputs

Device Preset (fills common values — edit freely)

Horizontal Resolutionpx

Vertical Resolutionpx

Diagonal Screen Sizein

Results

Pixel Density (PPI)

81.59 PPI

Diagonal Resolution2202.9 px

Aspect Ratio16:9

Physical Width23.53 in (59.8 cm)

Physical Height13.24 in (33.6 cm)

Dot Pitch0.3113 mm

Total Pixels2.07 MP

Pixels Indistinguishable Beyond42.1 in (3.51 ft)

Tip

Handy every time you compare two monitors, plan a desk layout, or work out whether a higher-resolution panel would be visible at the distance you actually sit.

Formula

PPI and pixel density formulas

Diagonal Pixels = √(Width² + Height²)
PPI = Diagonal Pixels ÷ Diagonal Inches
Physical Width = Width Pixels ÷ PPI
Physical Height = Height Pixels ÷ PPI
Dot Pitch (mm) = 25.4 ÷ PPI
Aspect Ratio = Width : Height reduced by their greatest common divisor
Viewing Distance = 1 ÷ (PPI × tan(1 arcminute)) ≈ 3438 ÷ PPI

The pixel diagonal comes straight from Pythagoras, and dividing it by the physical diagonal gives density in pixels per inch. Because pixels on a display are square, that single figure applies horizontally and vertically as well as diagonally. The viewing distance is the range beyond which one pixel subtends less than one arcminute of visual angle — the conventional threshold at which a person with 20/20 vision stops resolving individual pixels.

Step by step

How the calculation works

1Enter the native resolution in pixels and the advertised diagonal in inches. Use the panel's native resolution, not whatever your operating system is currently scaled to — a 4K display running at a 1080p desktop scale is still physically a 4K panel.
2PPI is the headline result and the number to compare across devices. Rough anchors: a 27-inch 1080p monitor is about 82 PPI, a 27-inch 1440p about 109 PPI, a 15.6-inch 4K laptop about 282 PPI, and a modern phone screen sits above 400 PPI.
3Physical width and height are derived, not entered, which makes this useful for desk planning and monitor-arm clearance — manufacturers publish the diagonal and the bezel-inclusive case size, rarely the active panel dimensions.
4Dot pitch is the same measurement expressed as millimetres per pixel rather than pixels per inch, and is the figure most display datasheets quote. Lower is denser: 0.31 mm is a 1080p 27-inch panel, 0.09 mm is a 4K laptop screen.
5If you only need to reduce a resolution to its aspect ratio or resize an image while preserving proportions, the [aspect ratio calculator](/calculators/aspect-ratio-calculator) does that without the physical-size arithmetic.

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Screen Resolution & PPI Calculator

Calculate pixel density, dot pitch, aspect ratio, and physical panel size from a resolution and diagonal.

Formula Verified by Dr. James Callahan, PhD

How to understand and use this calculator

Quick Answer — How Do You Calculate PPI?

Pixel density is the pixel diagonal divided by the physical diagonal: PPI = (√(w^2 + h^2))/d, where w and h are the horizontal and vertical resolution in pixels and d is the advertised diagonal in inches. Because display pixels are square, the same figure describes density horizontally and vertically too.

Worked example: a 27-inch 1920×1080 monitor. Diagonal pixels = √(1920² + 1080²) = 2,202.9. PPI = 2,202.9 ÷ 27 = 81.59 PPI.

Common configurations, all computed with this calculator:

24″ 1920×1080 — 91.79 PPI, 0.2767 mm dot pitch, 20.92″ × 11.77″ panel
27″ 1920×1080 — 81.59 PPI, 0.3113 mm dot pitch, 23.53″ × 13.24″ panel
27″ 2560×1440 — 108.79 PPI, 0.2335 mm dot pitch, same 23.53″ × 13.24″ panel
27″ 3840×2160 — 163.18 PPI, 0.1557 mm dot pitch, same panel again
32″ 3840×2160 — 137.68 PPI, 0.1845 mm dot pitch, 27.89″ × 15.69″ panel
15.6″ 3840×2160 — 282.42 PPI, 0.0899 mm dot pitch, 13.60″ × 7.65″ panel
6.1″ 2556×1179 — 461.44 PPI, 0.0550 mm dot pitch, 5.54″ × 2.56″ panel

The three 27-inch rows make the useful point: identical physical panel, three densities. Resolution alone tells you nothing about how sharp a screen looks — density does.

How to Use This Calculator: A 27-Inch 1080p Monitor

Enter the native resolution and the advertised diagonal. For a 27-inch 1920×1080 display: diagonal pixels = √(1920² + 1080²) = √(3,686,400 + 1,166,400) = √4,852,800 = 2,202.91 px, so PPI = 2,202.91 ÷ 27 = 81.59.

Everything else follows from that density. Physical width = 1920 ÷ 81.59 = 23.53 inches (59.8 cm); physical height = 1080 ÷ 81.59 = 13.24 inches (33.6 cm). Dot pitch = 25.4 ÷ 81.59 = 0.3113 mm. Total pixels = 1920 × 1080 = 2.07 megapixels. Aspect ratio reduces to 16:9.

The last output is the one people are usually really asking about: individual pixels stop being resolvable beyond 1 ÷ (81.59 × tan(1 arcminute)) = 42.1 inches, about 3.5 feet. Most people sit closer than that to a 27-inch monitor, which is exactly why 1080p looks soft at this size and 1440p does not.

A Second Example: A 15.6-Inch 4K Laptop Panel

Shrink the panel and hold the resolution and the density explodes. For 3840×2160 on a 15.6-inch laptop screen: diagonal pixels = √(3840² + 2160²) = 4,405.81 px, so PPI = 4,405.81 ÷ 15.6 = 282.42 — three and a half times the density of the 27-inch 1080p monitor above, from a panel with less than a third of its area.

Physical width = 3840 ÷ 282.42 = 13.60 inches; height = 7.65 inches. Dot pitch drops to 0.0899 mm, and the one-arcminute threshold falls to 12.2 inches. Since almost nobody uses a laptop from closer than about 20 inches, the pixels on this panel are genuinely invisible in normal use — which is the real argument for a high-density laptop screen, and equally the reason a 4K panel on a 32-inch desktop monitor (137.68 PPI, threshold 25.0 inches) is a much more marginal upgrade at typical desk distance.

It is also why such a panel almost always ships with display scaling switched on. At 282 PPI, unscaled interface text renders at roughly a third the physical size it would occupy on the 81.59 PPI monitor.

PPI, Dot Pitch, and Aspect Ratio: Three Views of the Same Panel

Dot pitch is pixel density inverted — millimetres per pixel instead of pixels per inch — and is what most display datasheets publish, since the panel industry works in metric. Convert either way with 25.4 ÷ PPI: 0.31 mm and 81.6 PPI describe exactly the same screen, and lower dot pitch means higher density.

Aspect ratio is the resolution reduced by its greatest common divisor, which is why 1920×1080, 2560×1440, and 3840×2160 all reduce to 16:9 and are interchangeable for full-screen content. Phone panels frequently do not reduce cleanly — 2556×1179 comes out as 284:131, not any recognisable named ratio — because the resolution is designed around a specific physical panel and cutout rather than a standard. If aspect ratio is all you need, the aspect ratio calculator handles resizing and ratio reduction without the physical-dimension arithmetic.

Physical width and height are worth calculating in their own right. Manufacturers publish the diagonal and the bezel-inclusive case dimensions, but the active panel size — the part that matters for a monitor arm, a recessed mount, or fitting three screens across a desk — usually has to be derived, and the density figure gives it to you directly.

Limitations

This calculator computes exact geometry from the resolution and diagonal you enter, and it assumes square pixels and a flat rectangular panel. On a curved monitor the advertised diagonal is measured along the curve, so the derived flat width will run slightly wide. Some ultra-wide and phone panels also have rounded corners or a notch, which the raw pixel dimensions ignore.

Density is not sharpness. Two panels at the same PPI can look markedly different depending on subpixel layout — RGB stripe against a PenTile arrangement, where the vendor's stated resolution counts subpixels that are not evenly distributed — as well as anti-glare coating, contrast, and how the operating system renders text. PPI tells you how much detail the panel can hold, not how well it renders any particular content.

The viewing distance figure is a single acuity convention (one arcminute per pixel, roughly 20/20 vision) and nothing more. Real visual acuity varies widely between people and some can resolve detail finer than that threshold, so treat the number as a comparison point between displays rather than a hard limit on what anyone can see.

Related Calculators

For proportional resizing and ratio reduction without the physical measurements, use the Aspect Ratio Calculator. If you are working with footage at the resolution you just checked, the Video File Size Calculator turns bitrate and running time into gigabytes, and the Data Storage Calculator sizes a whole photo or video library. To find out what connection speed streaming at a given resolution actually needs, the Bandwidth Calculator works from concurrent streams and per-stream bitrate.

Related concepts

Pixel Density (PPI)

How many pixels occupy one inch of screen. It combines resolution and physical size into the single figure that actually predicts perceived sharpness.

Dot Pitch

The millimetre spacing between adjacent pixel centres, equal to 25.4 ÷ PPI. The same measurement as density, expressed the way display datasheets publish it.

One-Arcminute Threshold

The viewing distance at which a single pixel subtends one arcminute of visual angle — the conventional point beyond which a person with 20/20 vision stops resolving individual pixels.

Frequently Asked Questions

How do I calculate PPI from resolution and screen size?+

Take the square root of (width² + height²) to get the diagonal in pixels, then divide by the diagonal screen size in inches. For a 27-inch 1920×1080 monitor: √(1920² + 1080²) = 2,202.9 pixels, ÷ 27 = 81.59 PPI.

What is a good PPI for a monitor?+

For a desktop monitor viewed at arm's length, roughly 90–110 PPI is comfortable without scaling and around 140–160 PPI looks noticeably sharper with scaling enabled. A 27-inch 1440p panel lands at 108.79 PPI, which is why that combination is so common; the same 27-inch panel at 1080p is only 81.59 PPI and looks visibly soft at desk distance.

Why do two screens with the same resolution have different PPI?+

Because density depends on physical size as well as resolution. A 3840×2160 panel is 163.18 PPI at 27 inches, 137.68 PPI at 32 inches, and 282.42 PPI on a 15.6-inch laptop — identical pixel counts spread across very different areas.

What is dot pitch and how does it relate to PPI?+

Dot pitch is the centre-to-centre distance between pixels in millimetres, and it is simply the inverse of PPI: dot pitch = 25.4 ÷ PPI. A 0.2767 mm pitch is the same thing as 91.79 PPI. Display datasheets tend to quote pitch; consumer marketing tends to quote PPI. Lower pitch means higher density.

How far away do pixels become invisible?+

At the standard one-arcminute acuity threshold, roughly 3438 ÷ PPI inches. That is 42.1 inches for an 81.59 PPI monitor, 21.1 inches for a 163.18 PPI 27-inch 4K panel, and 12.2 inches for a 282.42 PPI laptop screen. Compare it against how far you actually sit — if your viewing distance already exceeds the threshold, more pixels will not look sharper.

Should I enter my scaled resolution or the native one?+

Always the native panel resolution. Display scaling changes how large interface elements are drawn, not how many physical pixels exist. A 4K display running a 1080p-equivalent desktop scale is still a 4K panel and still has 4K density.

Why does my phone's aspect ratio come out as an odd number like 284:131?+

Because phone resolutions are designed around a specific physical panel, camera cutout, and corner radius rather than a standard ratio. The calculator reduces the resolution by its greatest common divisor and reports what it finds, so an unusual ratio is a correct answer, not an error.

Does higher PPI always look better?+

Only up to the point your eyes can resolve it at your actual viewing distance, and only if other factors hold. Subpixel layout, panel coating, contrast, and text rendering all affect perceived sharpness independently of density — two panels at the same PPI can look quite different.

Diagonal Pixels = √(Width² + Height²) PPI = Diagonal Pixels ÷ Diagonal Inches Physical Width = Width Pixels ÷ PPI Physical Height = Height Pixels ÷ PPI Dot Pitch (mm) = 25.4 ÷ PPI Aspect Ratio = Width : Height reduced by their greatest common divisor Viewing Distance = 1 ÷ (PPI × tan(1 arcminute)) ≈ 3438 ÷ PPI

How the calculation works

1Enter the native resolution in pixels and the advertised diagonal in inches. Use the panel's native resolution, not whatever your operating system is currently scaled to — a 4K display running at a 1080p desktop scale is still physically a 4K panel.

2PPI is the headline result and the number to compare across devices. Rough anchors: a 27-inch 1080p monitor is about 82 PPI, a 27-inch 1440p about 109 PPI, a 15.6-inch 4K laptop about 282 PPI, and a modern phone screen sits above 400 PPI.

3Physical width and height are derived, not entered, which makes this useful for desk planning and monitor-arm clearance — manufacturers publish the diagonal and the bezel-inclusive case size, rarely the active panel dimensions.

4Dot pitch is the same measurement expressed as millimetres per pixel rather than pixels per inch, and is the figure most display datasheets quote. Lower is denser: 0.31 mm is a 1080p 27-inch panel, 0.09 mm is a 4K laptop screen.

5If you only need to reduce a resolution to its aspect ratio or resize an image while preserving proportions, the [aspect ratio calculator](/calculators/aspect-ratio-calculator) does that without the physical-size arithmetic.

How to understand and use this calculator

Quick Answer — How Do You Calculate PPI?

Worked example: a 27-inch 1920×1080 monitor. Diagonal pixels = √(1920² + 1080²) = 2,202.9. PPI = 2,202.9 ÷ 27 = 81.59 PPI.

Common configurations, all computed with this calculator:

24″ 1920×1080 — 91.79 PPI, 0.2767 mm dot pitch, 20.92″ × 11.77″ panel
27″ 1920×1080 — 81.59 PPI, 0.3113 mm dot pitch, 23.53″ × 13.24″ panel
27″ 2560×1440 — 108.79 PPI, 0.2335 mm dot pitch, same 23.53″ × 13.24″ panel
27″ 3840×2160 — 163.18 PPI, 0.1557 mm dot pitch, same panel again
32″ 3840×2160 — 137.68 PPI, 0.1845 mm dot pitch, 27.89″ × 15.69″ panel
15.6″ 3840×2160 — 282.42 PPI, 0.0899 mm dot pitch, 13.60″ × 7.65″ panel
6.1″ 2556×1179 — 461.44 PPI, 0.0550 mm dot pitch, 5.54″ × 2.56″ panel

The three 27-inch rows make the useful point: identical physical panel, three densities. Resolution alone tells you nothing about how sharp a screen looks — density does.

How to Use This Calculator: A 27-Inch 1080p Monitor

A Second Example: A 15.6-Inch 4K Laptop Panel

PPI, Dot Pitch, and Aspect Ratio: Three Views of the Same Panel

Limitations

Related Calculators

Related concepts

Pixel Density (PPI)

How many pixels occupy one inch of screen. It combines resolution and physical size into the single figure that actually predicts perceived sharpness.

Dot Pitch

The millimetre spacing between adjacent pixel centres, equal to 25.4 ÷ PPI. The same measurement as density, expressed the way display datasheets publish it.

One-Arcminute Threshold

The viewing distance at which a single pixel subtends one arcminute of visual angle — the conventional point beyond which a person with 20/20 vision stops resolving individual pixels.

Frequently Asked Questions

How do I calculate PPI from resolution and screen size?+

What is a good PPI for a monitor?+

Why do two screens with the same resolution have different PPI?+

What is dot pitch and how does it relate to PPI?+

How far away do pixels become invisible?+

Should I enter my scaled resolution or the native one?+

Why does my phone's aspect ratio come out as an odd number like 284:131?+

Does higher PPI always look better?+

Screen Resolution & PPI Calculator

Inputs

Results

PPI and pixel density formulas

How the calculation works

Learn more about this calculation

How to Use Do The Calculation Calculators: A Practical Step-by-Step Guide

Understanding Calculator Formulas: How DTC Turns Inputs into Results

Aspect Ratio Calculator

Video File Size Calculator

Data Storage Calculator

Bandwidth Calculator

Screen Resolution & PPI Calculator

Inputs

Results

Key output metrics

Physical Panel Dimensions (inches)

How to understand and use this calculator

Quick Answer — How Do You Calculate PPI?

How to Use This Calculator: A 27-Inch 1080p Monitor

A Second Example: A 15.6-Inch 4K Laptop Panel

PPI, Dot Pitch, and Aspect Ratio: Three Views of the Same Panel

Limitations

Related Calculators

Related concepts

Frequently Asked Questions

PPI and pixel density formulas

How the calculation works

Learn more about this calculation

How to Use Do The Calculation Calculators: A Practical Step-by-Step Guide

Understanding Calculator Formulas: How DTC Turns Inputs into Results

Aspect Ratio Calculator

Video File Size Calculator

Data Storage Calculator

Bandwidth Calculator

Key output metrics

Physical Panel Dimensions (inches)

How to understand and use this calculator

Quick Answer — How Do You Calculate PPI?

How to Use This Calculator: A 27-Inch 1080p Monitor

A Second Example: A 15.6-Inch 4K Laptop Panel

PPI, Dot Pitch, and Aspect Ratio: Three Views of the Same Panel

Limitations

Related Calculators

Related concepts

Frequently Asked Questions