# Pixel density

Pixels per centimeter (ppcm), Pixels per inch (PPI) or pixel density is a measurement of the resolution of devices in various contexts: typically computer displays, image scanners, and digital camera image sensors.

Ppcm can also describe the resolution, in pixels, of an image to be printed within a specified space. Note, the unit is not square centimeters. For instance, a 100×100 pixel image that is printed in a 1cm square has a resolution of 100 pixels per centimeter (ppcm). Used in this way, the measurement is meaningful when printing an image. It has become commonplace to refer to PPI as DPI, which is incorrect because PPI always refers to input resolution. Good quality photographs usually require 300 pixels per inch, at 100% size, when printed onto coated paper stock, using a printing screen of 150 lines per inch (lpi). This delivers a quality factor of 2, which delivers optimum quality. The lowest acceptable quality factor is considered to be 1.5, which equates to printing a 225ppi image using a 150 lpi screen onto coated paper. Screen frequency is determined by the type of paper that the image is to be printed on. An absorbent paper surface, uncoated recycled paper for instance, will allow the droplets of ink to spread (dot gain), and so requires a more open printing screen. Input resolution can therefore be reduced in order to minimise file size without any loss in quality, as long as the quality factor of 2 is maintained. This is easily determined by doubling the line frequency. For example, printing on an uncoated paper stock often limits the printing screen frequency to no more than 120 lpi, therefore, a quality factor of 2 is achieved with images of 440 ppi.

The square shown above is 200 pixels by 200 pixels at zoom 100%. To determine a monitor's ppcm, set the browser's zoom at 100%, then measure the width and height, in cm, of the square as displayed on a given monitor. Dividing 200 by the measured width or height gives the monitor's horizontal or vertical ppcm, respectively, at the current screen resolution.

## Computer displays

The PPI of a computer display is related to the size of the display in inches and the total number of pixels in the horizontal and vertical directions. This measurement is often referred to as dots per inch, though that measurement more accurately refers to the resolution of a computer printer.

For example, a 15 inch (38 cm) display whose dimensions work out to 12 inches (30.48 cm) wide by 9 inches (22.86 cm) high, capable of a maximum 1024×768 (or XGA) pixel resolution, can display around 85 PPI in both the horizontal and vertical directions. This figure is determined by dividing the width (or height) of the display area in pixels by the width (or height) of the display area in inches. It is possible for a display’s horizontal and vertical PPI measurements to be different (e.g., a typical 4:3 ratio CRT monitor showing a 1280×1024 mode computer display at maximum size, which is a 5:4 ratio, not quite the same as 4:3). The apparent PPI of a monitor depends upon the screen resolution (that is, the number of pixels) and the size of the screen in use; a monitor in 800×600 mode has a lower PPI than does the same monitor in a 1024×768 or 1280×960 mode.

The dot pitch of a computer display determines the absolute limit of possible pixel density. Typical circa-2000 cathode ray tube or LCD computer displays range from 67 to 130 PPI, though desktop monitors have exceeded 200 PPI and contemporary small-screen mobile devices often exceed 300 PPI.

In January 2008, Kopin Corp. announced a 0.44 inch (1.12 cm) SVGA LCD with an astonishing pixel density of 2272 PPI (each pixel only 11¼ μm).[1][2] According to the manufacturer, the LCD was designed to be optically magnified to yield a vivid image and therefore expected to find use in high-resolution eye-wear devices.

Holography applications demand even greater pixel density, as higher pixel density results in a larger image size and viewing angle. Spatial light modulators can be used to reduce pixel pitch to 2.5 μm, giving a pixel density of 10,160 PPI.[3]

Some observations have indicated that the unaided human eye can generally not differentiate detail beyond 300 PPI;[4] however, this figure depends both on the distance between viewer and image, and the viewer’s visual acuity. The human eye also responds differently to bright, evenly lit and interactive display, than prints on paper.

High pixel density display technologies would make supersampled antialiasing obsolete, enable true WYSIWYG graphics and, potentially enable a practical “paperless office” era.[5] For perspective, such a device at 15 inch (38 cm) screen size would have to display more than four Full HD screens (or WQUXGA resolution).

Development of a display with ~900 ppi allows for three pixels with 16-bit color act as sub-pixels to form a "pixel cluster". These "pixel clusters" act as regular pixels at ~300 ppi to produce true 48-bit color display.

The PPI pixel density specification of a display is also useful for calibrating a monitor with a printer. Software can use the PPI measurement to display a document at "actual size" on the screen.

### Calculation of monitor PPI

Theoretically, PPI can be calculated from knowing the diagonal size of the screen in inches and the resolution in pixels (width and height). This can be done in two steps:

1. Calculate diagonal resolution in pixels using the Pythagorean theorem:

$d_p = \sqrt{w_p^2 + h_p^2}$

2. Calculate PPI:

$PPI = \frac{d_p}{d_i}$

where

• $d_p$ is diagonal resolution in pixels
• $w_p$ is width resolution in pixels
• $h_p$ is height resolution in pixels
• $d_i$ is diagonal size in inches (this is the number advertised as the size of the display).

For example, for a 21.5 inch (54.61 cm) screen with a 1920×1080 resolution (in which $w_p$ = 1920, $h_p$ = 1080 and $d_i$ = 21.5), we get 102.46 PPI; for a typical 10.1 inch netbook screen with a 1024×600 resolution (in which $w_p$ = 1024, $h_p$ = 600 and $d_i$ = 10.1), we get 117.5 PPI.

Note that these calculations may not be very precise. Frequently, screens advertised as “X inch screen” can have their real physical dimensions of viewable area differ, for example:

• Apple Inc.'s Mid-2011 iMac is advertised as a "21.5 inch (viewable) [...] display,"[6] but its actual viewable area is 545.22 mm or 21.465 inches.[7] The more precise figure increases the calculated PPI from 102.46 (using 21.5) to 102.63.
• The HP LP2065 20 inch (50.8 cm) monitor has an actual viewable area of 20.1 inch (51 cm).[8]

### Calculating PPI of camera screens

Camera manufacturers often quote camera screens in 'number of dots'. This is not the same as the number of pixels, because there are 3 'dots' per pixel – red, green and blue. For example, the Canon 50d is quoted as having 920,000 dots.[9] This translates as 307,200 pixels (x3 = 921,600 dots). Thus the screen is 640×480 pixels[10]

This must be taken into account when working out the PPI. Using the above calculations, you require the screen's dimensions, but other methods require you to have the total pixels, not total dots.

'Dots' and 'pixels' are often confused in reviews and specs when viewing information about digital cameras specifically.

## Scanners and cameras

"PPI" or "pixel density" may also be used to describe the resolution of an image scanner. In this context, PPI is synonymous with samples per inch.

In digital photography, pixel density is the number of pixels divided by the area of the sensor. A typical DSLR circa 2013 will have 1–6.2 MP/cm2; a typical compact will have 20–70 MP/cm2. For example Sony Alpha SLT-A58 has 20.1 megapixels on an APS-C sensor having 6.2 MP/cm2 since a compact camera like Sony Cyber-shot DSC-HX50V has 20.4 megapixels on an 1/2.3" sensor having 70 MP/cm2. Interestingly, as can be seen here, the professional camera has a lower PPI than does a compact, because it has larger photodiodes due to having far larger sensors.

## Named pixel densities

The Google Android developer documentation[11] groups displays by their approximate pixel densities into the following categories:

• LDPI: Low density, ~120 dots per inch
• MDPI: Medium density, ~160 dots per inch
• HDPI: High density, ~240 dots per inch
• XHDPI: eXtra High density, ~320 dots per inch
• XXHDPI: eXtra eXtra High density, ~480 dots per inch[12]

The term XHDPI is commonly used to describe handset and tablet displays with pixel densities similar to that of Apple Retina displays[13].

## Metrication

The digital publishing industry often uses "pixels per centimeter" instead of "pixels per inch".[14][15][16]