# Pixel density

### Pixel density

Pixels per inch (PPI) or pixels per centimeter (PPCM) is a measurement of the pixel density (resolution) of an electronic image device, such as a computer monitor or television display, or image digitizing device such as a camera or image scanner. Horizontal and vertical density are usually the same, as most devices have square pixels, but differ on devices that have non-square pixels.

PPI can also describe the resolution, in pixels, of an image file. The unit is not square centimeters—a 100×100 pixel image printed in a 1 cm square has a resolution of 100 pixels per centimeter (ppcm). Used this way, the measurement is meaningful when printing an image. It has become commonplace to refer to PPI as DPI, even though PPI refers to input resolution. Industry standard, 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 is optimum. The lowest acceptable quality factor is considered 1.5, which equates to printing a 225 ppi image using a 150 lpi screen onto coated paper.

Screen frequency is determined by the type of paper the image is printed on. An absorbent paper surface, uncoated recycled paper for instance, lets ink droplets spread (dot gain)—so requires a more open printing screen. Input resolution can therefore be reduced to minimise file size without 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 printing screen frequency to no more than 120 lpi, therefore, a quality factor of 2 is achieved with images of 240 ppi.

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

## Contents

• Computer displays 1
• Calculation of monitor PPI 1.1
• Calculating PPI of camera view screens 1.2
• Scanners and cameras 2
• Smartphones 3
• Named pixel densities 4
• Metrication 5
• References 7

## 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 to have different horizontal and vertical PPI measurements (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, sometimes by a wide margin.

In January 2008, Kopin Corporation announced a 0.44 inch (1.12 cm) SVGA LCD with a pixel density of 2272 PPI (each pixel only 11.25μm).[1][2] In 2011 they followed this up with a 3760 DPI 0.21” diagonal VGA colour display.[3] The manufacturer says they designed the LCD to be optically magnified, as in high-resolution eyewear devices.

Holography applications demand even greater pixel density, as higher pixel density produces a larger image size and wider viewing angle. Spatial light modulators can reduce pixel pitch to 2.5 μm, giving a pixel density of 10,160 PPI.[4]

Some observations indicate that the unaided human generally can't differentiate detail beyond 300 PPI.[5] However, this figure depends both on the distance between viewer and image, and the viewer’s visual acuity. The human eye also responds in a different way to a bright, evenly lit interactive display than to 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.[6] 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 to act as sub-pixels to form a pixel cluster. These pixel clusters act as regular pixels at ~300 ppi to produce a 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.
• For 27 inch screen with a 2560x1440 resolution we get = sqrt(2560^2+1440^2)/27 = 109 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. advertized their mid-2011 iMac as a "21.5 inch (viewable) [...] display,"[7] but its actual viewable area is 545.22 mm or 21.465 inches.[8] 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).[9]

### Calculating PPI of camera view screens

Camera manufacturers often quote view 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.[10] This translates as 307,200 pixels (x3 = 921,600 dots). Thus the screen is 640×480 pixels.[11]

This must be taken into account when working out the PPI. Using the above calculations requires the screen's dimensions, but other methods require 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 describe image scanner resolution. 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, has 1–6.2 MP/cm2; a typical compact has 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 a compact camera, because it has larger photodiodes due to having far larger sensors.

## Smartphones

Smartphones use small displays, but modern smartphone displays have a larger PPI rating, such as the Fujitsu F-02G with a quad HD display at 564 PPI,[12] the LG G3 with quad HD display at 534 PPI or - XHDPI or Oppo Find 7 with 534ppi on 5.5" display - XXHDPI (see section below).[13]

## Named pixel densities

The Google Android developer documentation[14] groups displays by their approximate pixel densities into the following categories:

• LDPI: Low density, ~120 dots per inch
• MDPI: Medium density, ~120-160 dots per inch
• TVDPI: Medium High density, ~160-213 dots per inch
• HDPI or HiDPI: High density, ~213-240 dots per inch
• XHDPI: eXtra High density, ~240-320 dots per inch
• XXHDPI: eXtra eXtra High density, ~320-480 dots per inch[15]
• XXXHDPI: eXtra eXtra eXtra High density, ~480-640 dots per inch[16]

## Metrication

The digital publishing industry primarily uses "pixels per inch" but sometimes "pixels per centimeter" is used or a conversion factor is given.[17][18][19]

The PNG image file format only allows the meter as the unit for pixel density.[20]

## References

1. ^ "Kopin unveils smallest color SVGA display". optics.org. 11 January 2008. Retrieved 6 June 2008.
2. ^ "Company Debuts World’s Smallest Color SVGA Display" (PDF). SID, Information Display magazine May 2008 Vol. 24, No. 05. 31 May 2008. Retrieved 6 June 2008.
3. ^ "Innovations". kopin corporation. Retrieved 22 May 2014.
4. ^ Horizontally scanning holography to enlarge both image size and viewing zone angle Naoya Okada and Yasuhiro Takaki, Proc. of SPIE Vol. 7233 723309-1
5. ^ "Apple Retina Display". Jonesblog. 24 June 2010. Retrieved 25 September 2011.
6. ^ "Electronic displays for information technology". IBM Journal of Research and Development Volume 44, Number 3, 2000. 10 November 1999. Retrieved 6 June 2008.
7. ^ Apple iMac Tech Specs, Apple Inc.. Accessed on 27 January 2012.
8. ^ LM215WF3 LCD Product Specification, LG Display. Accessed on 27 January 2012.
9. ^ HP LP2065 20-inch (50.8 cm) LCD Monitor - Specifications and Warranty (Hewlett-Packard Company official website)
10. ^ dpreview.com, Canon EOS 50d
11. ^ Techcrunch.com, dots vs pixels
12. ^ 村上万純 (October 7, 2014). "富士通が最新のドコモスマホやタブレットを披露　5G通信の取り組みも".
13. ^ Richard Lai (February 12, 2014). "Oppo's next smartphone due in March with 2K and 1080p display options".
14. ^ Providing Resources, Android Developers
15. ^ Android reference for developers
16. ^ Android reference for developers
17. ^ "Web Graphics Basics".
18. ^ "Utads.com Glossary of Terms".
19. ^ "Resolution, dpi and ppi".
20. ^ "PNG file format, pHYs chunk".