# Pixels Per Inch PPI Calculator

## Calculator Use

The PPI Calculator finds pixels per inch (PPI) and pixels per centimeter (PPcm). It will calculate PPI when inches are entered and calculate both PPI and PPcm when centimeters are entered.

PPI is a measure of pixel density or resolution of a computer screen, television screen or other display device. Pixels per inch or PPcm indicates how many pixels are in a 1 inch line or 1 cm line on a display. Also calculated are dot pitch, diagonal in pixels and total number in megapixels.

## Follow These Two Steps to Calculate PPI:

- Use the Pythagorean Theorem and the screen width and height in pixels to calculate the diagonal length in pixels:

\( \text{diagonal} = \sqrt{\text{width}^2 + \text{height}^2} \) -

- Use the formula to calculate PPI, dividing the length of the diagonal in pixels by the length of the diagonal in inches

\( \text{PPI} = \dfrac{\text{diagonal in pixels}}{\text{diagonal in inches}} \)

The number of pixels per inch or PPI tells you how many pixels are in a 1 inch line on a display screen. The PPI will be the same whether it's a horizontal or vertical or diagonal inch because pixels are square and therefore symmetric. If a display does not have square pixels then this calculator does not apply.

You can use the same PPI formula above to calculate pixels per centimeter, PPcm. Just substitute cm for inches to find PPcm.

## How to Calculate PPI^{2} or Pixels per Square Inch

Multiply PPI × PPI to get pixels per square inch. The number of pixels in a square inch represents the resolution or pixel density of an area of one square inch. Substitute 1 cm for 1 inch to find pixels per square centimeter or PPcm^{2}.

## Example: Calculate Pixels per Inch PPI

You have a computer screen that is 1920 pixels wide by 1080 pixels high. The diagonal is 10 inches. You want to find the pixel density in one linear inch of display.

**Calculate the diagonal length in pixels with the Pythagorean Theorem:**

*diagonal _{pixels}* = √(1920

^{2}+ 1080

^{2})

*diagonal _{pixels}* = √(3686400 + 1166400)

*diagonal _{pixels}* = √4852800

*diagonal _{pixels}* = 2202.91 pixels

**Now divide:**

PPI = *diagonal _{pixels}* /

*diagonal*

_{inches}PPI = 2202.91 / 10

PPI = 220.29 pixels

So there are 220.29 pixels in a 1 inch line on the display.

## Example: Calculate Pixels per Square Inch, PPI^{2}

Using this same computer screen, PPI^{2} will be:

220.29^{2} = 48528 pixels per square inch

So there are 48528 pixels in an area of the screen that is 1 inch wide by one inch high.

## How to Calculate the diagonal dot pitch

Diagonal dot pitch is the diagonal distance from the center of one pixel to the center of the next. Dot pitch is calculated from the diagonal length in inches and pixels then converted from inches per pixel to millimeters per pixel but normally only expressed in millimeters (mm).

If a screen diagonal is 15.4 inches and has 3396 pixels. Dot pitch = (15.4/3396) × 25.4 ≈ 0.1152 mm.

## How to Calculate Aspect Ratio

For example, let's say you have a screen width equal to 1920 pixels and height equal to 1080 pixels. The ratio of width to height is 1920:1080. To reduce this to lowest terms we find the greatest common factor of 1920 and 1080 which is GCF(1920,1080) = 120. Reduce our ratio of 1920:1080 by dividing both terms by the GCF of 120. 1920/120 = 16 and 1080/120 = 9 so our reduced ratio is 1920:1080 = 16:9. 16:9 is the aspect ratio, the ratio of width to height in lowest terms.

In some cases we want to know the aspect ratio in terms of 1 as the second term. In that case, divide both terms by the second term to get 1920/1080 = 1.7 and 1080/1080 = 1. The aspect ratio in terms of 1 is 1.7:1 and we can say 1920:1080 = 16:9 = 1.7:1

**Cite this content, page or calculator as:**

Furey, Edward "Pixels Per Inch PPI Calculator" at https://www.calculatorsoup.com/calculators/technology/ppi-calculator.php from CalculatorSoup,
*https://www.calculatorsoup.com* - Online Calculators

Last updated: July 10, 2023