How to Calculate PPI: A Comprehensive Guide
Step 1: Calculate the Diagonal Length in Pixels
To determine the diagonal length in pixels, use the Pythagorean Theorem and the screen width and height in pixels:
diagonal_pixels = √(width^2 + height^2)
You can use online tools like our Aspect Ratio Calculator to quickly find the screen height, width, and diagonal.
Step 2: Calculate PPI (Pixels Per Inch)
Next, use the following formula to calculate PPI by dividing the diagonal length in pixels by the diagonal length in inches:
PPI = diagonal_pixels / diagonal_inches
The PPI value represents the number of pixels in a 1-inch line on the display, which remains consistent for horizontal, vertical, or diagonal lines. This calculator is applicable only for displays with square pixels.
To calculate pixels per centimeter (PPcm), simply replace inches with centimeters in the formula.
Calculating PPI^2 (Pixels Per Square Inch)
To find the pixel density of an area of one square inch, multiply PPI by itself:
PPI^2 = PPI × PPI
For pixels per square centimeter (PPcm^2), substitute 1 cm for 1 inch in the equation.
Example: Calculating PPI for a Computer Screen
Consider a computer screen with a width of 1920 pixels, a height of 1080 pixels, and a diagonal of 10 inches. To find the pixel density in one linear inch of the display, follow these steps:
- 1. Calculate the diagonal length in pixels using the Pythagorean Theorem:
diagonal_pixels = √(1920^2 + 1080^2) = 2202.91 pixels
- 2. Divide the diagonal length in pixels by the diagonal length in inches to find PPI:
PPI = 2202.91 / 10 = 220.29 pixels
Thus, there are 220.29 pixels in a 1-inch line on the display.
Example: Calculating PPI^2 for a Computer Screen
Using the same computer screen with a PPI of 220.29, calculate PPI^2:
PPI^2 = 220.29^2 = 48,528 pixels per square inch
Therefore, there are 48,528 pixels in a 1-inch by 1-inch area of the screen.
Calculating Diagonal Dot Pitch
Diagonal dot pitch refers to the diagonal distance between the centers of two adjacent pixels. Calculate dot pitch using the diagonal length in inches and pixels, then convert from inches per pixel to millimeters per pixel (expressed in mm):
dot_pitch = (diagonal_inches / diagonal_pixels) × 25.4
For example, if a screen diagonal is 15.4 inches and has 3,396 pixels, the dot pitch is approximately 0.1152 mm:
dot_pitch = (15.4 / 3396) × 25.4 ≈ 0.1152 mm