Pixels Per Inch (PPI) Calculator

How to Calculate PPI (Pixels Per Inch)

Follow these two steps to calculate PPI manually:

1. Find the diagonal in pixels using the Pythagorean Theorem: diagonal = √(width² + height²)
2. Divide the diagonal in pixels by the diagonal size in inches: PPI = diagonal in pixels ÷ diagonal in inches

You can apply the same method using centimeters to get PPcm (pixels per centimeter).

For instance, if you want to calculate display proportions or pixel relationships, you can use the Aspect Ratio Calculator to find accurate screen ratios like 16:9 or 4:3.

Example: Calculate Pixels Per Inch (PPI)

Suppose your screen is 1920 pixels wide and 1080 pixels high, with a 10-inch diagonal.

Step 1: Calculate the diagonal in pixels.
diagonal = √(1920² + 1080²)
diagonal = √(3686400 + 1166400)
diagonal = √4852800
diagonal = 2202.91 pixels

Step 2: Calculate PPI.
PPI = 2202.91 ÷ 10 = 220.29 pixels per inch

That means your screen packs 220.29 pixels into every inch, resulting in sharp image quality.

How to Calculate Pixels per Square Inch (PPI²)

To find the number of pixels in one square inch of the screen area, square the PPI value:

PPI² = PPI × PPI

For example:
PPI² = 220.29² = 48528 pixels per square inch

This gives the total pixel density over an area of one inch by one inch.

If you prefer calculating ratios or converting screen proportions, the Ratio to Fraction Calculator is a quick and accurate companion for display and resolution-related math.

How to Calculate Dot Pitch

Dot pitch measures the distance between the centers of adjacent pixels, typically expressed in millimeters (mm). It’s inversely related to PPI—the smaller the dot pitch, the higher the pixel density.

Use this simple formula:

dot pitch = (diagonal in inches ÷ diagonal in pixels) × 25.4

Example:
If a screen’s diagonal is 15.4 inches and it has 3396 pixels along the diagonal:

dot pitch = (15.4 ÷ 3396) × 25.4 = 0.1152 mm

Smaller dot pitch values indicate sharper image quality.

How to Calculate Aspect Ratio

Aspect ratio describes the proportional relationship between a display’s width and height.

For example, a screen with 1920 pixels (width) and 1080 pixels (height) has a ratio of:

1920 : 1080

Find the greatest common factor (GCF) of 1920 and 1080, which is 120.

1920 ÷ 120 = 16
1080 ÷ 120 = 9

So the aspect ratio is 16:9, the standard format for most HD and 4K displays.

You can also express it as 1.7:1 by dividing both terms by the height (1080).

Why PPI Matters

PPI affects everything from the sharpness of a display to how text, images, and videos appear. Designers and developers use PPI to ensure consistent visual quality across devices. Photographers and print designers also rely on pixel density to maintain accurate resolution when transferring digital images to physical prints.

If you work with proportional scaling or image design, the Ratio Simplifier Calculator is handy for reducing ratios to their simplest forms before applying them in design or code.

The Pixels Per Inch (PPI) Calculator gives a clear view of your screen’s pixel density, letting you evaluate display quality, print resolution, or aspect ratios quickly and accurately.

Key Formulas Recap:

• PPI = √(width² + height²) ÷ diagonal (inches)
• PPI² = PPI × PPI
• Dot Pitch (mm) = (diagonal in inches ÷ diagonal in pixels) × 25.4

Use the PPI Calculator to calculate your display’s pixel density in seconds, and explore other ratio tools on CalculatorCave for precise, technical measurements.