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Screen Size, PPI, and Pixel Pitch Formulas

Review screen width, height, area, unit conversion, diagonal pixels, PPI, pixel pitch, megapixel, and aspect-ratio mismatch formulas.

How do the Screen Size Calculator formulas work?

This formula page defines the variables used by the Screen Size Calculator, shows how those values are combined, and explains the order of operations behind the result. Use the worked steps to verify an estimate, compare scenarios, and understand which assumptions or rounding rules can affect the displayed answer.

Formula Overview

The physical screen is modeled as a rectangle. Its diagonal is the hypotenuse of a right triangle, while the entered aspect components determine the relative lengths of the two legs. Optional pixel dimensions use the same diagonal relationship.

Variable Definitions

  • D: physical screen diagonal
  • a: aspect-ratio width component
  • b: aspect-ratio height component
  • W: physical viewable width
  • H: physical viewable height
  • Pw: horizontal pixel count
  • Ph: vertical pixel count
  • Dpx: diagonal pixel count

Screen Width and Height

s=Da2+b2s=\frac{D}{\sqrt{a^2+b^2}}
W=as,H=bsW=as,\qquad H=bs

Equivalently, multiply the diagonal by each aspect component divided by the ratio hypotenuse. This guarantees that W² + H² = D².

Viewable Screen Area

Area=W×HArea=W\times H

The calculation uses unrounded width and height. Square-centimeter output multiplies square inches by 2.54².

Inch and Centimeter Conversion

centimeters=inches×2.54centimeters=inches\times2.54
inches=centimeters÷2.54inches=centimeters\div2.54

The international inch is exactly 2.54 centimeters.

Diagonal Pixel Count

Dpx=Pw2+Ph2D_{px}=\sqrt{P_w^2+P_h^2}

This is the hypotenuse of the rectangular pixel grid.

Pixels per Inch

PPI=DpxDinPPI=\frac{D_{px}}{D_{in}}

The physical diagonal must be expressed in inches. PPI assumes square pixels and that the full entered pixel grid spans the measured viewable area.

Pixel Pitch

Pixel pitchmm=25.4PPIPixel\ pitch_{mm}=\frac{25.4}{PPI}

This gives approximate millimeters per pixel position. A higher PPI therefore produces a smaller pitch.

Total Megapixels

Megapixels=PwPh1,000,000Megapixels=\frac{P_wP_h}{1{,}000{,}000}

Physical and Resolution Aspect Mismatch

Mismatch%=∣(Pw/Ph)(a/b)−1∣×100Mismatch\%=\left|\frac{(P_w/P_h)}{(a/b)}-1\right|\times100

The calculator shows a warning when this value is greater than 1%.

Worked 10-Inch 4:3 Calculation

Because √(4² + 3²) = 5, a 10-inch diagonal has scale 2:

W=4×2=8 in,H=3×2=6 inW=4\times2=8\text{ in},\qquad H=3\times2=6\text{ in}
Area=8×6=48 in2Area=8\times6=48\text{ in}^2
PPI=10242+768210=128010=128PPI=\frac{\sqrt{1024^2+768^2}}{10}=\frac{1280}{10}=128

Precision and Assumptions

Intermediate geometry retains JavaScript numeric precision. Physical dimensions, area, and PPI display two decimals; pixel pitch and megapixels display three. The model assumes a flat rectangular viewable surface, square pixels, and a diagonal that excludes the bezel. It excludes curved-surface depth, manufacturer rounding, software scaling, and subpixel layout.

References

These references support the calculation method, assumptions, or current program guidance.

Corrections and Review

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