Splitting the diagonal into width and height
The diagonal is the hypotenuse of the width-height rectangle, so Pythagoras splits it by the aspect ratio. For 16:9 the divisor is √(256+81) ≈ 18.36, which gives width ≈ diagonal × 0.872 and height ≈ diagonal × 0.490. Multiply inches by 2.54 for centimeters.
Common 16:9 sizes
| Diagonal | Width | Height |
|---|---|---|
| 24" | 20.9" (53.1 cm) | 11.8" (29.9 cm) |
| 27" | 23.5" (59.7 cm) | 13.2" (33.6 cm) |
| 32" | 27.9" (70.8 cm) | 15.7" (39.8 cm) |
| 55" | 47.9" (121.7 cm) | 27.0" (68.5 cm) |
| 65" | 56.7" (144.0 cm) | 31.9" (81.0 cm) |
All 16:9. A 16:10 screen of the same diagonal is a little shorter in width and taller in height.
The diagonal hides how much area you gain
Area grows with the square of the size, so a 32-inch screen is not twice the surface of a 16-inch — it is four times. When you compare screens, compare width and height, not the single diagonal number.
A third more diagonal (24" to 32") is about 78 percent more screen area, because area scales with the square of the size.
Common questions
How do you get width and height from a screen diagonal?
Split the diagonal in the ratio of the aspect. For 16:9, width is the diagonal times 16 divided by the square root of (16 squared plus 9 squared), and height uses 9 the same way. That square root works out to about 18.36.
What are the dimensions of a 27-inch 16:9 monitor?
About 23.5 inches wide and 13.2 inches tall, which is 59.7 by 33.6 centimeters. The 27 inches is only the corner-to-corner diagonal, never the width.
Do two screens with the same diagonal have the same size?
Not if their aspect ratios differ. A 24-inch 16:10 screen is a little taller and slightly larger in area than a 24-inch 16:9 screen, even though both are called 24 inches.
