When choosing a monitor, its size is often described by its diagonal length, measured in inches. However, to truly understand the usable screen space, it's crucial to know the width and height of the display. This calculator helps you determine these dimensions based on the diagonal measurement and the monitor's aspect ratio.
The Math Behind the Calculation
The relationship between a monitor's width (W), height (H), and diagonal length (D) is governed by the Pythagorean theorem, as the diagonal, width, and height form a right-angled triangle.
The aspect ratio (AR) is a ratio of the screen's width to its height. Common aspect ratios include 16:9 (widescreen), 4:3 (standard definition), and 21:9 (ultrawide).
Let ARwidth be the width part of the aspect ratio and ARheight be the height part.
The aspect ratio can be expressed as:
AR = ARwidth / ARheight
This means we can express the width in terms of height (or vice versa):
W = H * (ARwidth / ARheight)
Now, applying the Pythagorean theorem (a² + b² = c²), where 'a' is height, 'b' is width, and 'c' is the diagonal:
H² + W² = D²
Substitute the expression for W into the Pythagorean theorem:
H² + (H * (ARwidth / ARheight))² = D²
Factor out H²:
H² * (1 + (ARwidth / ARheight)²) = D²
Solve for H:
H = D / sqrt(1 + (ARwidth / ARheight)²)
Once we have the height (H), we can easily calculate the width (W):
W = H * (ARwidth / ARheight)
Use Cases
Content Creation: Understanding the exact pixel dimensions of your display helps in designing graphics, editing videos, or coding websites that fit perfectly.
Gaming: Knowing your monitor's width and height can be useful for adjusting in-game settings for optimal field of view.
Productivity: For tasks requiring precise spatial arrangement of windows or elements, knowing the physical dimensions provides context beyond pixel counts.
Monitor Comparison: Compare the actual usable screen area of different monitors with varying aspect ratios but similar diagonal sizes.
This calculator simplifies these calculations, providing you with the essential width and height dimensions of your monitor.
function calculateScreenDimensions() {
var diagonalLength = parseFloat(document.getElementById("diagonalLength").value);
var aspectRatioWidth = parseFloat(document.getElementById("aspectRatioWidth").value);
var aspectRatioHeight = parseFloat(document.getElementById("aspectRatioHeight").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = "Results will appear here."; // Reset message
// Input validation
if (isNaN(diagonalLength) || diagonalLength <= 0) {
resultDiv.innerHTML = "Please enter a valid positive diagonal length.";
return;
}
if (isNaN(aspectRatioWidth) || aspectRatioWidth <= 0) {
resultDiv.innerHTML = "Please enter a valid positive aspect ratio width.";
return;
}
if (isNaN(aspectRatioHeight) || aspectRatioHeight <= 0) {
resultDiv.innerHTML = "Please enter a valid positive aspect ratio height.";
return;
}
// Calculate aspect ratio value
var aspectRatioValue = aspectRatioWidth / aspectRatioHeight;
// Calculate height (H) using Pythagorean theorem
// H = D / sqrt(1 + AR²)
var heightSquared = 1 + Math.pow(aspectRatioValue, 2);
var height = diagonalLength / Math.sqrt(heightSquared);
// Calculate width (W)
// W = H * AR
var width = height * aspectRatioValue;
// Display the results
resultDiv.innerHTML =
"Screen Width: " + width.toFixed(2) + " inches" +
"Screen Height: " + height.toFixed(2) + " inches";
}