Calculate the physical screen width based on its diagonal measurement and aspect ratio.
— inches
Understanding Screen Width Calculation
This calculator helps you determine the actual physical width of a screen in inches, given its diagonal measurement and its aspect ratio. This is useful for various applications, from choosing the right monitor for your desk setup to understanding display specifications for design and multimedia projects.
The Math Behind the Calculation
The calculation relies on the Pythagorean theorem and basic algebraic manipulation. A screen's diagonal, width, and height form a right-angled triangle, where the diagonal is the hypotenuse.
Let:
D be the diagonal length (input).
W be the width (what we want to find).
H be the height.
AR be the aspect ratio, typically expressed as width:height (e.g., 16:9).
From the Pythagorean theorem:
W² + H² = D²
The aspect ratio gives us the relationship between width and height. If the aspect ratio is width:height, we can express height in terms of width:
Let the aspect ratio be A:B. Then, W / H = A / B.
This means H = W * (B / A).
Now, substitute this expression for H into the Pythagorean theorem:
W² + (W * B / A)² = D² W² + W² * (B² / A²) = D²
Factor out W²:
W² * (1 + B² / A²) = D²
To simplify the term in the parenthesis:
W² * ((A² + B²) / A²) = D²
Now, solve for W²:
W² = D² * (A² / (A² + B²))
Finally, take the square root to find the width W:
W = D * sqrt(A² / (A² + B²))
Or, equivalently:
W = D * (A / sqrt(A² + B²))
How to Use the Calculator
Screen Diagonal: Enter the diagonal measurement of your screen in inches. This is usually stated in the product specifications (e.g., 27 inches, 32 inches).
Aspect Ratio: Enter the aspect ratio of your screen, typically in the format 'Width:Height' (e.g., 16:9 for most modern monitors and TVs, 21:9 for ultrawide displays, 4:3 for older monitors).
Click the "Calculate Width" button.
The calculator will then display the calculated physical width of the screen in inches. This is the horizontal dimension of the display area itself.
Use Cases
Desktop Setup Planning: Determine if a monitor will fit comfortably on your desk and how much horizontal space it will occupy.
Multimedia & Design: Understand the actual screen dimensions for video editing, graphic design, or web development to ensure content displays as intended.
Purchasing Decisions: Compare the physical sizes of different monitors beyond just the diagonal measurement, especially when considering aspect ratios like ultrawide.
Home Theater Setup: Estimate screen dimensions for optimal viewing distances and room layout.
function calculateScreenWidth() {
var diagonalInput = document.getElementById("diagonal");
var aspectRatioInput = document.getElementById("aspectRatio");
var resultValueElement = document.getElementById("resultValue");
var diagonal = parseFloat(diagonalInput.value);
var aspectRatioStr = aspectRatioInput.value;
// Clear previous result
resultValueElement.textContent = "–";
// Validate inputs
if (isNaN(diagonal) || diagonal <= 0) {
alert("Please enter a valid positive number for the screen diagonal.");
return;
}
if (aspectRatioStr.trim() === "") {
alert("Please enter the aspect ratio (e.g., 16:9).");
return;
}
var parts = aspectRatioStr.split(':');
if (parts.length !== 2) {
alert("Aspect ratio must be in the format Width:Height (e.g., 16:9).");
return;
}
var aspectRatioW = parseFloat(parts[0]);
var aspectRatioH = parseFloat(parts[1]);
if (isNaN(aspectRatioW) || aspectRatioW <= 0 || isNaN(aspectRatioH) || aspectRatioH <= 0) {
alert("Aspect ratio values must be positive numbers.");
return;
}
// Calculation
// W = D * (A / sqrt(A^2 + B^2))
var aSquared = aspectRatioW * aspectRatioW;
var bSquared = aspectRatioH * aspectRatioH;
var denominator = Math.sqrt(aSquared + bSquared);
var width = diagonal * (aspectRatioW / denominator);
// Display result, rounded to 2 decimal places
resultValueElement.textContent = width.toFixed(2);
}