Screen Dimensions Calculator

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Screen Dimensions Calculator :root { –primary-blue: #004a99; –success-green: #28a745; –light-background: #f8f9fa; –border-color: #dee2e6; –text-color: #333; –secondary-text: #6c757d; } body { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; line-height: 1.6; color: var(–text-color); background-color: var(–light-background); margin: 0; padding: 20px; display: flex; justify-content: center; align-items: flex-start; min-height: 100vh; } .loan-calc-container { background-color: #fff; padding: 30px; border-radius: 8px; box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1); width: 100%; max-width: 700px; box-sizing: border-box; } h1 { color: var(–primary-blue); text-align: center; margin-bottom: 30px; font-weight: 600; } .input-group { margin-bottom: 20px; display: flex; flex-direction: column; gap: 8px; } .input-group label { font-weight: 500; color: var(–secondary-text); } .input-group input[type="number"], .input-group input[type="text"] { padding: 12px 15px; border: 1px solid var(–border-color); border-radius: 4px; font-size: 1rem; box-sizing: border-box; width: 100%; } .input-group input[type="number"]:focus, .input-group input[type="text"]:focus { outline: none; border-color: var(–primary-blue); box-shadow: 0 0 0 3px rgba(0, 74, 153, 0.2); } .input-group .unit { font-size: 0.9rem; color: var(–secondary-text); align-self: center; margin-left: 10px; } .button-group { text-align: center; margin-top: 25px; margin-bottom: 30px; } button { background-color: var(–primary-blue); color: white; border: none; padding: 12px 30px; border-radius: 5px; font-size: 1.1rem; cursor: pointer; transition: background-color 0.3s ease, transform 0.2s ease; font-weight: 500; } button:hover { background-color: #003366; transform: translateY(-2px); } button:active { transform: translateY(0); } #result { background-color: var(–success-green); color: white; padding: 20px; border-radius: 6px; margin-top: 30px; text-align: center; font-size: 1.4rem; font-weight: bold; box-shadow: 0 2px 10px rgba(40, 167, 69, 0.4); display: none; /* Hidden by default */ } #result.visible { display: block; } .article-section { margin-top: 40px; border-top: 1px solid var(–border-color); padding-top: 25px; } .article-section h2 { color: var(–primary-blue); margin-bottom: 15px; font-weight: 600; } .article-section p, .article-section ul { margin-bottom: 15px; color: var(–secondary-text); } .article-section ul li { margin-bottom: 8px; } strong { color: var(–text-color); } .form-row { display: flex; align-items: center; gap: 15px; flex-wrap: wrap; } .input-wrapper { flex: 1; min-width: 150px; } .error-message { color: #dc3545; font-size: 0.9rem; margin-top: 5px; text-align: center; display: none; /* Hidden by default */ } .error-message.visible { display: block; } /* Responsive adjustments */ @media (max-width: 600px) { .loan-calc-container { padding: 20px; } .form-row { flex-direction: column; gap: 15px; } .input-wrapper { width: 100%; } .input-group .unit { margin-left: 0; margin-top: 5px; } button { font-size: 1rem; padding: 10px 25px; } #result { font-size: 1.2rem; } }

Screen Dimensions Calculator

Understanding Screen Dimensions

Screen dimensions are fundamental to understanding the physical size and viewing area of displays like monitors, televisions, and mobile devices. The most commonly referenced dimension is the diagonal measurement, typically given in inches. However, the aspect ratio provides crucial information about the screen's proportions – the relationship between its width and height.

This calculator helps you determine the precise width and height of a screen when you know its diagonal size and aspect ratio. This is useful for various purposes, including:

  • Choosing a monitor or TV: Understanding physical dimensions for desk space or wall mounting.
  • Graphic design and video editing: Ensuring content fits correctly within specified screen resolutions.
  • Virtual reality (VR) and augmented reality (AR): Calculating field of view and display requirements.
  • Understanding pixel density: Relating physical size to the number of pixels for clarity.

The Math Behind the Calculation

The calculation is based on the Pythagorean theorem and the definition of aspect ratio.

Let:

  • D be the diagonal length (in inches).
  • W be the width of the screen.
  • H be the height of the screen.
  • AR_W be the aspect ratio width (e.g., 16 in 16:9).
  • AR_H be the aspect ratio height (e.g., 9 in 16:9).

The aspect ratio gives us the relationship between width and height:
W / H = AR_W / AR_H
This can be rewritten as:
W = H * (AR_W / AR_H)

The Pythagorean theorem relates the width, height, and diagonal of a rectangle:
W^2 + H^2 = D^2

Now, we can substitute the expression for W from the aspect ratio into the Pythagorean theorem:
(H * (AR_W / AR_H))^2 + H^2 = D^2
H^2 * (AR_W^2 / AR_H^2) + H^2 = D^2
Factor out H^2:
H^2 * ( (AR_W^2 / AR_H^2) + 1 ) = D^2
Solve for H^2:
H^2 = D^2 / ( (AR_W^2 / AR_H^2) + 1 )
Simplify the denominator:
H^2 = D^2 / ( (AR_W^2 + AR_H^2) / AR_H^2 )
H^2 = (D^2 * AR_H^2) / (AR_W^2 + AR_H^2)
Take the square root to find H:
H = (D * AR_H) / sqrt(AR_W^2 + AR_H^2)

Once we have the height (H), we can find the width (W) using the aspect ratio:
W = H * (AR_W / AR_H)

Example Calculation

Consider a common widescreen monitor with a 27-inch diagonal and an aspect ratio of 16:9.

  • Diagonal (D) = 27 inches
  • Aspect Ratio Width (AR_W) = 16
  • Aspect Ratio Height (AR_H) = 9

First, calculate the height (H):
H = (27 * 9) / sqrt(16^2 + 9^2)
H = 243 / sqrt(256 + 81)
H = 243 / sqrt(337)
H = 243 / 18.3575...
H ≈ 13.24 inches

Next, calculate the width (W):
W = 13.24 * (16 / 9)
W ≈ 13.24 * 1.777...
W ≈ 23.53 inches

So, a 27-inch monitor with a 16:9 aspect ratio has approximate physical dimensions of 23.53 inches (width) by 13.24 inches (height).

function calculateScreenDimensions() { var screenDiagonal = parseFloat(document.getElementById("screenDiagonal").value); var aspectRatioWidth = parseFloat(document.getElementById("aspectRatioWidth").value); var aspectRatioHeight = parseFloat(document.getElementById("aspectRatioHeight").value); var resultDiv = document.getElementById("result"); var errorDiv = document.getElementById("errorMessage"); resultDiv.innerHTML = ""; resultDiv.classList.remove("visible"); errorDiv.innerHTML = ""; errorDiv.classList.remove("visible"); var isValid = true; var errors = []; if (isNaN(screenDiagonal) || screenDiagonal <= 0) { errors.push("Please enter a valid positive number for Diagonal."); isValid = false; } if (isNaN(aspectRatioWidth) || aspectRatioWidth <= 0) { errors.push("Please enter a valid positive number for Aspect Ratio Width."); isValid = false; } if (isNaN(aspectRatioHeight) || aspectRatioHeight <= 0) { errors.push("Please enter a valid positive number for Aspect Ratio Height."); isValid = false; } if (!isValid) { errorDiv.innerHTML = errors.join(""); errorDiv.classList.add("visible"); return; } var aspectRatioRatio = aspectRatioWidth / aspectRatioHeight; var diagonalSquared = screenDiagonal * screenDiagonal; var aspectRatioRatioSquared = aspectRatioRatio * aspectRatioRatio; var heightSquared = diagonalSquared / (aspectRatioRatioSquared + 1); var height = Math.sqrt(heightSquared); var width = height * aspectRatioRatio; resultDiv.innerHTML = "Width: " + width.toFixed(2) + " inchesHeight: " + height.toFixed(2) + " inches"; resultDiv.classList.add("visible"); }

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