Scale Factor Calculator

Scale Factor Calculator

Calculate ratios, find missing dimensions, or determine scale percentages.

Calculation Results

Scale Factor:

Percentage Change:

Area Scale Factor:

Volume Scale Factor:

function calculateScale() { var original = parseFloat(document.getElementById('origDim').value); var scaled = parseFloat(document.getElementById('scaledDim').value); var resultDiv = document.getElementById('scaleResults'); if (isNaN(original) || isNaN(scaled) || original === 0) { alert("Please enter valid numbers. Original dimension cannot be zero."); resultDiv.style.display = 'none'; return; } var factor = scaled / original; var percent = (factor * 100); var areaFactor = Math.pow(factor, 2); var volFactor = Math.pow(factor, 3); document.getElementById('resFactor').innerText = factor.toLocaleString(undefined, {maximumFractionDigits: 4}); document.getElementById('resPercent').innerText = percent.toLocaleString(undefined, {maximumFractionDigits: 2}) + "%"; document.getElementById('resArea').innerText = areaFactor.toLocaleString(undefined, {maximumFractionDigits: 4}) + "x"; document.getElementById('resVol').innerText = volFactor.toLocaleString(undefined, {maximumFractionDigits: 4}) + "x"; var explanation = ""; if (factor > 1) { explanation = "This is an enlargement. The scaled object is " + factor.toFixed(2) + " times larger than the original."; } else if (factor < 1) { explanation = "This is a reduction. The scaled object is " + (factor * 100).toFixed(2) + "% of the original size."; } else { explanation = "The scale factor is 1, meaning the objects are identical in size."; } document.getElementById('scaleExplanation').innerText = explanation; resultDiv.style.display = 'block'; }

What is a Scale Factor?

In geometry and mathematics, a scale factor is a number which scales, or multiplies, some quantity. It is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger (enlargement). If the scale factor is a fraction between 0 and 1, the copy will be smaller (reduction).

The Scale Factor Formula

To find the scale factor, you simply divide the dimension of the new (scaled) shape by the dimension of the original shape:

Scale Factor = Scaled Dimension ÷ Original Dimension

Area and Volume Ratios

It is important to note that when you scale a linear dimension (like length), the area and volume do not change linearly:

• Area Scale Factor: This is the linear scale factor squared (k²). If you double the length of a square, its area becomes four times larger.
• Volume Scale Factor: This is the linear scale factor cubed (k³). If you double the length of a cube, its volume becomes eight times larger.

Real-World Examples

Scenario	Original	Scaled	Scale Factor
Model Car	400 cm	16 cm	0.04 (or 1:25)
Photo Print	4 inches	12 inches	3 (300%)
Blueprints	50 feet	5 inches	1/120

How to use this calculator

1. Enter the Original Dimension: This is the size of the object you are starting with.

2. Enter the Scaled Dimension: This is the size of the new object (the copy, model, or blueprint).

3. The calculator will instantly provide the linear scale factor, the percentage of the original size, and how the area and volume are affected by this change.