Enter the change in x and change in y of a length along with a shape or image pre and post-scaling to calculator the scale factor dilation. This is also known as a scale factor calculator.

Scale Factor Dilation Calculator

Enter the original point, scale factor, and optional center of dilation. If no center is provided, the origin (0, 0) will be used.

Scale Factor Dilation Formula

The following formula is used to calculate the scale factor dilation of an image or shape. 

SF = X2/X1 = Y2/Y1
  • Where SF is the scale factor dilation
  • X2 and Y2 are the change in X and Y of the final image
  • X1 and Y1 are the change in X and Y of the original image

To calculate the scale factor dilation, divide the dimensions of of the final image by those of the original image.

Scale Factor Dilation Definition

A scale factor dilation is a ratio of the length or area of an image before and after it has been enlarged or shrunk.

Scale Factor Dilation Example

How to calculate a scale factor dilation?

  1. First, determine the change in X and Y of the original image.

    Measure the change in X and Y of a single length of the original image.

  2. Next, determine the change in X and Y of the modified image.

    Measure the change in X and Y of the same length on the modified image.

  3. Finally, calculate the scale factor dilation.

    Calculate the total scale factor dilation using the equation above.

Example Problem:

The following is a step-by-step example problem for calculating a scale factor dilation. This example follows the how-to calculate instructions from directly above.

First, the change in x and y of the original image must be determined. Measuring these two values we find these to be 5 and 7 respectively.

Next, the change in x and y of the modified image must be measured. For this example, these are found to be 10 and 14 respectively.

Finally, we can calculate the scale factor dilation using the formula above:

SF = X2/X1 = Y2/Y1

SF = 10/5 = 14/7

SF = 2 = 2

FAQ

What is scale factor dilation?

A scale factor dilation is a rate at which an image or shape is enlarged or shrunk to produce a scaled version of the image.