Scale Factor Dilation Calculator

Scale Factor Dilation Calculator

Enter your original length and new length measurements in scale factor Dilation calculator. Select shape type for dimension analysis. Choose whether to calculate scale factor or new dimensions. The calculator provides the scale factor and corresponding changes in area and volume.

  • Inputs: Original = 10 units, New = 20 units
  • Process: Enter values, select shape type
  • Result: 2x scale factor, 4x area increase

Scale Factor Dilation Example Chart

ExampleOriginal DimensionNew DimensionCalculationScale Factor
Enlargement5 units15 units(15 / 5) = 33
Reduction8 units4 units(4 / 8) = 0.50.5
Inversion6 units-12 units(-12 / 6) = -2-2
No Change10 units10 units(10 / 10) = 11
Fractional Scaling12 units9 units(9 / 12) = 0.750.75

How to Calculate Scale Factor Dilation

To find the scale factor, divide the new length by the original length. For areas, square the scale factor. For volumes, cube it. Consider shape dimensions when calculating total size changes.

  • Inputs: Square side increases from 5 to 15 units
  • Calculations: 15 ÷ 5 = 3 (length), 3² = 9 (area)
  • Result: 3x scale factor, 9x area increase

Scale Factor Dilation Formula

Linear Scale = New Length ÷ Original Length
Area Scale = (Linear Scale)²
Volume Scale = (Linear Scale)³

Where:
Linear Scale = Change in one dimension
Area Scale = Change in two dimensions
Volume Scale = Change in three dimensions

Square Enlargement

  • Inputs: Original = 8 units, New = 24 units
  • Calculations: Scale = 24/8 = 3x, Area = 3² = 9x
  • Result: 3x larger sides, 9x larger area

Circle Reduction

  • Inputs: Original = 10 units, New = 5 units
  • Calculations: Scale = 5/10 = 0.5x, Area = 0.5² = 0.25x
  • Result: 0.5x radius, 0.25x area

Cube Expansion

  • Inputs: Original = 4 units, New = 12 units
  • Calculations: Scale = 12/4 = 3x, Volume = 3³ = 27x
  • Result: 3x edges, 27x volume

Rectangle Scale

  • Inputs: Original = 6 units, New = 15 units
  • Calculations: Scale = 15/6 = 2.5x, Area = 2.5² = 6.25x
  • Result: 2.5x sides, 6.25x area

Model Scale

  • Inputs: Original = 100 units, New = 25 units
  • Calculations: Scale = 25/100 = 0.25x, Volume = 0.25³ = 0.016x
  • Result: 0.25x length, 0.016x volume

What is Scale Factor Dilation?

Scale Factor Dilation transforms shapes by multiplying all dimensions by the same factor. A factor greater than 1 enlarges the shape, while less than 1 reduces it. The scale factor affects areas by its square and volumes by its cube, making this relationship crucial in geometric transformations and real-world applications.

Enlargement: Scale > 1
Reduction: Scale < 1
No Change: Scale = 1

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