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
Example | Original Dimension | New Dimension | Calculation | Scale Factor |
---|---|---|---|---|
Enlargement | 5 units | 15 units | (15 / 5) = 3 | 3 |
Reduction | 8 units | 4 units | (4 / 8) = 0.5 | 0.5 |
Inversion | 6 units | -12 units | (-12 / 6) = -2 | -2 |
No Change | 10 units | 10 units | (10 / 10) = 1 | 1 |
Fractional Scaling | 12 units | 9 units | (9 / 12) = 0.75 | 0.75 |
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