What is a dilation?
A similarity transform that scales distances from a fixed center by factor k.
Dilation Calculator
Apply a geometric dilation (homothety) to a point in the plane.
Enter point, scale, and center
Choose origin or custom center, then provide k and (x,y).
About this calculator
How to use Dilation Calculator, plus the formulas and logic behind the results.
Tool description
A dilation maps each point along the ray from the center by factor k. About the origin this is simply (kx, ky).
How to use
- Select origin or custom center.
- Enter the point and scale factor k.
- If custom, enter the center coordinates.
- Select Calculate to view the image point.
Formulas & reference
About origin: (x′, y′) = (kx, ky)About C: X′ = C + k(X − C)
Dilation notes
- k = 1 leaves the point fixed
- k = −1 is a point reflection through the center
- Distances from center scale by |k|
- Shapes remain similar
Calculation logic
Translates relative to the center, scales by k, then translates back.
k > 1 enlarges, 0 < k < 1 shrinks, k < 0 reflects through the center while scaling.
Dilation Calculator FAQ
Common questions about this calculator and how to use the results.
What if the center is the origin?
Multiply both coordinates by k.
Can k be negative?
Yes. The point is scaled and reflected through the center.
What if k = 0?
Every point maps to the center.
Does dilation preserve angles?
Yes. It is a similarity (with possible orientation reversal if k < 0).
How do I dilate a whole shape?
Apply the same rule to every vertex.