Dilation Transformation Calculator

Work out dilation transformation instantly with clear inputs, formula shown and shareable results.

About Dilation Transformation Calculator

A dilation centred at C multiplies every displacement from C by k: P' = C + k(P − C). Lengths scale by |k| and areas by k²; a negative k also rotates the figure by 180° about the centre.

Formula

Dilation

P' = C + k(P − C), area scale = k²

Worked example

With the default values below, Dilation Transformation Calculator returns Image point of (8.5, 13.5). Change any input above and every figure here is recalculated in your browser.

Inputs used

Point x: 4
Point y: 6
Scale factor k: 2.5
Centre of dilation (x, y): 1, 1

Results

Image point: (8.5, 13.5)
New x: 8.5000
New y: 13.5000
Area multiplier k²: 6.2500

Step by step

1Values used
2Dilation
3Image point= (8.5, 13.5)
4New x= 8.5000
5New y= 13.5000
6Area multiplier k²= 6.2500

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What does k between 0 and 1 do?

It shrinks the figure toward the centre while keeping the same shape.

What does a negative k do?

It enlarges by |k| and simultaneously turns the figure through 180° about the centre.