Translation Transformation Calculator

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

About Translation Transformation Calculator

A translation adds a fixed vector to every point: (x, y) → (x + dx, y + dy). It preserves lengths, angles and orientation, so the shape is congruent to the original.

Formula

Translation

(x, y) → (x + dx, y + dy), distance = √(dx² + dy²)

Worked example

With the default values below, Translation Transformation Calculator returns Image point of (7, -1). Change any input above and every figure here is recalculated in your browser.

Inputs used

Point x: 2
Point y: 3
Shift in x: 5
Shift in y: -4

Results

Image point: (7, -1)
New x: 7.0000
New y: -1.0000
Distance moved: 6.4031

Step by step

1Values used
2Translation
3Image point= (7, -1)
4New x= 7.0000
5New y= -1.0000
6Distance moved= 6.4031

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

Translating (2, 3) by (5, −4)?

The image is (7, −1) and the point has moved √41 ≈ 6.403124 units.

Does translation change the shape?

No. Every translation is an isometry, so lengths and angles are unchanged.