ConverterHub

Point Translation Calculator

Find the new coordinates of a point after shifting it by a given vector.

How it is calculated

A translation adds the same vector to every coordinate: x′ = x + dx and y′ = y + dy. Here (x, y) is the starting point, (dx, dy) is the shift, and (x′, y′) is the new point. A positive dx moves the point to the right and a positive dy moves it up, in the usual maths axes where y grows upwards; a negative value moves it the other way. All four values are required and can be negative or have decimals. The results are rounded to two decimals, so a shift smaller than 0.005 does not show. The shift has no units of its own, so the point and the vector must use the same unit. The tool moves one point; to move a shape, apply the same vector to each of its corners one by one. Screen systems where y grows downwards simply need the sign of dy to be flipped.

Worked example

Start at the point (−2.5, 4) and shift it by the vector (6, −7.25). New x = −2.5 + 6 = 3.50. New y = 4 + (−7.25) = −3.25. The tool shows the new point as 3.50 and −3.25. The point has moved 6 units to the right and 7.25 units down. To check, subtract the vector from the new point: 3.50 − 6 = −2.50 and −3.25 + 7.25 = 4, which gives the original point back.

Try this example →

Common mistakes

  • Entering the destination point as the vector. The vector is the amount of the shift, not where the point ends up; to go from (1, 2) to (4, 6) enter dx = 3 and dy = 4.
  • Forgetting the sign of the shift. Moving a point down or left needs a negative dy or dx, so a shift of 7 down must be typed as −7.
  • Using a screen or image coordinate system without flipping the sign. On screens y often grows downwards, so a positive dy moves the point down, the opposite of the usual maths graph.
  • Mixing units, such as a point in metres and a shift in centimetres. The tool just adds the numbers, so convert first.
  • Expecting rotation or scaling. A translation slides the point only; turning it around the origin or resizing it needs a different transformation.

About this calculator

Translating a point simply slides it in a straight line by a fixed horizontal and vertical amount, without rotating, resizing or flipping it. It is the most basic of the rigid geometric transformations, and every other transformation, like rotation about an arbitrary point, is often built by combining a translation with a simpler operation about the origin.

This calculation is everywhere in computer graphics, where moving an object across the screen is a translation applied every frame, and in CAD and mapping software, where shifting an entire drawing or a set of coordinates by a fixed offset is a routine step. Game level designers and animators use it constantly for repositioning objects without altering their shape.

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