What is a geometric translation?

A translation moves every point of a figure the same distance in the same direction. It is defined by a vector (tx, ty) in 2D or (tx, ty, tz) in 3D. The shape does not rotate, reflect, or resize — only its position changes.

How is translation different from rotation or reflection?

Translation is a pure shift — every point moves by the same vector. Rotation turns the figure around a center point. Reflection flips it over a line or plane. All three are rigid transformations (they preserve distances), but only translation keeps orientation and angle unchanged.

Can I enter negative translation values?

Yes. A negative tx shifts points left (2D) or in the negative x direction (3D), and a negative ty shifts them down. Negative values simply move in the opposite direction of their positive counterparts.

Does this tool work for 3D coordinates?

Yes. Switch to 3D mode and enter a third component tz along with each point's z value. The formula extends naturally: x' = x + tx, y' = y + ty, z' = z + tz.

How many points can I translate at once?

You can add as many points as you need. Each row in the results table shows the original and translated coordinates side by side.

Translation Calculator

Name: Translation Calculator
Availability: InStock
Author: Nham Vu

Enter points and a translation vector to shift coordinates in 2D or 3D space instantly.

Coordinate Mode

Translation Vector

Add Point

Quick Examples

Translated Coordinates

No points yet

Set the translation vector and add points above.

#	Original	+	Vector	Translated

Summary

Enter points and a translation vector to shift coordinates in 2D or 3D space instantly.

How it works

Choose 2D or 3D mode depending on your coordinate space.
Enter the translation vector components (tx, ty, and optionally tz).
Add one or more points using their x, y (and z) coordinates.
The calculator adds the vector to each point: x' = x + tx, y' = y + ty, z' = z + tz.
Results appear instantly in a table alongside the original coordinates.
Copy the results or clear the list to start a new calculation.

Use cases

Shift polygon vertices when repositioning a shape on a coordinate grid.
Translate 3D model anchor points in game development or CAD work.
Verify manual translation homework answers step by step.
Move a set of data points by a fixed offset for chart alignment.
Compute new robot or drone waypoints after an origin change.
Check vector addition results in a linear algebra course.

Frequently Asked Questions

Last updated: 2026-07-26 · Reviewed by Nham Vu