Calculator Inputs
Use the responsive grid below. It shows three columns on large screens, two on smaller screens, and one on mobile.
Formula Used
The calculator works in any dimension from 2D to 6D and applies the same core vector rules.
This gives the translation vector from start point A to end point B.
The magnitude measures straight-line translation distance in Euclidean space.
C′ translates the probe point once. C″ repeats the same translation using scale factor k.
The unit vector keeps direction while normalizing the vector length to one.
How to Use This Calculator
- Select the number of dimensions you want to analyze.
- Enter the coordinates of the start point A.
- Enter the matching coordinates of the end point B.
- Enter the probe point C if you want another point shifted by the same vector.
- Set the repeat factor k when you want a scaled translation preview.
- Choose the number of decimals for cleaner output formatting.
- Press the calculate button to show the result above the form.
- Use the CSV or PDF buttons to export the summary.
Example Data Table
These sample rows show how translation vectors connect two points and shift another point by the same movement.
| Case | Dimensions | Start Point A | End Point B | Vector v = B − A | Magnitude | Probe Point C | Translated C + v |
|---|---|---|---|---|---|---|---|
| Planar shift | 2D | (2, 3) | (7, 1) | ⟨5, -2⟩ | 5.3852 | (-1, 4) | (4, 2) |
| Spatial move | 3D | (1, -2, 4) | (5, 1, 10) | ⟨4, 3, 6⟩ | 7.8102 | (0, 0, 1) | (4, 3, 7) |
| Four-dimensional | 4D | (3, 1, 0, -2) | (6, 5, -1, 4) | ⟨3, 4, -1, 6⟩ | 7.8740 | (2, 2, 2, 2) | (5, 6, 1, 8) |
Frequently Asked Questions
1) What is a translation vector?
A translation vector shows how far and in what direction a point moves from one location to another. It is found by subtracting the start coordinates from the end coordinates component by component.
2) Why does the calculator need both A and B?
Point A is the starting location and point B is the destination. Their difference creates the exact vector that describes the translation from A to B in every dimension used.
3) What does the probe point C do?
The probe point lets you apply the same translation to another point. This is useful when checking how a whole figure, object, or coordinate sample moves under the same vector.
4) What is the repeat factor k?
The factor k scales the translation vector. When k equals 1, the original shift is applied once. When k equals 2, the same movement is doubled before being added to the probe point.
5) Why does the chart change for dimensions above three?
True geometric plotting is practical in two or three dimensions only. For higher dimensions, the calculator switches to a component chart so you can still inspect the translation pattern clearly.
6) What does the unit vector tell me?
The unit vector preserves direction but reduces the vector length to one. It helps compare directions fairly when different translations have very different magnitudes.
7) Is the translation distance always the vector magnitude?
Yes for Euclidean distance. The vector magnitude equals the straight-line distance between A and B. The Manhattan distance is also shown because some workflows compare coordinate-by-coordinate movement instead.
8) Can I use decimals and negative values?
Yes. The calculator accepts positive numbers, negative numbers, and decimals. That makes it suitable for classroom math, coordinate geometry, physics-style displacement work, and higher-dimensional vector analysis.