What is a scaling transformation?

A scaling transformation multiplies each coordinate of a point by a scale factor along that axis. In 2D the result is (x * sx, y * sy); in 3D it is (x * sx, y * sy, z * sz). Scale factors greater than 1 enlarge, between 0 and 1 shrink, and negative values also flip the point across that axis.

What is uniform vs. non-uniform scaling?

Uniform scaling uses the same factor for all axes (sx = sy = sz), preserving shape proportions. Non-uniform scaling uses different factors, which stretches or squashes the object along one or more axes.

How is the scaling matrix constructed?

For 2D the matrix is [[sx, 0], [0, sy]]. For 3D it is [[sx, 0, 0], [0, sy, 0], [0, 0, sz]]. Multiplying this matrix by a column vector of the point's coordinates gives the scaled point.

What happens when a scale factor is negative?

A negative scale factor flips the coordinate across that axis in addition to scaling it. For example, sx = -1 mirrors the point across the Y-axis while keeping its distance from the origin unchanged.

Can I scale multiple points at once?

Yes — enter each point on its own line. All points share the same scale factors you entered at the top. The results list each input point alongside its scaled output.

Scaling Transformation Calculator

Name: Scaling Transformation Calculator
Availability: InStock
Author: Nham Vu

Enter one or more 2D or 3D points and scale factors to compute the scaled coordinates instantly.

Dimensions

Scale Factors

Input Points

one per line: x, y

Enter scale factors and at least one point, then click Calculate.

Scaled Points

Scaling Matrix

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Summary

Enter one or more 2D or 3D points and scale factors to compute the scaled coordinates instantly.

How it works

Choose 2D or 3D mode using the toggle at the top.
Enter scale factors sx and sy (and sz for 3D).
Type one or more points — one per line in the format "x, y" or "x, y, z".
The calculator multiplies each coordinate by its corresponding scale factor.
Results appear instantly with both the transformed points and the scaling matrix.

Use cases

Scale geometry objects in 2D and 3D graphics pipelines.
Verify scaling matrix output when learning linear algebra.
Quickly compute uniform or non-uniform scale for game assets.
Apply scale factors to engineering or physics simulation coordinates.
Check transformation results before coding them into shaders or engines.
Teach or demonstrate affine transformations in a classroom setting.

Frequently Asked Questions

Last updated: 2026-07-24 · Reviewed by Nham Vu