What is the Euclidean distance formula?

For two points A = (a1, a2, ..., an) and B = (b1, b2, ..., bn), the Euclidean distance is sqrt((a1-b1)^2 + (a2-b2)^2 + ... + (an-bn)^2). In 2D it simplifies to sqrt((x2-x1)^2 + (y2-y1)^2).

What is the difference between Euclidean and Manhattan distance?

Euclidean distance is the straight-line ("as the crow flies") distance between two points. Manhattan distance sums the absolute differences along each axis, as if traveling along a grid. Euclidean is always less than or equal to Manhattan distance.

What does L2 distance mean?

L2 distance is another name for Euclidean distance. It comes from the L2 norm (also called the Frobenius norm in matrices), which is the standard way to measure lengths in Euclidean space.

Can this calculator handle more than 3 dimensions?

Yes. Use the custom dimension option to enter as many coordinates as needed. The formula extends identically to N dimensions by summing the squared differences for all coordinate pairs.

Is the Euclidean distance the same as the straight-line distance?

Yes. Euclidean distance measures the length of the shortest path between two points through space, which is a straight line. It is the standard geometric distance most people think of.

Euclidean Distance Calculator

Enter coordinates for two points in any number of dimensions and get the straight-line Euclidean distance instantly.

Coordinates

Dimensions

Point A (x₁, y₁, ...)

Point B (x₂, y₂, ...)

Enter coordinates and click Calculate

Euclidean Distance

Squared distance:

Step-by-Step Formula

Coordinate Differences

Axis	A	B	B − A	(B−A)²
Sum of squares

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Summary

The Euclidean distance is the straight-line distance between two points in any number of dimensions, calculated as the square root of the sum of squared differences between corresponding coordinates. It is the most common distance metric in geometry, machine learning, and data science, also called the L2 norm or L2 distance. This tool supports 2D, 3D, and arbitrary N-dimensional vectors.

How it works

Select the number of dimensions (2D, 3D, or custom).
Enter the coordinates for Point A and Point B.
Click Calculate to compute the straight-line distance.
The result shows the distance along with the squared distance and the step-by-step formula.
Adjust dimensions dynamically to add or remove coordinate fields.

Use cases

Find the straight-line distance between two GPS coordinates converted to Cartesian space.
Compute vector similarity in machine learning and recommendation systems.
Measure distances in 3D modeling and computer graphics.
Validate distance calculations in physics and engineering problems.
Calculate the L2 norm for data normalization tasks.
Find nearest neighbors in N-dimensional feature spaces.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu