What is the Euclidean distance formula?

In 2D: d = sqrt((x2-x1)^2 + (y2-y1)^2). In 3D: d = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2). It is derived directly from the Pythagorean theorem.

Does the order of the points matter?

No. The distance from A to B is always equal to the distance from B to A because the differences are squared, making any negative sign disappear.

Can I use decimal or negative coordinates?

Yes. The calculator accepts any real number including decimals (e.g. -3.5) and negative values for all coordinate fields.

What is the difference between 2D and 3D distance?

In 2D you only have x and y axes (a flat plane). In 3D you add a z axis (depth), so the formula includes one extra squared-difference term under the square root.

Is this the same as the straight-line distance?

Yes. Euclidean distance is always the shortest straight-line path between two points, sometimes called "as the crow flies."

Distance Between Points Calculator

Name: Distance Between Points Calculator
Availability: InStock
Author: Nham Vu

Enter two points in 2D or 3D space and instantly get the Euclidean distance with step-by-step working.

Coordinates

Point A

x₁

y₁

z₁

Point B

x₂

y₂

z₂

Enter coordinates and click Calculate

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Summary

Enter two points in 2D or 3D space and instantly get the Euclidean distance with step-by-step working.

How it works

Select whether your points are in 2D or 3D space.
Enter the coordinates for Point A and Point B.
Click Calculate to apply the Euclidean distance formula.
The result appears instantly with a full step-by-step breakdown.
Use the Swap button to reverse the two points, or Reset to start over.

Use cases

Check homework answers for distance formula problems.
Calculate straight-line distances in geometry or physics problems.
Measure distances between GPS-like coordinate pairs.
Verify distances in computer graphics and game development.
Solve engineering problems involving spatial measurements.
Compute distances in robotics path planning.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu