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

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

Coordinates

Point A

x₁

y₁

Point B

x₂

y₂

Enter coordinates and click Calculate

Copied!

Summary

This calculator computes the straight-line (Euclidean) distance between two points using the standard distance formula derived from the Pythagorean theorem. It works in both 2D (x, y) and 3D (x, y, z) coordinate space. Each calculation shows the full working so you can follow every step.

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: 2026-05-29 · Reviewed by Nham Vu

Distance Between Points Calculator

Coordinates

Step-by-Step Solution

Component Breakdown

Summary

How it works

Use cases

Frequently Asked Questions

Distance Between Points Calculator

Use the Distance Between Points Calculator

Coordinates

Step-by-Step Solution

Component Breakdown

Summary

How it works

Use cases

Frequently Asked Questions