Distance Formula Calculator

Distance Formula Calculator

Calculate the distance between two points in 2D or 3D space using the distance formula.

Last updated: April 2026 | By Patchworkr Team

Result will appear here...

What is the Distance Formula?

The distance formula calculates the straight-line distance between two points in a coordinate system.

  • 2D Formula: d = √((x₂ - x₁)² + (y₂ - y₁)²)
  • 3D Formula: d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)

This formula is derived from the Pythagorean theorem and is fundamental in coordinate geometry. It measures the shortest path between two points.

How to Use the Distance Formula Calculator

  1. Choose 2D or 3D mode depending on your coordinate system.
  2. Enter the coordinates for Point 1 (x₁, y₁) or (x₁, y₁, z₁).
  3. Enter the coordinates for Point 2 (x₂, y₂) or (x₂, y₂, z₂).
  4. Click Calculate Distance to compute the result.

Real-World Example

Finding Distance Between Two Cities (2D)

Given:
City A at (0, 0) and City B at (3, 4)
Formula:
d = √((3-0)² + (4-0)²) = √(9 + 16) = √25 = 5
Result:
5 units

Frequently Asked Questions

What's the difference between 2D and 3D distance?

2D uses x and y coordinates, while 3D adds the z coordinate for depth. Both use the Pythagorean theorem extended to their respective dimensions.

Can I use negative coordinates?

Yes. The distance formula works with negative values since we square the differences.

Is distance always positive?

Yes. Distance is always non-negative because it's the square root of squared differences.

What are practical applications?

Navigation, surveying, robotics, physics simulations, and any system requiring spatial measurements.

Does order of points matter?

No. Distance from (x₁, y₁) to (x₂, y₂) equals distance from (x₂, y₂) to (x₁, y₁).

What if both points are the same?

The distance will be 0, as there is no separation between the points.

Can I find distances in higher dimensions?

The formula extends to any dimension: add a squared difference for each additional coordinate.

Is this related to the Pythagorean theorem?

Yes. The distance formula is a direct extension of the Pythagorean theorem (a² + b² = c²).

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