Geometry Tool

Distance Formula Calculator

Calculate the distance between two points on a 2D plane.

Point 1

Point 2

Σ The Formula

d = √((x₂-x₁)² + (y₂-y₁)²)

Real World Examples

Origin to Point
(0,0) to (3,4) → d = √(9+16) = 5
Two Points
(1,1) to (4,5) → d = √(9+16) = 5
City Distance
(-2,3) to (4,-1) → d = √(36+16) = 7.21
Negative Coordinates
(-5,-2) to (3,4) → d = √(64+36) = 10

# About This Calculator

The distance formula calculates the straight-line distance between two points on a coordinate plane. It's derived from the Pythagorean theorem: the distance forms the hypotenuse of a right triangle where the legs are the differences in x and y coordinates.

This formula is fundamental in coordinate geometry, GPS navigation, game development, computer graphics, physics simulations, and data analysis. It's used to calculate distances between cities on maps, positions in video games, clustering in machine learning, and countless other applications.

The formula d = √((x₂-x₁)² + (y₂-y₁)²) works regardless of which point you call "point 1" or "point 2" - the distance is always the same. It handles negative coordinates perfectly and extends to 3D space by adding a z-coordinate term.

This calculator provides instant distance calculations for any two points, showing the step-by-step computation. It's perfect for homework, verifying manual calculations, game development, or any situation requiring precise distance measurements on a coordinate plane.

How To Use

  1. Enter coordinates for Point 1.
  2. Enter coordinates for Point 2.
  3. Click Calculate.

Frequently Asked Questions

How is this related to the Pythagorean theorem?+

The distance formula IS the Pythagorean theorem applied to coordinates! The horizontal distance (x₂-x₁) and vertical distance (y₂-y₁) form the legs of a right triangle, and the distance is the hypotenuse: d = √(a² + b²).

Does it matter which point I call point 1 vs point 2?+

No! Distance is the same either way. (x₂-x₁)² = (x₁-x₂)² because squaring eliminates the negative. For example, (5-2)² = 9 and (2-5)² = 9. The formula is symmetric.

Can I use this for 3D points?+

Yes! Extend the formula: d = √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²). For example, (0,0,0) to (1,2,2) gives d = √(1+4+4) = 3. This calculator handles 2D, but the concept extends to any dimension.

How is this used in GPS and navigation?+

GPS coordinates (latitude, longitude) are treated as (x, y) points. The distance formula (with adjustments for Earth's curvature) calculates distances between locations. This is fundamental to mapping apps, delivery routing, and location-based services.

What if I get a negative number under the square root?+

You can't! Both (x₂-x₁)² and (y₂-y₁)² are always positive (or zero) because squaring any real number gives a non-negative result. The sum of two non-negative numbers is always non-negative, so √ is always valid.

Is Distance Formula Calculator free to use?+

Yes, Distance Formula Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

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