2D Distance Calculator — Distance Between Two Points

Compute straight-line distance on a 2D plane. Private by design—everything runs locally in your browser.

Coordinates & Actions

D = —

Formula: D = √((x₂ − x₁)² + (y₂ − y₁)²). Tip: Press Enter in any field to calculate.

Preview

The preview auto-scales to fit your points. Axes are illustrative (not to exact scale ticks).

Understanding the 2D Distance Formula

The 2D distance formula is a fundamental concept in mathematics, used to calculate the straight-line distance between two points on a flat plane. It is directly derived from the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Suppose you have two points: P₁ = (x₁, y₁) and P₂ = (x₂, y₂). If you draw a horizontal line from P₁ to align with P₂ and a vertical line to complete a right-angled triangle, the horizontal leg has a length of |x₂ − x₁| and the vertical leg has a length of |y₂ − y₁|.

By the Pythagorean theorem, we know that: (x₂ − x₁)² + (y₂ − y₁)² = D², where D is the distance between the two points. Taking the square root of both sides gives us the classic distance formula: D = √((x₂ − x₁)² + (y₂ − y₁)²).

This formula works for all real-number coordinates, including positive, negative, and decimal values. Whether you are calculating distances on a graph, finding the straight-line path in a 2D game, or performing basic geometry, this method remains accurate and reliable.

How This 2D Distance Calculator Works

Our online tool runs entirely in your browser using JavaScript—no data is sent to any server. When you enter your four coordinates (x₁, y₁, x₂, y₂) and click “Calculate Distance,” the calculator:

  • Reads and validates your input values.
  • Computes the horizontal difference (x₂ − x₁) and vertical difference (y₂ − y₁).
  • Squares both differences.
  • Adds the squared values together.
  • Finds the square root of the sum to return the final distance.

Because everything happens locally, your privacy is fully protected while you enjoy instant results.

5 Fun Facts about 2D Distance

Pythagoras everywhere

The distance formula is just the Pythagorean theorem in disguise. Any straight-line gap in 2D is a hidden right triangle’s hypotenuse.

Triangle core

Rotation-proof

Spin the plane any way you like: distances stay the same. That’s why games and CAD tools rely on it for stable camera moves and object placement.

Invariant

Pixels to meters

Distance works across any consistent unit—metres, inches, pixels. Mix units and it breaks; match units and the math is happy.

Unit agnostic

Shortest path guarantee

Straight-line distance is the unique shortest route in flat space. Any detour or zigzag is strictly longer—handy for “as-the-crow-flies” checks.

Geodesic

Distance powers circles

Every circle is the set of points exactly one distance (the radius) from a center. Change the distance, the whole circle scales instantly.

Shape engine

2D Distance Calculator: Frequently Asked Questions

What formula does this calculator use?

It uses the standard 2D distance formula derived from the Pythagorean theorem: D = √((x₂ − x₁)² + (y₂ − y₁)²).

Can I use negative or decimal coordinates?

Yes. The calculator supports negative numbers and decimal values, making it suitable for a wide range of coordinate systems and real-world applications.

Is my data private?

Absolutely. All computations are performed directly in your browser. Your input is never transmitted or stored online.

Where can this formula be applied?

The distance formula is used in mathematics, physics, computer graphics, navigation, and engineering to calculate the shortest path between two points in a two-dimensional space.

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