2D Distance Calculator — Distance Between Two Points
Coordinates & Actions
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.
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.