Formula: D = √((x₂ − x₁)² + (y₂ − y₁)²). Tip: Press Enter in any field to calculate.
x and y), for example meters with meters.x₁, y₁, x₂, and y₂.0.The preview auto-scales to fit your points. Axes are illustrative (not to exact scale ticks).
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:
v1.1 (February 17, 2026)
(x₂ − x₁) and vertical difference (y₂ − y₁).Because everything happens locally, your privacy is fully protected while you enjoy instant results.
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.
The distance formula is just the Pythagorean theorem in disguise. Any straight-line gap in 2D is a hidden right triangle’s hypotenuse.
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.
Distance works across any consistent unit—metres, inches, pixels. Mix units and it breaks; match units and the math is happy.
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.
Every circle is the set of points exactly one distance (the radius) from a center. Change the distance, the whole circle scales instantly.
It uses the standard 2D distance formula derived from the Pythagorean theorem:
D = √((x₂ − x₁)² + (y₂ − y₁)²).
Yes. The calculator supports negative numbers and decimal values, making it suitable for a wide range of coordinate systems and real-world applications.
Absolutely. All computations are performed directly in your browser. Your input is never transmitted or stored online.
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.