Distance Calculator (2D)

2D distance is the straight-line (Euclidean) distance between two points in a two-dimensional coordinate plane. It represents the shortest path between the two points, calculated using the Pythagorean theorem applied to the horizontal (Δx) and vertical (Δy) differences.

The formula is d = √((x2 − x1)² + (y2 − y1)²). You subtract the x-coordinates to get Δx, subtract the y-coordinates to get Δy, square both, add them together, and take the square root of the result.

Enter the x and y coordinates for both Point 1 and Point 2. The calculator computes Δx = x2 − x1 and Δy = y2 − y1, then returns d = √(Δx² + Δy²) as the straight-line distance between the two points.

Using the formula: d = √((7−4)² + (13−3)²) = √(9 + 100) = √109 ≈ 10.4403. You can verify this by entering those coordinates into the calculator above.

Yes. The calculator accepts any real number as input — positive, negative, decimal, or zero. For example, coordinates like (−7, 11) and (5, 6) are perfectly valid entries.

2D distance measures the gap between two points on a flat plane using x and y coordinates. 3D distance extends this by adding a z-coordinate, using the formula d = √((x2−x1)² + (y2−y1)² + (z2−z1)²). This calculator covers the 2D case only.

When you draw a line between two points on a coordinate plane, Δx and Δy form the two legs of a right triangle, while the straight-line distance d forms the hypotenuse. The Pythagorean theorem (a² + b² = c²) directly gives the length of that hypotenuse.

Distance squared, d² = (x2−x1)² + (y2−y1)², is an intermediate step in the calculation before taking the square root. It's sometimes used in algorithms and comparisons where computing the full square root isn't necessary — comparing d² values is equivalent to comparing distances.