Calculate distances between points instantly with our advanced distance formula calculator. Support for 2D and 3D coordinates, step-by-step solutions, and visual representations.
Enter coordinates to calculate distance
The distance formula calculates the straight-line distance between two points in a 2D coordinate system using: √[(x₂-x₁)² + (y₂-y₁)²]. This is derived from the Pythagorean theorem.
The distance formula is derived from the Pythagorean theorem and used to find the distance between two points in a coordinate system. In 2D, for points (x₁, y₁) and (x₂, y₂), the distance is √[(x₂-x₁)² + (y₂-y₁)²]. In 3D, we add the z-component: √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²].
Our distance formula calculator handles both 2D and 3D coordinates, making it perfect for geometry problems, physics calculations, engineering applications, and computer graphics work.
d = √[(x₂-x₁)² + (y₂-y₁)²]
Example: Distance between (1, 2) and (4, 6) is √[(4-1)² + (6-2)²] = √(9 + 16) = 5
d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]
Example: Distance between (1, 2, 3) and (4, 6, 8) is √[(4-1)² + (6-2)² + (8-3)²] = √(9 + 16 + 25) = √50 ≈ 7.07
d = |x₂-x₁| + |y₂-y₁| (in 2D) or |x₂-x₁| + |y₂-y₁| + |z₂-z₁| (in 3D)
Useful for grid-based calculations and pathfinding algorithms
The standard straight-line distance we calculate using the Pythagorean theorem. This is the most common type of distance used in mathematics.
Beyond Cartesian coordinates, distances can be calculated in polar, cylindrical, and spherical coordinate systems, each useful for specific applications.
Distance formulas extend to high-dimensional spaces for machine learning, clustering algorithms, and similarity measurements.
2D distance calculates between points on a plane using x and y coordinates. 3D distance includes the z-coordinate for points in three-dimensional space.
Our calculator finds distance between two points. For multiple points, calculate each pair separately or use our distance matrix tool.
Our calculator provides exact results for rational inputs and high-precision decimal results (up to 15 decimal places) for all calculations.
The distance formula works with negative coordinates. The squaring operation makes differences positive, so the calculation is the same.