Quadratic Equation Solver (ax² + bx + c = 0)
About Distance Formula Calculator
The 2D & 3D Coordinate Distance Formula Calculator computes Euclidean straight-line distance ($d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$), Manhattan distance ($L_1$), Chebyshev distance ($L_\infty$), and midpoint coordinates between two points.
How to Use Distance Formula Calculator
Step 1
Enter coordinates for Point 1 and Point 2.
Step 2
Select coordinate space (2D or 3D).
Step 3
Review computed Euclidean distance, step-by-step Pythagorean proof, and midpoint.
Step 4
Click "Copy Distance".
Practical Use Cases for Distance Formula Calculator
Analytical Geometry & Map Coordinate Distance Calculations
Calculate exact geometric distance between two coordinate points $(x_1, y_1)$ and $(x_2, y_2)$ with step-by-step radical simplification.
Game Physics & Grid-Based Pathfinding (A* Algorithm)
Compute Manhattan grid distances ($|\Delta x| + |\Delta y|$) and Euclidean distances for collision detection and AI heuristics.
Input & Output Examples
Calculating Distance Between (1, 2) and (4, 6)
Point 1: `(1, 2)`, Point 2: `(4, 6)`
Euclidean Distance: `5.0` (Exact: `√((4-1)² + (6-2)²) = √(9+16) = √25 = 5`) | Manhattan Distance: `7.0` | Midpoint: `(2.5, 4.0)`
Key Features & Performance
- ✓Distance Metrics: Euclidean Distance ($L_2$), Manhattan Distance ($L_1$), Chebyshev Distance ($L_\infty$), Minkowski Distance.
- ✓Supports 2D ($x, y$), 3D ($x, y, z$), and 4D Cartesian coordinates.
- ✓Exact Radical Mode: outputs exact simplified radical distances (e.g. $2\sqrt{5}$) alongside decimal values.
- ✓100% Client-Side geometry engine.
- ✓1-Click Copy distance proof.
Key Terminology & Definitions
Euclidean Distance Formula
The straight-line distance between two points in Cartesian space derived from the Pythagorean theorem: $d = \sqrt{\sum (p_i - q_i)^2}$.
Manhattan Distance ($L_1$ Norm)
The sum of the absolute differences of their Cartesian coordinates ($d = |x_2 - x_1| + |y_2 - y_1|$), representing distance along grid streets.