2D Distance Calculator
Calculate the distance between any two points in a two-dimensional coordinate system
Calculate 2D Distance
Coordinates of the first point: (0, 0)
Coordinates of the second point: (0, 0)
Distance Result
Formula used: d = √((x₂-x₁)² + (y₂-y₁)²)
Points: (0, 0) and (0, 0)
Distance: 0.0000 units
Step-by-Step Calculation
Example Calculation
Example: Distance between (4,3) and (7,13)
Point 1: (4, 3)
Point 2: (7, 13)
Formula: d = √((x₂-x₁)² + (y₂-y₁)²)
Step-by-Step Solution
d = √((7-4)² + (13-3)²)
d = √((3)² + (10)²)
d = √(9 + 100)
d = √109
d = 10.4403 units
2D Distance Formula
d = √((x₂-x₁)² + (y₂-y₁)²)
d: Distance between the two points
(x₁, y₁): Coordinates of the first point
(x₂, y₂): Coordinates of the second point
Distance Properties
Distance is always non-negative (≥ 0)
Distance between identical points is 0
Distance is symmetric: d(A,B) = d(B,A)
Based on Pythagorean theorem
Quick Tips
Works with positive, negative, and decimal coordinates
Also known as Euclidean distance
Useful in geometry, physics, and computer graphics
Forms the basis for distance calculations in higher dimensions
Understanding 2D Distance
What is 2D Distance?
The 2D distance is the straight-line distance between any two points in a two-dimensional coordinate system. Each point is defined by its x and y coordinates, written as an ordered pair (x, y). This distance represents the shortest path between the two points.
Why is it Important?
- •Essential in geometry and coordinate mathematics
- •Used in physics for displacement calculations
- •Foundation for computer graphics and game development
- •Applied in navigation and GPS systems
Formula Derivation
d = √((x₂-x₁)² + (y₂-y₁)²)
Based on the Pythagorean theorem
Step 1: Find the horizontal distance (Δx = x₂ - x₁)
Step 2: Find the vertical distance (Δy = y₂ - y₁)
Step 3: Apply Pythagorean theorem: d² = Δx² + Δy²
Step 4: Take the square root to get the distance
Note: This formula works for any two points in a 2D plane, regardless of their position relative to the origin.
Real-World Applications
🎯 Navigation & GPS
Calculate straight-line distances between locations on maps and coordinate systems.
🎮 Game Development
Determine distances between game objects, collision detection, and pathfinding algorithms.
📐 Engineering & Design
Measure distances in technical drawings, blueprints, and CAD applications.
🔬 Data Analysis
Calculate Euclidean distances in data science, clustering algorithms, and pattern recognition.
🏃 Sports & Fitness
Measure distances traveled, track movement patterns, and analyze athletic performance.
🏗️ Construction
Calculate distances for surveying, land measurement, and architectural planning.