Coordinate Distance Calculator
Calculate the distance between two points in 2D or 3D coordinate space using the Euclidean distance formula
Calculate Distance Between Coordinates
First Point
Second Point
Distance Results
Step-by-Step Calculation
Formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Step 1: Calculate coordinate differences
Δx = x₂ - x₁ = 0 - 0 = 0
Δy = y₂ - y₁ = 0 - 0 = 0
Step 2: Square the differences
(Δx)² = (0)² = 0
(Δy)² = (0)² = 0
Step 3: Sum the squares
Sum = 0 + 0 = 0
Step 4: Take the square root
d = √0 = 0.0000
Example Calculation
3D Distance Example
Point 1: (-1, 0, 2)
Point 2: (3, 5, 4)
Formula: d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]
Calculation
d = √[(3-(-1))² + (5-0)² + (4-2)²]
d = √[4² + 5² + 2²]
d = √[16 + 25 + 4]
d = √45
d = 6.7083 units
Distance Formulas
2D Distance
d = √[(x₂-x₁)² + (y₂-y₁)²]
Euclidean distance in 2D space
3D Distance
d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]
Euclidean distance in 3D space
Midpoint
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Center point between two coordinates
Quick Tips
The distance formula comes from the Pythagorean theorem
Distance is always positive (absolute value)
For 2D points, set z coordinates to 0
The midpoint is the average of coordinates
Understanding Coordinate Distance
What is Coordinate Distance?
Coordinate distance, also known as Euclidean distance, is the straight-line distance between two points in a coordinate system. It represents the shortest path between two points in space.
Mathematical Foundation
- •Based on the Pythagorean theorem
- •Extends to multiple dimensions
- •Always returns a positive value
- •Commutative: d(A,B) = d(B,A)
Formula Derivation
For 2D space:
d² = (x₂ - x₁)² + (y₂ - y₁)²
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
For 3D space:
d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
Key Insight: The distance formula creates a right triangle where the hypotenuse is the distance between points.
Real-World Applications
Navigation
GPS systems, mapping, route planning
Computer Graphics
3D modeling, game development, animation
Data Science
Machine learning, clustering, pattern recognition
Physics
Motion analysis, field calculations, astronomy
Coordinate Systems
Cartesian (x, y, z)
Rectangular coordinate system with perpendicular axes
Polar (r, θ)
Uses distance from origin and angle
Spherical (r, θ, φ)
3D system with radius and two angles