ReadyCalculator

Distance Calculator

Calculate distance between two points

Point 1

Point 2

Distance Formulas

2D Euclidean Distance

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Example: Distance from (0,0) to (3,4) = √[(3-0)² + (4-0)²] = √[9 + 16] = √25 = 5

3D Euclidean Distance

d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Example: Distance from (0,0,0) to (1,2,2) = √[1² + 2² + 2²] = √9 = 3

Manhattan Distance (Taxicab)

d = |x₂ - x₁| + |y₂ - y₁| + |z₂ - z₁|

Distance if you can only move along axes (like city blocks). Always ≥ Euclidean distance.

Quick Examples

(0, 0) to (3, 4)

Classic 3-4-5 triangle

5
(1, 2) to (4, 6)

Right triangle

5
(-1, -1) to (2, 3)

With negative coordinates

5
(0, 0) to (5, 12)

5-12-13 Pythagorean triple

13
(0, 0) to (8, 15)

8-15-17 Pythagorean triple

17
(0, 0) to (7, 24)

7-24-25 Pythagorean triple

25

Real-World Applications

🗺️ Navigation & GPS

  • • Calculate distance between locations
  • • Route planning
  • • Delivery optimization
  • • Proximity searches

🎮 Game Development

  • • Character movement
  • • Collision detection
  • • AI pathfinding
  • • Range calculations

📊 Data Science

  • • Clustering algorithms
  • • K-nearest neighbors
  • • Pattern recognition
  • • Similarity measures

🏗️ Engineering

  • • CAD design
  • • Structural analysis
  • • Robotics
  • • Manufacturing

Distance Metrics Comparison

Euclidean DistanceMost common

Straight-line distance. "As the crow flies." Used in most real-world distance calculations.

Manhattan DistanceGrid-based

Distance along axes only. Like navigating city blocks. Used in grid-based pathfinding.

Chebyshev DistanceChess king moves

Maximum coordinate difference. Number of moves a chess king needs to reach a square.

How to Use This Calculator

1

Enter Your Values

Input the required values in the calculator fields above. Make sure all inputs are valid numbers.

2

Click Calculate

Press the "Calculate" button to perform the calculation and see your results.

3

Review Results

Review the calculated results displayed below. Use these values for your needs.

About Distance Calculator

The Distance Calculator is a useful tool for calculating distance values. This calculator helps you quickly and accurately determine the results you need for your calculations.

When to Use This Calculator

  • Quick Calculations: Get instant results without manual computation
  • Accuracy: Ensure precise calculations every time
  • Planning: Use for project planning and estimation
  • Verification: Double-check your manual calculations

Why Use Our Calculator?

  • Instant Results: Get accurate calculations immediately
  • Easy to Use: Simple interface for all skill levels
  • 100% Free: No registration or payment required
  • Mobile Friendly: Works on all devices
  • Accurate: Precise mathematical calculations

Tips for Best Results

  • Double-Check Inputs: Verify all values before calculating
  • Use Valid Numbers: Ensure inputs are valid numbers
  • Review Results: Check results for reasonableness
  • Clear and Retry: Clear inputs if you need to recalculate
Frequently Asked Questions

What's the difference between 2D and 3D distance?

2D uses x and y coordinates (flat plane). 3D adds z coordinate (depth/height). Formula adds one more squared term: √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]

Can distance be negative?

No! Distance is always positive or zero. It represents magnitude only. If you need direction, use vectors instead.

What if my coordinates are negative?

No problem! The formula works with negative numbers. When squared, they become positive anyway. Example: (-3)² = 9.

How is this related to the Pythagorean theorem?

The distance formula IS the Pythagorean theorem! For (0,0) to (3,4): horizontal = 3, vertical = 4, hypotenuse = √(3² + 4²) = 5.

When should I use Manhattan distance instead?

Use Manhattan when movement is restricted to axes (city streets, grids). Use Euclidean for straight-line, unrestricted movement (flying, straight paths).