Distance Calculator
Calculate the distance between two points using the distance formula. Perfect for coordinate geometry, physics, and engineering calculations with step-by-step solutions.
2D Distance Calculator
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
Distance Formula
The distance formula is derived from the Pythagorean theorem and is used to find the straight-line distance between two points in coordinate space.
Distance Formulas
Understanding the formulas behind distance calculations:
Example: Distance between (0,0) and (3,4) = √[(3-0)² + (4-0)²] = √[9 + 16] = √25 = 5
Example: Distance between (0,0,0) and (3,4,5) = √[(3-0)² + (4-0)² + (5-0)²] = √[9 + 16 + 25] = √50 ≈ 7.07
Common Distance Examples
| Point 1 | Point 2 | Distance | Type |
|---|---|---|---|
| (0, 0) | (3, 4) | 5 | 2D |
| (1, 1) | (4, 5) | 5 | 2D |
| (-2, -3) | (1, 1) | 5 | 2D |
| (0, 0, 0) | (1, 1, 1) | √3 ≈ 1.73 | 3D |
| (0, 0, 0) | (3, 4, 5) | √50 ≈ 7.07 | 3D |
Applications
- Geometry: Calculate distances in coordinate geometry problems
- Physics: Find displacement and distance in motion problems
- Engineering: Calculate distances in design and construction
- Computer Graphics: Determine distances between objects in 2D/3D space
- Navigation: Calculate straight-line distances between locations
Frequently Asked Questions
How do you calculate distance between two points?
Use the distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²] for 2D points, or d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²] for 3D points.
What is the distance formula?
The distance formula is derived from the Pythagorean theorem. For two points (x₁,y₁) and (x₂,y₂), the distance is √[(x₂-x₁)² + (y₂-y₁)²].
Can you calculate 3D distance?
Yes, for 3D points (x₁,y₁,z₁) and (x₂,y₂,z₂), use the formula: d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²].
What's the difference between distance and displacement?
Distance is the total path length traveled, while displacement is the straight-line distance from start to end point. Our calculator finds displacement (straight-line distance).