Distance Between Two Points
Calculate Distance in 2D & 3D Space
Calculate the distance between two points in 2D or 3D coordinate space. Get midpoint, slope (2D), and detailed step-by-step solutions.
Enter Coordinates
Point 1
Point 2
Distance Formula
2D: d = √[(x₂-x₁)² + (y₂-y₁)²]
3D: d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]
About Distance Formula
The distance formula calculates the straight-line distance between two points in coordinate space. It is derived from the Pythagorean theorem.
In 2D space, the formula finds the length of the hypotenuse of a right triangle formed by the horizontal and vertical distances between points.
Applications:
- Navigation and GPS systems
- Computer graphics and game development
- Physics and engineering calculations
- Data analysis and clustering
Related Formulas
Distance (2D):
d = √[(x₂-x₁)² + (y₂-y₁)²]
Midpoint:
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Slope:
m = (y₂-y₁) / (x₂-x₁)
Example Calculations
| Point 1 | Point 2 | Distance |
|---|---|---|
| (0, 0) | (3, 4) | 5 |
| (1, 2) | (4, 6) | 5 |
| (-2, -3) | (1, 1) | 5 |
| (0, 0, 0) | (1, 1, 1) | √3 ≈ 1.732 |
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