Distance Formula calculates the straight-line distance between two points in coordinate geometry. Specifically, it finds the length of the segment connecting them.
This essential mathematical tool comes from the Pythagorean Theorem. Moreover, it works in both 2D and 3D coordinate systems. Consequently, it has wide applications across multiple fields.
For instance, navigation systems rely on distance calculations. Similarly, physics and engineering use it extensively. Furthermore, computer graphics depend on precise distance measurements.
A Distance Formula Calculator saves time and reduces errors. Manual calculations can become complex with decimal coordinates. Therefore, automation ensures perfect accuracy.
Additionally, students verify homework solutions efficiently. Professionals get instant results during planning. Also, complex problems become manageable quickly.
Finally, our calculator provides step-by-step explanations. Consequently, users understand the calculation process. Learning becomes interactive and effective.
1. Identify two points: (x₁, y₁) and (x₂, y₂)
2. Calculate difference: Δx = x₂ - x₁
3. Calculate difference: Δy = y₂ - y₁
4. Square both differences: (Δx)² and (Δy)²
5. Sum the squares: (Δx)² + (Δy)²
6. Take square root: √(sum)
7. Result is distance between points
Points: (3, 4) and (7, 1)
Δx = 7 - 3 = 4
Δy = 1 - 4 = -3
Sum of squares: 4² + (-3)² = 16 + 9 = 25
Distance: √25 = 5
Where (x₁, y₁) and (x₂, y₂) are coordinates of two points
Our Distance Formula Calculator processes coordinates in real-time. First, it collects your input values. Then, it calculates the differences between coordinates.
Next, it squares these differences. After that, it sums the squared values. Finally, it computes the square root. The result appears instantly.
Additionally, our calculator handles negative values. Decimal points are supported too. Complex calculations become effortless. Accuracy is mathematically guaranteed.
| Point A | Point B | Calculation | Distance |
|---|---|---|---|
| (0, 0) | (3, 4) | √(3² + 4²) = √25 | 5.00 |
| (1, 2) | (4, 6) | √(3² + 4²) = √25 | 5.00 |
| (-2, -3) | (1, 1) | √(3² + 4²) = √25 | 5.00 |
| (5, 8) | (2, 3) | √((-3)² + (-5)²) = √34 | 5.83 |
| (-1.5, 2.5) | (3.5, -1.5) | √(5² + (-4)²) = √41 | 6.40 |