Math

Euclidean Distance Calculator

Find the straight-line distance between two points in 3D.

x₁

y₁

z₁

x₂

y₂

z₂

Calculated Output

Distance 5

Formula: d = √(Δx² + Δy² + Δz²)

Step-by-Step Breakdown

1. Values used:

2. x₁ = 1

3. y₁ = 2

4. z₁ = 3

5. x₂ = 4

6. y₂ = 6

7. z₂ = 3

9. Distance = 5

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The math behind it

It generalises the Pythagorean theorem to any number of dimensions: square the differences, sum them, take the square root.

(1,2,3) to (4,6,3) → √(9 + 16 + 0) = 5.

How is it different from Manhattan distance?

Euclidean goes in a straight line; Manhattan sums the axis-aligned steps.