About Euclidean Distance

Euclidean distance is the straight-line distance between two points in space. It's fundamental in mathematics, physics, computer graphics, and machine learning. In 2D, it's calculated using the Pythagorean theorem, while 3D adds an additional dimension.

Calculation Formula

For 2D points A(x₁, y₁) and B(x₂, y₂):
d = √[(x₂ - x₁)² + (y₂ - y₁)²]

For 3D points A(x₁, y₁, z₁) and B(x₂, y₂, z₂):
d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Practical Examples

Example 1 (2D): Distance between (2, 3) and (5, 7)
d = √[(5-2)² + (7-3)²] = √[9 + 16] = √25 = 5.0000

Example 2 (3D): Distance between (1, 2, 3) and (4, 6, 9)
d = √[(4-1)² + (6-2)² + (9-3)²] = √[9 + 16 + 36] = √61 ≈ 7.8102

Frequently Asked Questions

Can I use negative coordinates?

Yes, negative coordinates are supported and will be calculated correctly.

What's the maximum number of decimal places?

Results are shown with up to 6 decimal places for precision.

Does this work for higher dimensions?

This calculator only supports 2D and 3D points. The Euclidean distance formula can be extended to higher dimensions, but that's beyond this calculator's scope.

Distance Calculator

Point A

Point B

Result

Visual Representation

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Distance Calculator - 2D and 3D Distance

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