2D Distance Calculator
Point 1
Point 2
The distance formula calculates the straight-line (Euclidean) distance between two points in a 2D coordinate plane. It is derived directly from the Pythagorean theorem — the distance is the hypotenuse of a right triangle formed by the horizontal and vertical differences.
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Tip: Check for Pythagorean triples first. If Δx and Δy are 3 and 4, the answer is exactly 5 — no calculator needed.
- 1Find the horizontal difference: Δx = x₂ − x₁
- 2Find the vertical difference: Δy = y₂ − y₁
- 3Square both differences and add them
- 4Take the square root: d = √(Δx² + Δy²)
(0,0) to (3,4)=5√(9+16)=√25=5 — a 3-4-5 triangle
(1,1) to (4,5)=5√(9+16)=5
(−2,3) to (4,−1)=7.211√(36+16)=√52≈7.211
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Fun Fact
GPS navigation uses a 3D version of the distance formula plus corrections for Earth's curvature to calculate positions accurate to within a few centimetres.
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