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Euclidean Distance Between Two 2D Points Calculator

The Cartesian distance formula applies the Pythagorean theorem to horizontal displacement Δx = |x₂ - x₁| and vertical displacement Δy = |y₂ - y₁| to find the Euclidean metric d = √(Δx² + Δy²).

d = √(Δx² + Δy²)
Pick which value you want to calculate (or type into any field):Solving for: d — Euclidean Distance
Calculated

Straight-line vector magnitude between points

0.01100,000.00

Horizontal coordinate difference

0100,000.00

Vertical coordinate difference

0100,000.00
Calculated Result · Euclidean Distance (d)
10m
Converted units:

Step-by-Step Calculation

01Canonical Law: d = √(Δx² + Δy²)
02Given Inputs (Base Units): Δx = 6 m, Δy = 8 m
03Solve for d (Euclidean Distance): d = 10 m

The Cartesian distance formula applies the Pythagorean theorem to horizontal displacement Δx = |x₂ - x₁| and vertical displacement Δy = |y₂ - y₁| to find the Euclidean metric d = √(Δx² + Δy²).

Real-World Reference Values

Euclidean L₂ Norm||v||₂ = √(Δx² + Δy²) = 10

Shortest straight-line geodesic in flat space

Manhattan Taxicab L₁ Norm||v||₁ = |Δx| + |Δy| = 14

Grid street distance along orthogonal axes

Line Slope & Anglem = Δy / Δx | θ = atan2(Δy, Δx)

At Δx = 6, Δy = 8, slope m = 1.333 (53.13°)

20-Row Comparison Table

Euclidean Distance (d) · Horizontal Delta |x₂ - x₁| (Δx)

Euclidean Distance Between Two 2D Points Calculator — Horizontal Delta |x₂ - x₁| → Euclidean Distance
#Horizontal Delta |x₂ - x₁| (m)Euclidean Distance (m)Δ %
016 mCurrent10 m0.00%
02724 m724.0442 m+7140.44%
031,448.00 m1,448.02 m+14380.22%
042,172.00 m2,172.01 m+21620.15%
052,896.00 m2,896.01 m+28860.11%
063,620.00 m3,620.01 m+36100.09%
074,344.00 m4,344.01 m+43340.07%
085,068.00 m5,068.01 m+50580.06%
095,792.00 m5,792.01 m+57820.06%
106,516.00 m6,516.00 m+65060.05%
117,240.00 m7,240.00 m+72300.04%
127,964.00 m7,964.00 m+79540.04%
138,688.00 m8,688.00 m+86780.04%
149,412.00 m9,412.00 m+94020.03%
1510,136.00 m10,136.00 m+101260.03%
1610,860.00 m10,860.00 m+108500.03%
1711,584.00 m11,584.00 m+115740.03%
1812,308.00 m12,308.00 m+122980.03%
1913,032.00 m13,032.00 m+130220.02%
2013,756.00 m13,756.00 m+137460.02%
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Frequently Asked Questions

How do I find the horizontal span Δx given total distance d and vertical rise Δy?+

Click SOLVE FOR on Δx to evaluate Δx = √(d² - Δy²).

Does the sign of (x₂ - x₁) affect Euclidean distance?+

No. Squaring Δx and Δy makes both terms non-negative regardless of quadrant direction.

How does this extend to 3D coordinates?+

In 3D space, add the squared z-axis difference: d = √(Δx² + Δy² + Δz²).