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Distance Formula (2D)

d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
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Worked example: (1,2) to (4,6) m → 3-4-5 hypotenuse, 5 m. Press Try an example to run it live, then adjust anything.

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Slope Between Two PointsSlope-Intercept Form of a Line

See also

Slope Between Two Points: Both use first point x-coordinate and first point y-coordinate.Slope-Intercept Form of a Line: Both use first point x-coordinate and first point y-coordinate.Distance Formula (3D): Both use distance between the points.
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Distance Formula (2D) explained

d(x1, y1)(x2, y2)x2 − x1y2 − y1

The distance formula is the Pythagorean theorem wearing coordinate clothing. Between any two points, the horizontal separation (x₂ − x₁) and the vertical separation (y₂ − y₁) form the two legs of a right triangle, and the straight-line distance is its hypotenuse. From (1, 2) to (4, 6) the legs are 3 and 4, so the distance is √(9 + 16) = 5: the beloved 3–4–5 triangle hiding in the grid.

Historically this formula marks the marriage of algebra and geometry: René Descartes's La Géométrie (1637) introduced the coordinate plane that lets shapes be handled as equations, and measuring distance was the first payoff. Today the same square-root-of-summed-squares expression computes GPS displacements, collision distances in games, and error magnitudes in statistics. Note that only d comes back unique: recovering a single coordinate from a known distance gives two equally valid mirror-image answers, so the page returns one, the first point to the left of or below the second, and says the other is its mirror.

Distance Formula (2D)

d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Where
  • x1x_1= First point x-coordinate (m)
  • y1y_1= First point y-coordinate (m)
  • x2x_2= Second point x-coordinate (m)
  • y2y_2= Second point y-coordinate (m)
  • dd= Distance between the points (m)
Revised 1 November 2026
Cite this page

formula.expert. (2026, November 1). Distance Formula (2D) Calculator. https://formula.expert/solvers/distance-formula-2d

formula.experthttps://formula.expert/solvers/distance-formula-2d