Distance Formula (2D)

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

x₁ =

y₁ =

x₂ =

y₂ =

d =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Learning zone

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 can be solved for directly — recovering a single coordinate from a known distance gives two equally valid mirror-image answers, so there is no unique inverse.

Distance Formula (2D)

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Where

$x_1$ = First point x-coordinate
$y_1$ = First point y-coordinate
$x_2$ = Second point x-coordinate
$y_2$ = Second point y-coordinate
$d$ = Distance between the points

Missing one of these? Work it out first, then come back

First point x-coordinate — Slope Between Two Points, Distance from a Point to a Line
First point y-coordinate — Slope Between Two Points, Distance from a Point to a Line
Second point x-coordinate — Slope Between Two Points, Distance from a Point to a Line
Second point y-coordinate — Slope Between Two Points, Distance from a Point to a Line
Distance between the points — Distance Formula (3D), Distance from a Point to a Line