Distance Between Two Points Calculator

The Distance Formula and the Pythagorean Theorem

The distance formula finds the straight-line distance between two points on a coordinate plane, (x₁, y₁) and (x₂, y₂), using d = √((x₂ − x₁)² + (y₂ − y₁)²). It is not a separate rule to memorize on its own: it is the Pythagorean theorem applied directly to coordinates. The horizontal gap between the points, x₂ − x₁, and the vertical gap, y₂ − y₁, form the two legs of a right triangle, and the straight-line distance between the points is that triangle’s hypotenuse.

The graph above draws that right triangle explicitly: the dashed horizontal and vertical segments show Δx and Δy, the two legs, while the solid diagonal line is the actual distance you are solving for. Squaring each leg, adding the results, and taking the square root of that sum is exactly the same three-step process used to find a missing hypotenuse in any right triangle. Because subtracting coordinates in either order just flips the sign of Δx or Δy, and squaring removes the sign entirely, the distance formula always gives the same positive result no matter which point you call first or second.

This formula underlies far more than a single calculation: it defines how far apart two locations are on a map, two points in a data set, or two objects on a screen, and it is the foundation for later concepts like the equation of a circle and vector length, making it one of the most frequently reused formulas in algebra, geometry, and applied fields like physics and computer graphics.