Distance & Midpoint Calculator
Find the distance between two points and their midpoint. Shows the distance and midpoint formulas with your values substituted in, step by step.
About this calculator
Enter the coordinates of two points (x₁, y₁) and (x₂, y₂). The calculator computes the straight-line distance using the distance formula d = √((x₂ − x₁)² + (y₂ − y₁)²) and the midpoint M = ((x₁ + x₂)/2, (y₁ + y₂)/2).
How the distance and midpoint formulas work
The distance formula d = √((x₂ − x₁)² + (y₂ − y₁)²) is the Pythagorean theorem applied to the horizontal gap (x₂ − x₁) and vertical gap (y₂ − y₁) between two points: those gaps are the legs of a right triangle and the distance is its hypotenuse. The midpoint M = ((x₁ + x₂)/2, (y₁ + y₂)/2) is simply the average of the two x-coordinates and the average of the two y-coordinates, which lands exactly halfway along the segment. When the two points share an x-value the segment is vertical, so there is no slope, but the distance and midpoint are still well defined.