Calculators

Distance and Midpoint Calculator

Use $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. For (1, 1) and (4, 5): $\sqrt{9 + 16} = \sqrt{25} = 5$.

Find the distance between two points and their midpoint, with the formulas and steps.

x1 y1 x2 y2

Distance: 10 · Midpoint: (3, 4) Distance = √(6² + 8²) = √100 = 10; Midpoint = ((0+6)/2, (0+8)/2) = (3, 4).

Distance and Midpoint

Two ideas, both about the line segment between two points:

The distance is how far apart they are in a straight line. Look at the horizontal gap and the vertical gap between the points: they form the two legs of a right triangle, and the distance is the hypotenuse. That is why the distance formula is really the Pythagorean theorem in disguise.
The midpoint is the point exactly halfway between, which you find by averaging the two x-values and the two y-values.

The graph plots both points, joins them, and marks the midpoint, so you can see the right triangle the distance comes from.

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

\text{midpoint} = \left( \frac{x_1 + x_2}{2},\ \frac{y_1 + y_2}{2} \right)

The distance formula is the Pythagorean theorem applied to the horizontal and vertical gaps between the points.

Point 1	Point 2	Distance	Midpoint
(1, 1)	(4, 5)	5	(2.5, 3)
(0, 0)	(6, 8)	10	(3, 4)
(2, 3)	(2, 9)	6	(2, 6)

Use $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ . For (1, 1) and (4, 5): $\sqrt{9 + 16} = \sqrt{25} = 5$ .

Average the x-coordinates and the y-coordinates: $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$ .

The horizontal and vertical gaps form the two legs of a right triangle, and the distance is the hypotenuse.