Midpoint Calculator

Enter the coordinates of the two endpoints. The first point is (x1, y1) and the second point is (x2, y2).

1. Enter the x and y of the first point. The example uses (2, 4).
2. Enter the x and y of the second point. The example uses (6, 10).
3. Press Calculate, or press Enter. The midpoint appears first and large, with the distance and the slope below.
4. Press Reset to clear the form and start over.

The midpoint is the point exactly halfway between two points, so it is the average of the two endpoints, one axis at a time. Add the two x values and divide by 2 to get the midpoint x. Add the two y values and divide by 2 to get the midpoint y.

The formula is M = ((x1 + x2) / 2, (y1 + y2) / 2). The midpoint always lies on the line segment between the two points, at the same distance from each end. That distance is half the total distance between the points.

The same idea gives the distance. The distance formula is d = sqrt((x2 - x1) squared + (y2 - y1) squared), which is the Pythagorean theorem applied to the horizontal and vertical gaps. Our distance calculator finds the distance between two points on its own, and our pythagorean theorem calculator covers the theorem behind it.

Find the midpoint of (2, 4) and (6, 10).

1. Average the x values. x = (2 + 6) / 2 = 8 / 2 = 4.
2. Average the y values. y = (4 + 10) / 2 = 14 / 2 = 7.
3. Read the answer. The midpoint is (4, 7).
4. Check the distance. d = sqrt((6 - 2) squared + (10 - 4) squared) = sqrt(16 + 36) = sqrt(52) = 7.21.

Each endpoint sits 3.61 from the midpoint, which is half of 7.21, so the midpoint is exactly halfway. As a second check, the points (6, 3) and (12, 7) give a midpoint of (9, 5) and a distance of 7.21, since sqrt((12 - 6) squared + (7 - 3) squared) is also sqrt(52). The same steps work for any two points, so try your own numbers in the tool above.

Two points give three useful answers. The midpoint tells you where the halfway point is. The distance tells you how long the segment is. The slope tells you how steep it is.

The slope is m = (y2 - y1) / (x2 - x1). For (2, 4) and (6, 10), the slope is (10 - 4) / (6 - 2) = 6 / 4 = 1.5. A positive slope rises from left to right, a negative slope falls, a zero slope is flat, and a vertical segment has no slope at all because the division is by zero. The calculator says undefined instead of inventing a number.

The midpoint is also the point where the two halves meet. If you walk from (2, 4) to (6, 10), you reach (4, 7) after 3.61 units, exactly half the trip. Our slope calculator finds the slope and the line equation for the same two points.

The most common mistake is averaging the wrong pair, adding x1 to y1 instead of x1 to x2. Keep the axes separate. Average the two x values for the midpoint x, and average the two y values for the midpoint y.

A second mistake is forgetting that the distance formula uses the differences, not the sums. The distance is sqrt((x2 - x1) squared + (y2 - y1) squared), not sqrt((x1 + x2) squared + (y1 + y2) squared). For (2, 4) and (6, 10), the differences are 4 and 6, and the distance is 7.21.

A third mistake is giving a slope for a vertical line. When x1 equals x2, the segment is vertical and the slope is undefined, because the formula divides by zero. A slope of zero means a flat horizontal line, which is a different thing entirely.

Midpoints show up wherever a halfway point matters. A meeting point halfway between two homes, the center of a line drawn on a map, the middle of a road between two junctions, all of these are midpoints. Hikers use the same idea to find the halfway point of a trail.

In geometry, the midpoint divides a segment into two equal parts, which is the starting point for bisectors, medians of triangles and the center of a circle through two points. In games and graphics, the midpoint is how a program finds the center between two positions on a screen. Our linear equation solver finds the equation of the line through the same two points.