What is the midpoint formula?

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is the point M = ((x1+x2)/2, (y1+y2)/2). You simply average the x-coordinates and average the y-coordinates to get the centre point of the segment.

How do you verify that a point is the midpoint of a segment?

Calculate the distance from the candidate midpoint to each endpoint. If both distances are equal and together they add up to the total length of the segment, the point is the true midpoint. You can also verify by checking that the midpoint's coordinates are exactly the averages of the two endpoint coordinates.

Can the midpoint have negative coordinates?

Yes. If one or both endpoints have negative x or y coordinates, the midpoint may also have negative coordinates. The formula works the same way regardless of the signs: average the two x values and average the two y values.

Midpoint Calculator

The midpoint of a line segment is the point that sits exactly halfway between its two endpoints. It is one of the most fundamental constructions in coordinate geometry and appears constantly in problems involving bisectors, centroids, and symmetry. The formula is straightforward: to find the midpoint between point one (x1, y1) and point two (x2, y2), you average the x-coordinates to get the midpoint's x value and average the y-coordinates to get the midpoint's y value. Written as a formula, the midpoint M = ((x1+x2)/2, (y1+y2)/2). This calculator takes the four coordinate values, computes the midpoint, and also returns the straight-line distance between the two endpoints using the distance formula (the square root of the sum of squared differences) and the slope of the line segment (rise over run). Having all three results together is useful because in many geometry problems you need to know both where the midpoint is and how far apart the original points are. Enter any four coordinates, positive or negative, integer or decimal, and the calculator updates instantly. The default example uses point one at (2, 4) and point two at (6, 8), which give a midpoint at (4, 6), a distance of 5.66, and a slope of 1. This tool is designed for students working through coordinate geometry, architects or draftspeople splitting lengths, and anyone who needs a quick centre-point calculation. Results are for reference only.

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(4, 6)

midpoint

Distance5.66

Slope (m)1.00

Midpoint x4.00

Midpoint y6.00

How it works

The midpoint formula averages the two x-coordinates and the two y-coordinates separately: M = ((x1+x2)/2, (y1+y2)/2). The distance between the endpoints uses the standard distance formula: d = √((x2−x1)² + (y2−y1)²). The slope is m = (y2−y1)/(x2−x1). For vertical lines where x1 = x2, the slope is undefined and the calculator notes this.

Worked example

Point 1 = (2, 4) and Point 2 = (6, 8) (the default values). Midpoint x = (2+6)/2 = 4. Midpoint y = (4+8)/2 = 6. So the midpoint is (4, 6). Distance = √((6−2)² + (8−4)²) = √(16+16) = √32 = 5.66. Slope = (8−4)/(6−2) = 4/4 = 1.00.

Related calculators

Distance Formula Calculator: full coordinate distance with midpoint, slope and line equation.
Slope Calculator: calculate the gradient of a line and its equation from two points.
Triangle Calculator: solve any triangle including finding side midpoints via geometry.
Hypotenuse Calculator: use Pythagoras's theorem to find the distance as a hypotenuse.

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