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Midpoint Calculator

MathAlgebra Tools
First endpoint
Second endpoint
Midpoint (x, y) —
Midpoint x
—
Midpoint y
—
Segment length
—
Distance from each endpoint to the midpoint
—
Slope of the segment
—

The midpoint of a segment is the average of its endpoints: M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). For the points (7, -2) and (9, 5), the x-values average to 8 and the y-values to 1.5, so the midpoint is (8, 1.5). It lies the same distance, about 3.64 units, from each end.

About this tool

Students checking coordinate-geometry homework, teachers preparing answer keys and anyone splitting a line segment in half on a grid can use this page. Type the two endpoints and it returns the midpoint as an ordered pair, the x and y coordinates separately, the full length of the segment, the distance from the midpoint to either end and the slope of the line through both points. Each averaging step is shown so the working can be copied into a solution. Decimals and negative coordinates are accepted. The calculation is for two-dimensional Cartesian points only; it does not handle three-dimensional points, latitude and longitude on a sphere, or a weighted split at some ratio other than one to one.

How to use it

  1. Enter the first endpoint

    Type x₁ and y₁ for one end of the segment. Negatives and decimals are fine.

  2. Enter the second endpoint

    Type x₂ and y₂ for the other end. The order of the two points does not change the midpoint.

  3. Read the midpoint and extras

    The ordered pair appears at the top, followed by the segment length, the half-length and the slope, with the averaging steps listed below.

Examples

From (7, -2) to (9, 5)

x₁
7
y₁
-2
x₂
9
y₂
5

Result Midpoint (x, y): (8, 1.5)
Midpoint x: 8
Midpoint y: 1.5
Segment length: 7.2801
Distance from each endpoint to the midpoint: 3.6401
Slope of the segment: 3.5

  1. x of midpoint = (7 + 9) ÷ 2 = 8
  2. y of midpoint = (-2 + 5) ÷ 2 = 1.5
  3. Segment length = √((2)² + (7)²) = 7.2801

Averaging 7 and 9 gives 8, and averaging -2 and 5 gives 1.5, so the segment balances at (8, 1.5).

Origin to (6, 8)

x₁
0
y₁
0
x₂
6
y₂
8

Result Midpoint (x, y): (3, 4)
Midpoint x: 3
Midpoint y: 4
Segment length: 10
Distance from each endpoint to the midpoint: 5
Slope of the segment: 1.333333

  1. x of midpoint = (0 + 6) ÷ 2 = 3
  2. y of midpoint = (0 + 8) ÷ 2 = 4
  3. Segment length = √((6)² + (8)²) = 10

A 6-8-10 right triangle: the midpoint (3, 4) sits exactly 5 units from both ends.

How it is calculated

M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2); d = √((x₂ − x₁)² + (y₂ − y₁)²)

x₁, y₁
coordinates of the first endpoint
x₂, y₂
coordinates of the second endpoint
M
the midpoint of the segment
d
length of the segment (distance formula)

Each coordinate of the midpoint is the arithmetic mean of the matching endpoint coordinates, so the point is halfway along both axes at once. The length comes from the Pythagorean theorem applied to the horizontal and vertical differences, and the midpoint is d ÷ 2 from each end. Slope is the vertical change divided by the horizontal change; when both x-values are equal the segment is vertical and its slope is undefined.

When not to use it

  • Points given as latitude and longitude need a great-circle midpoint, not a flat average.
  • Points in three dimensions need a z-coordinate averaged as well.
  • Dividing a segment in a ratio such as 1:3 needs the section formula, not the midpoint.

Common mistakes

  • Subtracting the coordinates instead of adding them before halving.
  • Averaging an x-value with a y-value by mixing up the order inside each pair.
  • Dropping the minus sign on a negative coordinate when adding.

Frequently asked questions

Does it matter which point I enter first?

No. Addition is commutative, so (x₁ + x₂) ÷ 2 equals (x₂ + x₁) ÷ 2. Reversing the order of the endpoints only flips the sign of the differences used for the slope, and since both differences flip together the slope stays the same too.

How do I find an endpoint if I know the midpoint and the other end?

Rearrange the formula: x₂ = 2·Mx − x₁ and y₂ = 2·My − y₁. For a midpoint of (8, 1.5) and one end at (7, -2), the other end is (16 − 7, 3 + 2) = (9, 5).

Is the midpoint the same as the centre of a circle?

If the two points are the ends of a diameter, yes: the midpoint of the diameter is the centre, and half the segment length is the radius. For two arbitrary points on a circle the midpoint lies inside the circle but is not its centre.

Why is the slope shown as undefined?

When both endpoints share the same x-value the segment is vertical. Slope divides the change in y by the change in x, and that change in x is zero, so no finite slope exists. The midpoint itself is still well defined.

Can the midpoint have fractional coordinates when the endpoints are whole numbers?

Yes. If the two x-values (or y-values) add to an odd number, halving gives a half. From (7, -2) to (9, 5) the y-values sum to 3, so the midpoint's y is 1.5, written 3/2 in many textbooks.

What does the half-length figure tell me?

It is the straight-line distance from the midpoint to either endpoint. Comparing it with the full segment length is a quick check that the midpoint really is equidistant from both ends.

Cite this tool

Using this tool in an assignment, article or report? Copy a citation, or a link for your website.

APA

Tools Directory Editorial Team. (2026, October 26). Midpoint Calculator. Tools Directory. Retrieved October 26, 2026, from https://tools.milunir.com/math/algebra-tools/midpoint-calculator/

MLA

Tools Directory Editorial Team. “Midpoint Calculator.” Tools Directory, 26 Oct. 2026, https://tools.milunir.com/math/algebra-tools/midpoint-calculator/. Accessed 26 Oct. 2026.

Chicago

Tools Directory Editorial Team. “Midpoint Calculator.” Tools Directory. Last modified October 26, 2026. Accessed October 26, 2026. https://tools.milunir.com/math/algebra-tools/midpoint-calculator/.

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