Midpoint Calculator

Find the point halfway between two coordinates. Enter the endpoints of a line segment to calculate its midpoint, view the plotted points and follow the formula.

Calculate Your Midpoint

Enter both points in the same coordinate system. Positive numbers, negative numbers and zero are supported.

Point A
Point B

x is the horizontal coordinate and y is the vertical coordinate. Enter decimals as numbers, such as 0.5 rather than 1/2.

Rounding changes the displayed answer, not the entered coordinates.

Enter all four coordinates to plot A, B and their midpoint M.

The midpoint divides a line segment into two equal parts. To calculate a right triangle’s longest side from its perpendicular legs, use the hypotenuse calculator.

QUICK START

How to Use the Midpoint Calculator

Enter the endpoints of a line segment. The calculator averages their horizontal and vertical coordinates separately to locate the halfway point.

  1. Enter the coordinates of point A

    Put the first point’s horizontal coordinate in x₁ and its vertical coordinate in y₁. Keep the usual ordered-pair format: x first, then y.

  2. Add point B in the same coordinate system

    Enter x₂ and y₂ for the other endpoint. Negative numbers, decimals and zero are valid. If a coordinate is a fraction, enter its decimal value, such as 0.5 for 1/2.

  3. Read the midpoint and coordinate diagram

    Once all four fields are filled, the result shows M = (xₘ, yₘ). The diagram plots the endpoints and midpoint automatically. Its grid is a visual guide, rather than a fixed one-unit scale.

  4. Review the averages and copy your answer

    Choose two, four or six decimal places, then follow the separate x and y calculations. Select Copy Result to copy the endpoints and midpoint, or Clear to start again.

Endpoint order does not matter: Swapping A and B gives the same midpoint. However, keep each point’s x and y coordinates in their correct fields; swapping x with y can change the answer.

For another visual explanation of averaging coordinates, explore the midpoint of a line segment on Math Is Fun.

WORKED EXAMPLES

Midpoint Calculations Step by Step

Average matching coordinates: x with x, then y with y. These examples show how to handle negative values and decimal endpoints.

EXAMPLE 01 · NEGATIVE COORDINATES

Find the midpoint across different quadrants

The segment connects A(−6, 8) and B(4, −2). Include each negative sign when substituting the coordinates into the formula.

GIVEN ENDPOINTS
Point A
(−6, 8)
Point B
(4, −2)
  1. Average the x coordinates

    xₘ = (−6 + 4) ÷ 2

    xₘ = −2 ÷ 2 = −1

  2. Average the y coordinates

    yₘ = [8 + (−2)] ÷ 2

    yₘ = 6 ÷ 2 = 3

  3. Write the midpoint as an ordered pair

    M = (xₘ, yₘ) = (−1, 3)

RESULT Midpoint M = (−1, 3)

From A to M and from M to B, the horizontal change is +5 and the vertical change is −5.

EXAMPLE 02 · DECIMAL COORDINATES

Average endpoints with decimal values

The endpoints are A(1.5, −3.2) and B(6.5, 4.8). Use the same formula without rounding the coordinates before calculating.

GIVEN ENDPOINTS
Point A
(1.5, −3.2)
Point B
(6.5, 4.8)
  1. Average the x coordinates

    xₘ = (1.5 + 6.5) ÷ 2

    xₘ = 8 ÷ 2 = 4

  2. Average the y coordinates

    yₘ = (−3.2 + 4.8) ÷ 2

    yₘ = 1.6 ÷ 2 = 0.8

  3. Combine the averaged coordinates

    M = (4, 0.8)

RESULT Midpoint M = (4, 0.8)

With four decimal places selected, the calculator displays this as (4.0000, 0.8000).

A vertical segment keeps the same x coordinate

For endpoints (3, −4) and (3, 10), the midpoint is (3, 3). The x coordinate stays at 3, while y = (−4 + 10) ÷ 2 = 3. Try these endpoints to see the vertical segment on the diagram.

UNDERSTAND THE FORMULA

Midpoint Formula at a Glance

A midpoint lies halfway along a line segment. Average the endpoints’ x coordinates to find its horizontal position, then average their y coordinates to find its vertical position.

A M B AM = MB
Two equal parts of one segment The midpoint belongs to the segment and has the same distance to each endpoint. The matching marks indicate equal lengths.
−4 0 8 2 Midpoint (−4 + 8) ÷ 2 = 2
Average one coordinate at a time Each coordinate follows the same averaging rule as a midpoint on a number line. Apply it separately to x and y.
A = (x₁, y₁), B = (x₂, y₂) and M = (xₘ, yₘ). Use coordinates from the same Cartesian coordinate system.
What to find Formula Meaning
Midpoint x coordinate xₘ = (x₁ + x₂) ÷ 2 Average horizontal position
Midpoint y coordinate yₘ = (y₁ + y₂) ÷ 2 Average vertical position
Midpoint ordered pair M = ((x₁ + x₂)/2, (y₁ + y₂)/2) Both averages combined
Missing endpoint x coordinate x₂ = 2xₘ − x₁ Recover x₂ from M and A
Missing endpoint y coordinate y₂ = 2yₘ − y₁ Recover y₂ from M and A

Midpoint and distance answer different questions

The midpoint is a location, written as an ordered pair. Distance is a length between two locations. The midpoint formula does not require a square root; it averages coordinates rather than measuring the segment.

Find an endpoint when the midpoint is known

Double each midpoint coordinate and subtract the corresponding known endpoint coordinate. If A = (1, 2) and M = (4, 5), then B = (2 × 4 − 1, 2 × 5 − 2) = (7, 8). This is a manual rearrangement of the midpoint formula.

Calculator scope: The tool above finds a two-dimensional midpoint from two endpoints. Missing-endpoint formulas are provided here as a manual reference. For identical endpoints, the midpoint is that same point.

COMMON QUESTIONS

Frequently Asked Questions

Answers about negative coordinates, endpoint order, special cases and what the midpoint calculator supports.

Can a midpoint have negative coordinates?

Yes. Each midpoint coordinate is the average of the corresponding endpoint coordinates, so it can be negative, positive or zero. For example, the midpoint of (−8, −6) and (−2, 4) is (−5, −1). Include the negative signs when adding the values.

Does swapping the endpoints change the midpoint?

No. Addition gives the same total in either order, so averaging A with B gives the same result as averaging B with A. Keep each point’s coordinates together, however: an ordered pair is (x, y), not (y, x).

How do I find the midpoint of a horizontal or vertical segment?

Use the same formula. For a horizontal segment, both endpoints share a y coordinate, which stays unchanged. For a vertical segment, the shared x coordinate stays unchanged. Average the other coordinate to locate the halfway point.

What happens if both endpoints are identical?

The midpoint is that same point. If A and B are both (3, −2), their midpoint is also (3, −2). The segment has zero length, and the diagram shows the endpoints and midpoint in one position.

Can I enter fractions or get an exact fraction answer?

The fields accept numbers and decimals, not fraction notation. Enter 0.5 for 1/2, for example. Results are displayed as decimals. For repeating fractions such as 1/3, a decimal input is an approximation; keep fractions in your manual working if you need an exact fraction answer.

Can I find a missing endpoint from a midpoint?

Yes, by rearranging the formula manually. If A and midpoint M are known, the other endpoint is B = (2xₘ − x₁, 2yₘ − y₁). The calculator above takes two endpoints as inputs; it does not have a separate missing-endpoint mode.

Is a midpoint the same as the distance between two points?

No. A midpoint is a location written as two coordinates. Distance is a single length, calculated with d = √[(x₂ − x₁)² + (y₂ − y₁)²] in a standard Cartesian plane. The midpoint lies on the segment and is half that distance from each endpoint.

Can I use this for 3D points or latitude and longitude?

This tool supports two-dimensional Cartesian points. For a 3D midpoint, also average the z coordinates: zₘ = (z₁ + z₂) ÷ 2. Latitude and longitude describe positions on a curved surface, so a geographic midpoint along Earth’s surface needs a different method.

HAVE YOUR ENDPOINTS READY?

Find the Point Halfway Between

Enter two coordinate pairs to locate their midpoint. View the plotted segment and follow the separate x and y calculations.

Use Midpoint Calculator