Starlight Tools

Midpoint Calculator

Find the midpoint between two points in 2D or 3D, with formula, graph, and steps.

Coordinates & Actions

Point A
Point B

Accepted: integers, decimals, fractions, mixed numbers (such as 2 1/3), and simple radicals (such as sqrt(3)).

M = —

Tip: Press Enter in any field to calculate.

Result graph

2D: true positions, with P₁, P₂, and M. 3D: simple isometric projection for orientation (axes indicative).

Try an example

Understanding the Midpoint Formula

Reviewed: 11 July 2026Reviewer: Starlight Tools mathematics editorMethod: coordinate-wise midpoint and endpoint formulasTested: positive, negative, fractional, decimal, radical, and 3D cases

A midpoint calculator is the quickest way to find the point exactly halfway between two coordinates. Whether you are working on geometry homework, plotting a line segment in a design tool, or building a game map, the midpoint gives you the precise center. This tool makes it simple: enter two points in 2D or 3D, and it returns the midpoint instantly, along with a clear visual preview.

The idea is straightforward. In 2D, with points P₁=(x₁,y₁) and P₂=(x₂,y₂), the midpoint is the average of the x-coordinates and the average of the y-coordinates: M=((x₁+x₂)/2,(y₁+y₂)/2). In 3D, you simply include the z-coordinate: M=((x₁+x₂)/2,(y₁+y₂)/2,(z₁+z₂)/2). This works for any real numbers, including negatives and decimals, because it is just coordinate-wise averaging.

Midpoints show up everywhere in math and applied fields. In coordinate geometry, they identify the center of a line segment. In physics and engineering, they represent balance points for uniform rods and beams. In graphics, midpoints help align shapes, split segments, or build curves. In robotics or mapping, they can serve as waypoints between two known positions.

How to use this midpoint calculator

  1. Select 2D or 3D mode depending on your coordinates.
  2. Enter the first point (x₁, y₁, and z₁ if needed).
  3. Enter the second point (x₂, y₂, and z₂ if needed).
  4. Click calculate to see the midpoint and the plotted preview.
  5. Use the share feature if you want a link with your values included.

Example use cases include finding the center of a line segment between two cities on a map, splitting a design element evenly in CAD software, or checking a mid-step position in a physics or vector problem. Because all calculations run locally in your browser, you get fast results without uploading any data.

Midpoint and endpoint guide

What is a midpoint?

The midpoint is the point exactly halfway along a line segment. It has the same distance from both endpoints.

Midpoint formula

Average matching coordinates: M=((x₁+x₂)/2,(y₁+y₂)/2). In 3D, also average z₁ and z₂.

How to find a midpoint step by step

Add the two x-coordinates and divide by 2. Repeat for y, and for z in three dimensions. Keep fractions exact until the end.

How to find a missing endpoint

Double each midpoint coordinate, then subtract the known endpoint: x₂=2xₘ−x₁, y₂=2yₘ−y₁, and similarly for z.

How to check your answer

Calculate the distance from the first endpoint to M and from M to the second. Equal distances confirm that M bisects the segment.

Common mistakes

Do not average x with y, forget to divide each sum by 2, round fractions too early, or omit the z-coordinate in a 3D problem.

Midpoint Calculator: Frequently Asked Questions

How do I find the midpoint of a line segment?

Add the endpoints' matching coordinates and divide each sum by 2. For A(0, 2) and B(2, 8), M=((0+2)/2,(2+8)/2)=(1,5).

How do I find the endpoint from a midpoint?

If A and M are known, use B=2M−A coordinate by coordinate. Select “Find missing endpoint” above to see the substitution steps.

Can the midpoint be a fraction?

Yes. When a coordinate sum is odd or fractional, its exact midpoint can be a fraction. This calculator preserves that exact form.

Do you round midpoint coordinates?

Keep the exact value unless a problem requests rounding. The calculator shows an exact answer and a decimal approximation when they differ.

What is the midpoint of a diameter?

The midpoint of a circle's diameter is the center of the circle.

How do you find a midpoint in 3D?

Average x, y, and z separately: M=((x₁+x₂)/2,(y₁+y₂)/2,(z₁+z₂)/2).

What is the midpoint between two numbers?

For numbers a and b on a number line, the midpoint is their average: (a+b)/2.

Explore more tools