Midpoint Calculator — Midpoint Between Two Coordinates (2D & 3D)

Find the midpoint between two points. Private by design—everything runs locally in your browser.

Coordinates & Actions

M = —

Formula (2D): M = ((x₁ + x₂)/2, (y₁ + y₂)/2). Formula (3D): M = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2). Tip: Press Enter in any field to calculate.

Preview

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

Understanding the Midpoint Formula

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.

5 Fun Facts about Midpoints

Average in disguise

A midpoint is just the component‑wise average of two points. Midpoints are “add then halve” baked right into geometry.

Mean point

Segment centroid

The midpoint is the centroid of a line segment. In physics it’s where a uniform rod’s mass would balance on a pin.

Balance point

Midpoint test

Two circles with equal radii intersect if the distance between centers is less than twice the radius. The midpoint between centers sits on the perpendicular bisector.

Intersection helper

Bezier DNA

Quadratic Bezier curves are built from midpoint blends. Repeatedly take midpoints along control segments and you trace the curve (De Casteljau’s algorithm).

Graphics roots

Midpoint circle trick

The classic raster “midpoint circle algorithm” picks the next pixel by testing the midpoint between two candidates—midpoints literally draw circles on old GPUs.

Pixel lore

Midpoint Calculator: Frequently Asked Questions

What formula does this calculator use?

2D: M=((x₁+x₂)/2,(y₁+y₂)/2). 3D adds the z term: M=((x₁+x₂)/2,(y₁+y₂)/2,(z₁+z₂)/2).

Can I use negative or decimal coordinates?

Yes. Inputs fully support negative and decimal values.

Is my data private?

Absolutely. All computations are performed directly in your browser; nothing is uploaded.

Where is the midpoint used?

Coordinate geometry, graphics, engineering drawings, robotics path planning, and game development.

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