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

The midpoint of two points is the coordinate exactly halfway between them. For 2D, with P₁=(x₁,y₁) and P₂=(x₂,y₂): M=\((x₁+x₂)/2,(y₁+y₂)/2\).

For 3D, with P₁=(x₁,y₁,z₁) and P₂=(x₂,y₂,z₂): M=\((x₁+x₂)/2,(y₁+y₂)/2,(z₁+z₂)/2\).

This is simply the average of each coordinate. It works for any real numbers (including negatives and decimals).

How This Midpoint Calculator Works

  • Validates your inputs (2D or 3D).
  • Computes the coordinate-wise average.
  • Displays a shareable URL and an instant visual.
  • Everything runs locally for full privacy.

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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