Midpoint Calculator: Find Center Point Between 2D/3D Coordinates Easily

How to use the tool

1. Enter Point A

• x₁ – type the x-coordinate, e.g., -6 or 13.2.
• y₁ – type the y-coordinate, e.g., 2 or -9.5.
• Optional 3-D: check “3-D” and add z₁, e.g., -3.

2. Enter Point B

• x₂ – e.g., 10 or -4.7.
• y₂ – e.g., -4 or 18.9.
• Optional 3-D: add z₂, e.g., 9.

3. Click “Calculate”

The tool applies the midpoint formulas:

2-D: $$M\,(x_m,y_m)=\left(rac{x_1+x_2}{2},rac{y_1+y_2}{2}\right)$$

3-D: $$M\,(x_m,y_m,z_m)=\left(rac{x_1+x_2}{2},rac{y_1+y_2}{2},rac{z_1+z_2}{2}\right)$$

4. Read & visualise the answer

• The midpoint appears to two decimals.
• A scatter plot marks both endpoints and the midpoint.

Example A (2-D)

• Point A (-6, 2)
• Point B (10, -4)

$$x_m=rac{-6+10}{2}=2,\; y_m=rac{2+(-4)}{2}=-1$$

Midpoint = (2, -1)

Example B (3-D)

• Point A (1, 8, -3)
• Point B (7, -2, 9)

$$x_m=rac{1+7}{2}=4,\; y_m=rac{8+(-2)}{2}=3,\; z_m=rac{-3+9}{2}=3$$

Midpoint = (4, 3, 3)

5. Reset if needed

Click “Reset” to clear all fields and chart.

Quick-Facts

• The midpoint formula first appeared in Elements Book 2 by Euclid (Heath, 1908).
• Chart visualisation uses Chart.js v4, MIT-licensed (Chart.js docs, 2023).
• ISO 10303-42 mandates right-handed Cartesian coordinates for 3-D CAD data (ISO 10303-42:2019).
• Double-precision floats keep ±1.0 × 10³⁰⁸ range (IEEE 754-2008).

FAQ

What is the midpoint?

The midpoint is the point exactly halfway between two endpoints on a line segment (NCES, 2019).

How does the calculator work?

It averages each corresponding coordinate, then rounds to two decimals and plots the result.

Can I use negative or decimal values?

Yes; the fields accept any real number supported by IEEE 754 double precision.

Is the formula different in 3-D?

No; you still average coordinates—there’s simply an extra z-term.

Why round to two decimals?

Two-decimal rounding matches typical classroom precision guidelines (Common Core, 2018).

What if I leave a field blank?

The form flags the omission and blocks calculation until all required inputs are numeric.

Does the chart scale automatically?

Chart.js autoscales axes to include every plotted point (Chart.js docs, 2023).

Is the tool mobile-friendly?

Yes; Tailwind’s responsive classes adapt layouts down to 320 px screen width.