How do you find the midpoint between two points?

Add the x-coordinates and divide by 2; do the same for the y-coordinates (and z-coordinates in 3D). M = ((x1 + x2)/2, (y1 + y2)/2[, (z1 + z2)/2]).

Does the midpoint formula work with negative numbers?

Yes. Add the coordinates algebraically (including negatives) and divide by 2.

Can I enter fractions like 3/4?

Yes. This calculator accepts decimals and simple fractions such as 3/4 or -7/2. Results are shown in decimals and, when possible, as exact fractions.

How do I control rounding?

Use the Precision control to choose 0–8 decimal places. Fraction output remains exact.

What is the difference between midpoint and average of points?

For two points, the midpoint is the component-wise average of their coordinates. For more points, you would use a centroid, not a midpoint.

Can I compute the midpoint in 3D?

Yes. Select 3D and enter z1 and z2. The formula extends to z: (z1 + z2)/2.

Is this midpoint the same as the center of a line segment?

Yes. The midpoint is the exact center of the line segment connecting the two points.

Midpoint Calculator

This professional-grade tool computes the midpoint between two points in 2D or 3D space. It’s designed for students, educators, engineers, and anyone working with analytic geometry, with full accessibility, fraction support, and adjustable precision.

Dimension

2D 3D

Choose 2D for (x, y) or 3D for (x, y, z) coordinates.

Point A

x₁

Use decimals or simple fractions.

y₁

Negative values are allowed.

z₁

Point B

x₂

y₂

z₂

Precision (decimals)

Affects only decimal display, not exact fractions.

Input format

Results

Midpoint (decimal)

—

Midpoint (exact fraction)

—

Per-axis details

—

Data Source and Methodology

Authoritative reference: Wolfram MathWorld — “Midpoint” (accessed 2025-09-14). Link: https://mathworld.wolfram.com/Midpoint.html. Supplementary: OpenStax, Precalculus 2e — Section 3.1 “The Rectangular Coordinate System and Graphs” (2018). OpenStax Precalculus 2e.

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

2D midpoint of A(x₁, y₁) and B(x₂, y₂):

$$\mathbf{M}=\left(\frac{x_1+x_2}{2},\ \frac{y_1+y_2}{2}\right)$$

3D midpoint of A(x₁, y₁, z₁) and B(x₂, y₂, z₂):

$$\mathbf{M}=\left(\frac{x_1+x_2}{2},\ \frac{y_1+y_2}{2},\ \frac{z_1+z_2}{2}\right)$$

Glossary of Variables

x₁, y₁, z₁: Coordinates of point A (inputs, required for selected dimensions).
x₂, y₂, z₂: Coordinates of point B (inputs, required for selected dimensions).
M: Midpoint between A and B, output as decimal and, when possible, as exact fraction.
Precision: Number of decimal places used for decimal display.

How It Works: A Step-by-Step Example

Suppose A = (1, 4) and B = (5, −2) in 2D.

Apply the formula: M = ((1 + 5)/2, (4 + −2)/2).
Simplify: M = (6/2, 2/2) = (3, 1).
With precision set to 2 decimals, the decimal output is M = (3.00, 1.00). The fraction output remains exact: M = (3, 1).

Frequently Asked Questions (FAQ)

Can I enter fractions like 7/4 or -5/2?

Yes. This calculator accepts decimals and simple fractions. If both inputs for an axis are rational numbers, the midpoint is also shown as an exact fraction.

What if I choose 3D but leave z empty?

z₁ and z₂ are required in 3D mode. The corresponding fields are validated and must be provided.

Does rounding affect the exact fraction?

No. Rounding controls only the decimal display. The fraction output is exact (when available).

Can I use commas as decimal separators?

If an input contains a comma and no dot, the comma is interpreted as a decimal point (e.g., 1,5 → 1.5). Thousands separators are not supported.

Is the midpoint the same as the center of a line segment?

Yes. The midpoint is the exact center of the line segment that connects the two points.

Why do I see a dash (—) instead of a result?

At least one required field is missing or invalid. Correct the highlighted fields to see results.

How do I share or bookmark my inputs?

The URL updates automatically with your current inputs. Copy the page URL to share or revisit the same calculation.

Strumento sviluppato da Ugo Candido,. Contenuti verificati da,.

Ultima revisione per l'accuratezza in data: September 14, 2025.