Midpoint Calculator

Find the midpoint between two points or calculate unknown endpoints

Calculator Options

First Point (A)

Second Point (B)

Results

(0.0000, 0.0000)
Midpoint Coordinates
Distance between endpoints: 0.0000 units

Points Summary

Point A: (0, 0)
Point B: (0, 0)
Midpoint M: (0.0000, 0.0000)

Step-by-Step Calculation

Midpoint Formula:
M = ((x₁ + x₂), (y₁ + y₂) / 2)
Substituting values:
M = ((0 + 0) / 2, (0 + 0) / 2)
Calculating each coordinate:
x: (0 + 0) / 2 = 0 / 2 = 0
y: (0 + 0) / 2 = 0 / 2 = 0
Final midpoint: (0.0000, 0.0000)

Example: Finding a Midpoint

Problem

Find the midpoint between points A(2, 4) and B(6, 10)

Solution

Step 1: Apply the midpoint formula: M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Step 2: Substitute values: M = ((2 + 6)/2, (4 + 10)/2)

Step 3: Calculate: M = (8/2, 14/2) = (4, 7)

Result: The midpoint is at coordinates (4, 7)

Key Formulas

2D Midpoint:
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
3D Midpoint:
M = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2)
Find Endpoint:
B = 2M - A
Distance:
d = √[(x₂-x₁)² + (y₂-y₁)²]

Calculator Modes

M

Find Midpoint

Calculate the center point between two coordinates

E

Find Endpoint

Calculate unknown endpoint from midpoint and one endpoint

Applications

📐

Geometry

Triangle centroids, line segment centers

🏗️

Engineering

Structural analysis, center of mass calculations

🎮

Game Development

Collision detection, object positioning

🗺️

Geography

Finding centers between locations

Tips

Midpoint is exactly halfway between two points

Works in any number of dimensions

Average of coordinates gives the midpoint

Useful for finding triangle centroids

Understanding Midpoints

What is a Midpoint?

A midpoint is a point that lies exactly halfway between two other points. It's the center of a line segment and is equidistant from both endpoints. The midpoint divides the line segment into two equal parts.

Mathematical Definition

For two points A(x₁, y₁) and B(x₂, y₂), the midpoint M is calculated as the average of their coordinates:

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Finding Unknown Endpoints

If you know the midpoint M and one endpoint A, you can find the unknown endpoint B using the formula:

B = 2M - A

Geometric Properties

  • The midpoint is equidistant from both endpoints
  • It divides the line segment into two equal parts
  • The concept extends to any number of dimensions
  • Used to find centroids of geometric shapes

Real-World Applications

Architecture & Engineering

Finding center points for structural balance and design symmetry

Computer Graphics

Animation paths, collision detection, and object positioning

Geography & Navigation

Finding meeting points, route planning, and geographic centers