Midpoint Calculator
Find the midpoint between two points or calculate unknown endpoints
Calculator Options
First Point (A)
Second Point (B)
Results
Points Summary
Step-by-Step Calculation
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
Calculator Modes
Find Midpoint
Calculate the center point between two coordinates
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