High School Distance and Midpoint Formula Calculator
Calculate the distance length and midpoint coordinates between two points in 2D or 3D space.
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
Distance (d)
—
Midpoint (M)
Steps
Visual Graph
Understanding the Distance and Midpoint Formula Calculator
In analytical geometry, knowing how to measure the space between two points and finding the exact center is fundamental. This calculator automates these processes for both 2D Cartesian planes (x, y) and 3D space (x, y, z).
The Distance Formula
The distance formula is derived directly from the Pythagorean Theorem. In a 2D plane, the distance d between two points (x₁, y₁) and (x₂, y₂) is the hypotenuse of a right triangle formed by the horizontal and vertical differences.
For 3D space, we simply add the z-component:
d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]
The Midpoint Formula
The midpoint is the average of the coordinates. It represents the exact center of the line segment connecting the two points.
Why use this Distance and Midpoint Formula Calculator?
While the math is simple arithmetic, handling negative numbers, squares, and square roots manually often leads to sign errors. This tool ensures precision and provides a step-by-step breakdown, which is invaluable for checking homework or visualizing spatial relationships in physics and engineering problems.
FAQ
Yes, this tool is 100% free for students and teachers.
No. Distance is a scalar quantity representing magnitude, so it is always non-negative. The calculation involves squaring differences (which makes them positive) and then taking the square root.
Absolutely. You can input integers, decimals, or even coordinates like 0.5 or -3.2.
Click the “3D” button at the top. This reveals the Z-input fields for both points.