Midpoint Calculator
Calculate coordinates of the midpoint between two points in 2D or 3D space
1 Point A (x₁, y₁, z₁)
2 Point B (x₂, y₂, z₂)
Calculated Midpoint (x, y, z)
(, , )
Distance
Direct path length
Slope (m)
Dimensions
Coordinate system
Step 1: Calculate Average X
(x₁ + x₂) / 2 = ( + ) / 2 =
Step 2: Calculate Average Y
(y₁ + y₂) / 2 = ( + ) / 2 =
Step 3: Calculate Average Z
(z₁ + z₂) / 2 = ( + ) / 2 =
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About Midpoint Calculator
What is a Midpoint?
The midpoint is the exact center point between two endpoints of a line segment. It is equidistant from both endpoints and lies directly on the line segment connecting them. In geometry, finding the midpoint is a fundamental operation used in everything from coordinate geometry to engineering and navigation.
Midpoint Formulas
2D Midpoint Formula
For two points in a 2D plane with coordinates $(x_1, y_1)$ and $(x_2, y_2)$, the midpoint $M$ is calculated as: $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$
3D Midpoint Formula
For two points in 3D space with coordinates $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$, the midpoint $M$ is calculated by including the z-axis: $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right)$$
Related Calculations
This calculator also provides additional useful geometry metrics:
Distance Formula (2D)
Calculates the straight-line distance between two points using the Pythagorean theorem: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
Slope Formula (2D)
Determines the steepness and direction of the line segment: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$
How to Use This Calculator
- Select Dimensions: Choose between 2D (Standard) or 3D coordinate systems.
- Enter Point 1: Input the $x, y$ (and $z$ for 3D) coordinates for the first point.
- Enter Point 2: Input the coordinates for the second point.
- Review Results: The calculator instantly provides the midpoint coordinates, distance, and slope.
Frequently Asked Questions
What if the two points are the same?
If both points have identical coordinates, the midpoint will be the same as the points themselves, and the distance between them will be zero.
Can coordinates be negative?
Yes, this calculator supports positive, negative, and decimal values for all coordinate axes.
Does the order of points matter?
No. The midpoint of Point A to Point B is exactly the same as the midpoint from Point B to Point A. The distance also remains the same.
What is the slope of a vertical line?
If $x_1 = x_2$, the run is zero, and the slope is considered "undefined" or vertical. The calculator will indicate this clearly.
Tip: This tool is perfect for finding the center of a room in construction, calculating mid-flight points in navigation, or solving geometry homework problems accurately.