Midpoint Calculator — Find the Midpoint Between Two Points (2D & 3D)
Calculate the midpoint between two coordinate points in 2D or 3D space. Covers the midpoint formula, segment bisector, and practical applications in geometry and mapping.
The midpoint is simply the point that lies exactly halfway between two given points. It's one of the first things you compute in coordinate geometry, and it comes up in everything from dividing line segments in construction to finding the center point between two GPS locations. Find midpoints instantly with the CalcHub Midpoint Calculator.
The Midpoint Formula
In 2D
For two points A(x₁, y₁) and B(x₂, y₂):
$$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$
Just average the x-coordinates and average the y-coordinates.
Example: Find the midpoint between A(3, 5) and B(9, 1).M = ((3+9)/2, (5+1)/2) = (12/2, 6/2) = (6, 3)
Verify: The distance from A(3,5) to M(6,3) = √((6-3)²+(3-5)²) = √(9+4) = √13 The distance from M(6,3) to B(9,1) = √((9-6)²+(1-3)²) = √(9+4) = √13 ✓In 3D
For points A(x₁, y₁, z₁) and B(x₂, y₂, z₂):
$$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2}\right)$$
Example: Midpoint between (1, 2, 3) and (5, 8, −3)M = ((1+5)/2, (2+8)/2, (3+(−3))/2) = (3, 5, 0)
Finding an Endpoint Given the Midpoint
If you know one endpoint and the midpoint, solve for the other endpoint:
$$x_2 = 2M_x - x_1 \quad y_2 = 2M_y - y_1$$
Example: Midpoint is (4, 6). One endpoint is (1, 3). Find the other.x₂ = 2×4 − 1 = 7
y₂ = 2×6 − 3 = 9
Other endpoint: (7, 9)
Practical Applications
Segment Bisector in Construction: When framing a wall, finding the center point for placing a window or outlet requires the midpoint formula applied to the wall's endpoint coordinates. Screen Layout in UI Design: Centering a widget between two elements — the center position is the midpoint of the element boundaries. Map Applications: The midpoint between two cities is often used for planning meeting points. Given two GPS coordinates (treated as flat 2D points for short distances):| City | Coordinates |
|---|---|
| Mumbai | (19.07°N, 72.87°E) |
| Pune | (18.52°N, 73.86°E) |
| Midpoint | (18.80°N, 73.37°E) |
Dividing a Segment in Any Ratio
The midpoint divides in ratio 1:1. For a general ratio m:n:
$$P = \left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right)$$
Example: Divide A(2, 1) to B(8, 7) in ratio 2:1 (2 parts from A, 1 part to B):P = ((2×8 + 1×2)/(2+1), (2×7 + 1×1)/(2+1)) = (18/3, 15/3) = (6, 5)
Does the midpoint formula work for negative coordinates?
Completely. Negative coordinates are just numbers — the average works identically.
Midpoint of (−5, 3) and (1, −7): ((−5+1)/2, (3+(−7))/2) = (−2, −2).
What's the midpoint of a line on a circle (chord)?
The midpoint of a chord is found using the same formula. Additionally, the perpendicular bisector of any chord passes through the circle's center — this is how you locate the center of a circle given three points on it.
Can this extend beyond 3D?
Yes. The midpoint formula generalizes to any number of dimensions: average each coordinate independently. In n-dimensional space with points A = (a₁, a₂, ..., aₙ) and B = (b₁, b₂, ..., bₙ), the midpoint is ((a₁+b₁)/2, (a₂+b₂)/2, ..., (aₙ+bₙ)/2).