Midpoint Calculator

1. Enter the coordinates of Point 1 (x₁, y₁) — the first endpoint of your line segment.
2. Enter the coordinates of Point 2 (x₂, y₂) — the second endpoint.
3. The midpoint appears instantly, along with the distance between the two points, the slope, and the Δx and Δy components.
4. Use the visualization to see the line segment and where the midpoint sits — useful for double-checking by eye.

The midpoint formula finds the point exactly halfway between two coordinates by averaging the x-values and the y-values separately.

Midpoint M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Where:
(x₁, y₁) = coordinates of the first point
(x₂, y₂) = coordinates of the second point

Example: Find the midpoint of (2, 3) and (8, 11).

• Midpoint x = (2 + 8) / 2 = 5
• Midpoint y = (3 + 11) / 2 = 7
• Midpoint = (5, 7)

The midpoint formula works in 3D too — just average the z-coordinates as well:

3D Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2)

The midpoint formula is one of the most-used tools in computational geometry, computer graphics, navigation, and data analysis. Three real applications worth knowing:

One nuance for spherical surfaces (like the Earth): the simple Cartesian midpoint formula doesn't give the great-circle midpoint between two latitude/longitude points. For navigation, use the great-circle midpoint formula:

Bx = cos(φ₂) · cos(λ₂ − λ₁)
By = cos(φ₂) · sin(λ₂ − λ₁)
φ_mid = atan2(sin(φ₁) + sin(φ₂), √((cos(φ₁)+Bx)² + By²))
λ_mid = λ₁ + atan2(By, cos(φ₁) + Bx)

For short distances (under ~50 miles), the simple Cartesian midpoint is accurate enough. For trans-continental routes, use the great-circle version.