LifeTally
3D distance and midpoint between two points
How far apart are your two points in space, and where is their midpoint?
Enter six Cartesian coordinates to find the straight-line distance and all three midpoint coordinates.
Your points
Use three perpendicular Cartesian axes with the same unit scale. Keep all six coordinates in one unit basis. Enter fractions as decimals, not a/b.
How the estimate works
Distance is √((x₁ − x₀)² + (y₁ − y₀)² + (z₁ − z₀)²). The midpoint is ((x₀ + x₁)/2, (y₀ + y₁)/2, (z₀ + z₁)/2). Coincident points are valid: distance is zero and the midpoint is that same point. Each midpoint coordinate needs only its two matching inputs; distance needs all six, even when other coordinates are zero.
d = √((x₁ − x₀)² + (y₁ − y₀)² + (z₁ − z₀)²)
M = ((x₀ + x₁) ÷ 2, (y₀ + y₁) ÷ 2, (z₀ + z₁) ÷ 2)Only straight-line Euclidean geometry of two declared points in three-dimensional Cartesian space. No latitude/longitude, geographic or road distance, travel time, curve or surface distance, unit conversion, graph, measurement validation, uncertainty estimate, collision test or physical or safety guarantee.
OpenStax: 3D coordinates, distance and vector addition ↗Check the filled example
Our chosen example: A = (−2, 3, −1), B = (4, −5, 23). Differences are 6, −8 and 24, so d = √676 = 26. The midpoint is (1, −1, 11). Swapping the points keeps these results. These are mathematical example inputs, not standard values or a forecast.
Accepted input values
- Point A: x₀
- -2
- Point A: y₀
- 3
- Point A: z₀
- -1
- Point B: x₁
- 4
- Point B: y₁
- -5
- Point B: z₁
- 23
Plan the next step
If your points have only x and y coordinates on a plane, use the two-dimensional distance and midpoint calculator. Check your coordinate system and unit scale before interpreting a distance.
Distance and midpoint in 2D →