Tips: Use scientific notation (e.g., 1e-3). Press Ctrl/Cmd + Enter to calculate.
Need a fast way to measure the straight-line distance between two points in three-dimensional space? This 3D distance calculator gives you an instant, accurate result using the classic Euclidean distance formula. It is designed for students, engineers, developers, and anyone who needs a reliable way to compute distance between coordinates without manual math. Whether you are checking a geometry problem or estimating a spatial gap in a 3D model, this tool provides a clear, approachable answer.
The idea comes from the Pythagorean theorem. In 2D, you square the horizontal and vertical differences,
add them, and take a square root. In 3D, you include depth as a third difference. For points
P₁ = (x₁, y₁, z₁) and P₂ = (x₂, y₂, z₂), the distance is:
D = √((x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²).
This works with negatives, decimals, and scientific notation, so it covers a wide range of real-world
coordinate systems.
You will see this formula in computer graphics, game development, robotics, CAD, physics, engineering, and GIS mapping. It is used to measure object separation, calculate displacement, evaluate robot path segments, and estimate straight-line distances in a 3D coordinate system. It also appears in data science and spatial analytics when comparing points in three dimensions.
Behind the scenes, the tool subtracts each coordinate to get dx, dy, and dz,
squares them, sums them, and takes the square root to return the final Euclidean distance. The calculation is
instantaneous, so it is perfect for homework checks, quick engineering sketches, or validating distances in 3D
models without leaving a browser tab.
Find the distance between P₁ = (5, 2, 6) and P₂ = (-3, 8, -4).
dx = -3 - 5 = -8, dy = 8 - 2 = 6, dz = -4 - 6 = -10.(-8)² = 64, 6² = 36, (-10)² = 100.64 + 36 + 100 = 200.√200 = 14.142136.Answer: The 3D distance is 14.142136 units.
d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²)
d = √((-3−5)² + (8−2)² + (-4−6)²)
d = √(64 + 36 + 100)
d = √200
d = 14.142136
v1.1 (May 20, 2026)
x₁, y₁, z₁.x₂, y₂, z₂.Use the 3D distance formula to measure the straight-line distance between two points in a 3D game world, check the length of a vector in physics, estimate the distance between drone waypoints, validate CAD dimensions, compare coordinates in robotics, or analyze spatial data in a 3D coordinate system.
It uses the 3D Euclidean distance formula: D = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²).
Yes. The calculator supports negative, decimal, and scientific notation such as 1e-3 for all coordinates.
Typical uses include computer graphics and game development, physics and engineering, robotics and path planning, GIS and mapping, and spatial analytics.
No. Distance is a scalar measurement, so the result is always zero or positive.
For a point (x, y, z), the distance from the origin is √(x² + y² + z²).
No. Swapping Point 1 and Point 2 gives the same distance because each coordinate difference is squared.
The result uses the same units as your coordinates. If your coordinates are in meters, the distance is in meters.
Yes. The distance between two 3D points is the magnitude of the displacement vector between them.
Yes. All calculations are performed locally in your browser; nothing is uploaded.
The longest straight line inside a cube is its body diagonal: edge length × √3. That’s just the 3D distance formula wrapped in a box.
Add more coordinates, add more squared differences. The 3D formula is the same pattern behind N‑dimensional Euclidean distance.
Translate or rotate everything in space—distances stay identical. That invariance powers physics engines and CAD constraints.
Collision check shortcut: two spheres intersect if center distance < sum of radii. One distance compare beats heavy mesh math.
Euclidean distance assumes flat space. Over Earth you need great‑circle math, but once you’re off-planet, 3D straight‑line distance rules again.