3D Distance Calculator

Compute D = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²). Private by design—everything runs locally in your browser.

Calculate Distance Between Two 3D Points

0–15; affects display only.

Point 1

Point 2

Distance
—

Tips: Use scientific notation (e.g., 1e-3). Press Ctrl/Cmd + Enter to calculate.

3D Distance Formula

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.

How the Formula Works

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.

Step-by-Step 3D Distance Example

Find the distance between P₁ = (5, 2, 6) and P₂ = (-3, 8, -4).

  1. Subtract coordinates: dx = -3 - 5 = -8, dy = 8 - 2 = 6, dz = -4 - 6 = -10.
  2. Square each difference: (-8)² = 64, 6² = 36, (-10)² = 100.
  3. Add them: 64 + 36 + 100 = 200.
  4. Take the square root: √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

How to Use the 3D Distance Calculator

Release Updates

v1.1 (May 20, 2026)

  • Added a crawlable step-by-step worked solution for the 3D distance formula.
  • Added dynamic solution lines that update with your coordinates and selected precision.
  • Improved page structure with a table of contents, clearer headings, expanded FAQs, and enhanced application schema.
  1. Enter the coordinates for Point 1: x₁, y₁, z₁.
  2. Enter the coordinates for Point 2: x₂, y₂, z₂.
  3. Click “Calculate” or press Ctrl/Cmd + Enter to compute the distance.
  4. Review the result and use Copy or Share if you want to save or send the values.
  5. Try the Swap or Example buttons to explore different scenarios quickly.

When to Use the 3D Distance Formula

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.

3D Distance Calculator FAQs

What formula does this calculator use?

It uses the 3D Euclidean distance formula: D = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²).

Can I use negative or decimal coordinates?

Yes. The calculator supports negative, decimal, and scientific notation such as 1e-3 for all coordinates.

What are common uses of the 3D distance formula?

Typical uses include computer graphics and game development, physics and engineering, robotics and path planning, GIS and mapping, and spatial analytics.

Can the 3D distance be negative?

No. Distance is a scalar measurement, so the result is always zero or positive.

What is the distance from the origin to a point in 3D?

For a point (x, y, z), the distance from the origin is √(x² + y² + z²).

Does the order of the two points matter?

No. Swapping Point 1 and Point 2 gives the same distance because each coordinate difference is squared.

What units does the calculator use?

The result uses the same units as your coordinates. If your coordinates are in meters, the distance is in meters.

Is this the same as vector magnitude?

Yes. The distance between two 3D points is the magnitude of the displacement vector between them.

Is my data private?

Yes. All calculations are performed locally in your browser; nothing is uploaded.

Advertisement

5 Fun Facts about 3D Distance

Cube diagonal secret

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.

Spatial diagonal

Scale to any dimension

Add more coordinates, add more squared differences. The 3D formula is the same pattern behind N‑dimensional Euclidean distance.

Dimension ladder

Rigid motions can’t touch it

Translate or rotate everything in space—distances stay identical. That invariance powers physics engines and CAD constraints.

Invariant

Sphere tests in one line

Collision check shortcut: two spheres intersect if center distance < sum of radii. One distance compare beats heavy mesh math.

Collision check

Flat vs. curved reality

Euclidean distance assumes flat space. Over Earth you need great‑circle math, but once you’re off-planet, 3D straight‑line distance rules again.

Context matters

Explore more tools