Free 3D Distance Between Two Points Calculator

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The distance formula extends naturally from 2D to 3D by adding a z-term under the square root — it's just the Pythagorean theorem applied twice in succession. This calculation is fundamental to 3D computer graphics and game engines (checking how far apart two objects or a player and an enemy are), CAD and mechanical design (verifying clearances between components), physics simulations (computing gravitational or electrostatic force, which depends on the distance between two bodies in space), and GPS/robotics applications that track position in three dimensions including altitude.

How it works

Enter both points' x, y, and z coordinates. The calculator finds the difference along each axis, squares each difference, adds the three squared differences together, and takes the square root: d=√((x2-x1)²+(y2-y1)²+(z2-z1)²). This is the same Euclidean distance formula from 2D, just with one more squared term added for the z-axis.

Enter point 1 — x1.
Enter point 1 — y1.
Enter point 1 — z1.
Enter point 2 — x2.
Enter point 2 — y2.
Enter point 2 — z2.
Click Calculate to see your results.

Examples

(1,2,3) to (4,6,3)

d=√((4-1)²+(6-2)²+(3-3)²)=√(9+16+0)=√25=5.

(0,0,0) to (2,3,6)

d=√(2²+3²+6²)=√(4+9+36)=√49=7.

Common mistakes to avoid

Forgetting the z-term entirely and computing only the 2D distance.
Forgetting to square the differences before summing them (adding raw differences instead).
Mixing up coordinates between the two points (e.g., pairing point 1's x with point 2's y).
Forgetting to take the final square root and reporting the sum of squares as the distance.

Frequently asked questions

Yes — a shared coordinate just contributes 0 to that term, effectively reducing the calculation to the 2D distance formula in the other two dimensions.

Applying the theorem once gives the diagonal distance across the x-y plane; applying it a second time, treating that diagonal and the z-difference as the two legs of a new right triangle, gives the full 3D distance.

No — adding a nonzero z-difference can only ever increase (or leave unchanged) the total distance, since it adds a non-negative term under the square root.

No — since each difference is squared, swapping which point is "first" and which is "second" gives exactly the same distance either way.

Game engines and physics simulations call this formula constantly — checking collision ranges, computing how far a projectile has traveled, or determining whether two objects in a 3D scene are close enough to interact all boil down to this same distance calculation.

Yes — the same pattern of summing squared differences across every axis and taking the square root generalizes to any number of dimensions, which is exactly how distance is computed in higher-dimensional data science applications.

The formula here gives the straight-line ("as the crow flies") distance through empty space; if movement is constrained to a surface or a specific path, the actual travel distance would instead require path-length or geodesic calculations, which are different (and generally harder) problems.