Find the straight-line distance between two points in 3D space
Result
3D Distance
Step-by-Step Derivation
3D Distance Formula
d = √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²)
The 3D distance formula extends the 2D distance formula by adding the z-coordinate change. The three coordinate differences form a space diagonal, and the square root gives its length.
⚠Enter real-number coordinates. Identical 3D points have distance 0.
How 3D Distance Works
Distance in 3D combines movement in x, y, and z directions into one straight-line length through space.
x Change
Difference between x coordinates.
y Change
Difference between y coordinates.
z Change
Depth or height difference.
Space Diagonal
The final distance is the 3D diagonal.
💡 Example: For (0,0,0) and (2,3,6), d=√(4+9+36)=7.
Applications of 3D Distance
3D GeometryPhysicsComputer GraphicsRobotics
Frequently Asked Questions
What is a 3D distance calculator?▼
It calculates straight-line distance between two points in three-dimensional space.
What is the 3D distance formula?▼
The formula is d=sqrt((x2-x1)^2+(y2-y1)^2+(z2-z1)^2).
How do I use this calculator?▼
Enter x, y, and z coordinates for two points and click Calculate.
Can 3D distance be negative?▼
No. Distance is a length, so it is always zero or positive.
Where is 3D distance used?▼
It is used in 3D geometry, physics, graphics, robotics, and engineering.
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