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Distance Formula (3D)

d=Δx2+Δy2+Δz2d = \sqrt{\Delta x^2 + \Delta y^2 + \Delta z^2}
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Worked example: 3-4-12 m separations → d = 13 m. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Where Distance Formula (3D) fits

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Distance Formula (2D)

See also

Distance Formula (2D): Both use point to point distance.
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Distance Formula (3D) explained

ΔxΔzΔyd

The 3D distance formula is the Pythagorean theorem applied twice: the separations along the three axes form the edges of a box, and d is its space diagonal. A drone that flies 30 m east, 40 m north, and climbs 120 m is 302+402+1202=16900=130\sqrt{30^2 + 40^2 + 120^2} = \sqrt{16900} = 130 m from its launch point in a straight line.

Solving for one separation runs it backward: a 10 m brace anchored 6 m away horizontally and 0 m sideways must rise 102−62=8\sqrt{10^2 - 6^2} = 8 m. The rearrangements return the positive root, since a separation's sign only encodes direction.

Distance Formula (3D)

d=Δx2+Δy2+Δz2d = \sqrt{\Delta x^2 + \Delta y^2 + \Delta z^2}
Where
  • dd= Distance (m)
  • Δx\Delta x= x-separation (m)
  • Δy\Delta y= y-separation (m)
  • Δz\Delta z= z-separation (m)
Revised 16 October 2026
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formula.expert. (2026, October 16). Distance Formula (3D) Calculator. https://formula.expert/solvers/distance-formula-3d

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