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Distance Formula (3D)

d=Δx2+Δy2+Δz2d = \sqrt{\Delta x^2 + \Delta y^2 + \Delta z^2}

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

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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 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 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
  • Δx\Delta x= x-separation
  • Δy\Delta y= y-separation
  • Δz\Delta z= z-separation
Missing one of these? Work it out first, then come back