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3D Box Diagonal Calculator

Result

Space Diagonal14.14 cm
Face Diagonal (L×W)12.81 cm
Face Diagonal (L×H)11.66 cm
Face Diagonal (W×H)10 cm
↗ Math

3D Box Diagonal Calculator This 3D box diagonal calculator finds the space diagonal of a rectangular box (cuboid) from its length, width, and height, along with the three face diagonals. The space diagonal is the longest straight line that fits inside the — free online calculator.

Formula

Space: √(l²+w²+h²); Face LW: √(l²+w²); Face LH: √(l²+h²); Face WH: √(w²+h²)
  • 3D Box Diagonal Calculator calculates its result from Space, Height, Length, Width, Face Lw, Face Lh, Face Wh. It uses the formula Space: √(l²+w²+h²); Face LW: √(l²+w²); Face LH: √(l²+h²); Face WH: √(w²+h²). Change any input to recalculate the result instantly.
  • The main inputs are Length, Width, Height. Enter them in the units and format shown in the calculator.
  • Keep comparable quantities in compatible units whenever the formula combines or compares them.
  • Changing any input above recalculates the result with the same calculation engine used by this page.

Example: 3D Box Diagonal

Inputs
  • Length: 10
  • Width: 8
  • Height: 6

Using Space = 2, Height = 3, Length = 4, Width = 5, Face Lw = 6, Face Lh = 7, Face Wh = 8, the calculated result is 1.3719886811.

Sample result: Calculating…

Frequently asked questions

What does the 3D Box Diagonal calculate?

3D Box Diagonal Calculator This 3D box diagonal calculator finds the space diagonal of a rectangular box (cuboid) from its length, width, and height, along with the three face diagonals. The space diagonal is the longest straight line that fits inside the — free online calculator.

Which values should I enter?

Enter Length, Width, Height using the units and format shown beside each field.

What formula does this calculator use?

The calculator uses the following relationship: Space: √(l²+w²+h²); Face LW: √(l²+w²); Face LH: √(l²+h²); Face WH: √(w²+h²).

Why might my result differ from another source?

Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.

Does the result update automatically?

Yes. Changing an input updates the result using the same calculation engine shown on this page.

Page information

Updated: October 10, 2026