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Geometry & Practical Projects

Diagonal Calculator

Calculate the diagonal of a square, rectangle or box, including the longest straight object that fits inside a box.

Your inputs

Results

Diagonal

5 m

Angle of the diagonal to the length
36.8699 °

✓Exact calculation — rounded only for display

What this calculator does

Will that pole fit in the box? Is the frame square? The diagonal answers both.

Formula and method

Square: s√2; Rectangle: √(l² + w²); Box: √(l² + w² + h²)

Worked example

Calculated by this tool with its default inputs:

Inputs

  • Length unit: Metres
  • Shape: Rectangle
  • Length (or side): 4
  • Width: 3
  • Height: 12

Results

  • Diagonal: 5 m
  • Angle of the diagonal to the length: 36.8699 °

How to read the results

Matching diagonals confirm a rectangle is square at the corners.

Assumptions and limitations

  • Use one length unit consistently; areas are in square units and volumes in cubic units of that length.

Quantities and costs are planning estimates. Add sensible allowances, and check with suppliers, carriers or professionals before buying, shipping or building.

Questions

How do builders check for square?

They measure both diagonals; equal diagonals mean right-angled corners.

Methodology and verification

Result type
Exact mathematical calculation (rounded only for display)
Formula version
1.0
Automated verification
4 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
Editorial review
Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.

Privacy

Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy