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Rectangle Width from Linked Length, Area or Boundary

Direct length/width entries can use either orientation. When only area and perimeter are supplied, the captured quadratic inverse chooses the larger side as length and the smaller side as width.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Example in initial displayed units: Length (h) 4, Width (w) 3 gives Diagonal (d) 5, Area (A) 12, Perimeter (P) 14.

A = l(P/2−l); P = 2(l+w); d² = l²+w²

Worked example

Enter these known values and leave the other values blank.

Length (h)
4 m
Width (w)
3 m
Diagonal (d)
5 m
Perimeter (P)
14 m
Area (A)
12 m²

Assumptions and limitations

  • Both sides are positive. Two independent supported measures are needed. Length need not be greater than width when directly supplied, but an area/perimeter inverse selects the larger length root, leaving the smaller width. A real area/perimeter pair requires P² at least 16A. A supplied diagonal exceeds each positive side. Area/diagonal alone is not supported by this captured dependency workflow.
  • Clear unknowns before solving backward and select compatible units. Original reference drawings do not scale to entered values. Independently rounded boundary measurements can be incompatible at finite precision.

Common questions

Does this always treat length as the longer side?

Direct length/width entries can use either orientation. When only area and perimeter are supplied, the captured quadratic inverse chooses the larger side as length and the smaller side as width.

How many measurements are needed?

Use the worked example or a verified independent input pair or triple. Supplying dependent measurements does not add enough information; a consistent shape still needs a length scale.

Which input pairs support the retained inverse controls?

Use both sides; length with area, perimeter or diagonal; width with perimeter or diagonal; or area with perimeter. Area with width alone, area with diagonal alone, or perimeter with diagonal alone does not solve the missing sides in these captured equations.

References

Require positive physical rectangle measures and real inverse roots, with equality allowed for square rectangles. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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