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Golden Rectangle Width, Extension and Full Area

The full rectangle has width a and length a+b. Segment b is the extension beyond an a-by-a square. The area is a(a+b), equal to a²φ, rather than the area ab of the smaller remainder.

Formula & worked example
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How to use this calculator

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

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Formula and method

Example in initial displayed units: Full rectangle width a 2 gives Extension segment b 1.236068, Full rectangle length a+b 3.236068, Full rectangle area 6.472136.

a/b = φ; full length = a+b = φa; full area = a(a+b)

Worked example

Enter these known values and leave the other values blank.

Full rectangle width a: 2 cm

Extension segment b: 1.236068 cm
Full rectangle length a+b: 3.23607 cm
Full rectangle area: 6.47214 cm²

Assumptions and limitations

The full rectangle has width a and length a+b. Segment b is the extension beyond the a-by-a square, not the full rectangle’s short side. Area is for the full a-by-(a+b) rectangle. The a-by-b remainder is a smaller similar rectangle with a different area.
Use compatible units and enough independent values. Clear unknowns before solving backward. Original reference drawings are schematic and do not scale to entered values.

Common questions

Which rectangle does the reported area describe?