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Golden Section Lengths and Whole Segment

Yes. The longer-to-shorter ratio equals the whole-to-longer ratio, both φ. The whole is also the sum of the two positive sections. Any one length determines the others.

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: Shorter section (b) 1 gives Longer section (a) 1.618034, Whole (a + b) 2.618034.

φ = (1+√5)/2; a = φb; a+b = φa

Worked example

Enter these known values and leave the other values blank.

Shorter section (b): 1 m

Longer section (a): 1.618 m
Whole (a + b): 2.618 m

Assumptions and limitations

The line segment is split into positive longer section a and shorter section b so that a/b = (a+b)/a = φ. The whole is their sum. Any one known length determines the other two.
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

Is the whole segment the longer section times φ?