How do I divide a length by the golden ratio?

For a whole length T, the long segment is T / φ and the short segment is T / φ², where φ = (1 + √5) / 2. A whole of 100 gives approximately 61.803398875 and 38.196601125.

Can I start with the long or short segment?

Yes. Select the known segment and enter its length. Starting with long a gives whole a × φ and short a / φ. Starting with short b gives long b × φ and whole b × φ². Changing the selector reinterprets the entered number.

Is this a true golden spiral?

The drawing uses connected quarter-circle arcs inside successively smaller squares. This is a geometric construction approximation, not a true logarithmic spiral. You can hide the arcs to inspect rectangle subdivision alone.

Does rounding change the rectangle geometry?

No. Decimal places control displayed and exported dimension labels only. Geometry uses unrounded floating-point values. Small positive dimensions may display as zero at low precision; increase decimal places to show them.

What is included in the SVG export?

The SVG includes a golden-section bar, a rectangle with sides equal to the long and short segments, 1–16 nested squares, and optional construction arcs. Both views use separate visual scales. Output width can be 320–4,096 pixels; the graphic remains scalable.

Do units convert or imply design quality?

Units are editable labels and do not convert values. The tool illustrates proportions only and makes no claims about attractiveness, anatomy or design quality. Inputs stay in your browser and are not saved automatically.

Golden Ratio Design Tool

Start with one known length to calculate the golden section, inspect exact phi expressions, and export a labeled rectangle construction as SVG.

Start with one known length

Known segmentKnown lengthUnit labelDecimal placesNested squaresSVG width (pixels)

Show quarter-circle construction arcs

Changing the known segment reinterprets the entered number. The unit is a label, not a conversion. Choose 1–16 nested squares and an export width of 320–4,096 pixels. Decimal places affect labels only; geometry uses unrounded values.

Whole T100.000mm
Exact expression: 100

Long segment a61.803mm
Exact expression: 100 / φ

Short segment b38.197mm
Exact expression: 100 / φ²

Golden section and rectangle

T = a + b · T / a = a / b = φ
φ = (1 + √5) / 2 ≈ 1.618033988749895

Golden section: whole 100.000, long 61.803, short 38.197 mm. Rectangle with 8 nested squares and quarter-circle construction arcs.

The top bar divides T into a and b. The rectangle below has sides a and b; these two views use separate scales. Squares are removed from the left, bottom, right and top in turn. Each square is smaller than the previous one by a factor of φ. Quarter-circle arcs approximate a spiral construction; they are not a true logarithmic spiral.

SVG export: 1200 × 1020 pixels with scalable vector geometry. All dimension labels use 3 decimal places.

Construction dimensions

Square	Exact side expression	Rounded side (mm)
1	b / φ^0	38.197
2	b / φ^1	23.607
3	b / φ^2	14.590
4	b / φ^3	9.017
5	b / φ^4	5.573
6	b / φ^5	3.444
7	b / φ^6	2.129
8	b / φ^7	1.316

Here b is the short segment from the results above. Exact expressions describe the mathematical values; numeric dimensions are floating-point approximations rounded for display.

Calculation summary

Golden ratio φ = (1 + √5) / 2 ≈ 1.618033988749895
Whole T: 100.000 mm = 100
Long a: 61.803 mm = 100 / φ
Short b: 38.197 mm = 100 / φ²
T = a + b; T/a = a/b = φ
Square 1: side 38.197 mm (b / φ^0)
Square 2: side 23.607 mm (b / φ^1)
Square 3: side 14.590 mm (b / φ^2)
Square 4: side 9.017 mm (b / φ^3)
Square 5: side 5.573 mm (b / φ^4)
Square 6: side 3.444 mm (b / φ^5)
Square 7: side 2.129 mm (b / φ^6)
Square 8: side 1.316 mm (b / φ^7)
Labels are rounded; construction geometry uses unrounded values.
Quarter-circle construction arcs are not a true logarithmic spiral.

Golden-section geometry using floating-point approximations to φ. Rounded labels do not change construction geometry. Quarter-circle construction arcs are not a true logarithmic spiral; no attractiveness, anatomy or design-quality claim. Inputs stay in your browser and are not automatically saved.

Common questions

How do I divide a length by the golden ratio?: For a whole length T, the long segment is T / φ and the short segment is T / φ², where φ = (1 + √5) / 2. A whole of 100 gives approximately 61.803398875 and 38.196601125.
Can I start with the long or short segment?: Yes. Select the known segment and enter its length. Starting with long a gives whole a × φ and short a / φ. Starting with short b gives long b × φ and whole b × φ². Changing the selector reinterprets the entered number.
Is this a true golden spiral?: The drawing uses connected quarter-circle arcs inside successively smaller squares. This is a geometric construction approximation, not a true logarithmic spiral. You can hide the arcs to inspect rectangle subdivision alone.
Does rounding change the rectangle geometry?: No. Decimal places control displayed and exported dimension labels only. Geometry uses unrounded floating-point values. Small positive dimensions may display as zero at low precision; increase decimal places to show them.
What is included in the SVG export?: The SVG includes a golden-section bar, a rectangle with sides equal to the long and short segments, 1–16 nested squares, and optional construction arcs. Both views use separate visual scales. Output width can be 320–4,096 pixels; the graphic remains scalable.
Do units convert or imply design quality?: Units are editable labels and do not convert values. The tool illustrates proportions only and makes no claims about attractiveness, anatomy or design quality. Inputs stay in your browser and are not saved automatically.