Golden ratio calculator
Enter a length to split it by the golden ratio and get the sides of a golden rectangle on it — for facades, openings or furniture.
Larger segment
2.034 ft
- Larger segment of the length2.034 ft
- Smaller segment of the length1.247 ft
- Long side of golden rectangle (length × φ)5.315 ft
- Short side of golden rectangle (length ÷ φ)2.034 ft
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How it's calculated (visible formula)
φ = (1 + √5) ÷ 2 ≈ 1.618; larger = length ÷ φ; smaller = length − larger
- Net geometric measurement, no waste.
- Adjustable waste % for cuts and breakage.
- Purchase rounded up to sellable units (boxes, bags, buckets, boards).
How to calculate it, step by step
- Pick the dimension to proportion (facade width, opening, furniture).
- Enter it in the calculator.
- Get the larger segment (length ÷ φ) and the smaller.
- For a golden rectangle, use length × φ for the long side.
- Apply and round to material modules if needed.
Worked example: A 40 in length
- 40 ÷ 1.618 = 24.7 in
- 40 − 24.7 = 15.3 in
- Rectangle: 40 × 64.7 in
→ Segments of 24.7 and 15.3 in.
Common mistakes
- Rounding φ to 1.6 on large dimensions.
- Applying it regardless of function.
- Confusing the larger segment with the rectangle's long side.
Pro tips
- Combine it with real material modules (brick, sheet goods).
- Use it as a guide — function comes first.
- It works well for windows and shelving proportions.
- Fibonacci numbers (5, 8, 13, 21) approximate φ in whole units.
From calculation to quote
Add labour, overhead and your margin, and generate the professional PDF.
FAQs
- What is the golden ratio?
- φ ≈ 1.618, where the whole relates to the larger part as the larger to the smaller.
- How is it used in design?
- To proportion facades, windows, rooms or furniture.
- Rule of thirds?
- A simplification: 0.667 vs 0.618.
- What is φ?
- The golden ratio, (1 + √5) ÷ 2 ≈ 1.618.
- How does it relate to Fibonacci?
- Ratios of successive Fibonacci numbers approach φ.
- Is it used in modern architecture?
- Yes — Le Corbusier's Modulor is based on it.
Sources and standards
Maintained by Srikanta M · Formula v1.0.0 · Verified 2026-09-10 · Updated 2026-09-10 · Limits: quantity estimation, not structural design or site supervision.