Golden Ratio Calculator

0.618 split, golden rectangle, Fibonacci

Quick Answer

Golden Ratio Calculator: 0.618 split, golden rectangle, Fibonacci. Golden Ratio Calculator uses standard geometry formulas to compute accurate results instantly.

Total length

Split 100 into golden ratio

61.803 / 38.197

Long part / short part

61.8

38.2

61.8% / 38.2%

Long part61.8034

Short part38.1966

Calculation steps

1Golden ratio φ = (1+√5)/2 = 1.6180339887…
2Long part = L ÷ φ = 100 ÷ 1.618034 = 61.8034
3Short part = L ÷ φ² = 100 ÷ 2.618034 = 38.1966
4Check: long ÷ short = 1.618034 = φ; (long+short) ÷ long = 1.618034 = φ

φ appears in the pentagon diagonal, nautilus growth spirals, galaxy arms and sunflower seed patterns — though many "golden ratio in nature/art" claims are retrofitting. Practical uses: the 0.618 optimization method (优选法) for searching unknown optima, pleasing aspect ratios in design/layout, and Fibonacci retracement levels (38.2%/61.8%) in trading.

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How to Use

Enter known values: fill sides, radius or angles in the Golden Ratio Calculator.
Auto-solve the rest: all unknowns are solved instantly — no manual derivation.
See formula and steps: the result panel shows the formula used and the substitution.
Try another case: change any known value to solve again.

Key Points

Golden Ratio Calculator is a free online geometry tool — open and use, no sign-up.
All calculations run locally in your browser; your data never leaves the device.
Key capability: 0.618 split, golden rectangle, Fibonacci.
Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Golden Ratio Calculator formula

Golden Ratio Calculator uses standard geometry formulas to compute accurate results instantly.

FAQ

How do I use the Golden Ratio Calculator?

Open the page and fill in the input fields — results update automatically. 0.618 split, golden rectangle, Fibonacci.

Are the results accurate?

Yes. Standard formulas and conversion factors are used and verified.

Is it free? Do I need to sign up?

Completely free. No registration, login or download required.

Does it work on mobile?

Yes. The responsive design works on phones, tablets and desktops.

Is my data saved?

No. Everything runs locally in your browser.

Related Guides

Source & Updates

Based on standard Euclidean geometry formulas. Last updated: 2025-07

Last updated: 2026-08-07

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Cite this page: YiJianSuan. Golden Ratio Calculator[EB/OL]. https://www.yijiansuan.com/en/c/geometry/golden-ratio

Results provided by this tool are for reference only and do not constitute professional advice.