Golden Ratio Calculator
The Golden Ratio Calculator computes proportions based on phi (φ ≈ 1.6180339887). Enter any value to find its golden ratio counterpart — multiply or divide by φ to create aesthetically pleasing proportions used in art, architecture, logo design, and typography.
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What is the Golden Ratio?
The Golden Ratio (φ, phi) equals approximately 1.6180339887. Two quantities are in the golden ratio if their ratio equals the ratio of their sum to the larger quantity: (A + B) / A = A / B = φ. This irrational number appears throughout nature, mathematics, and art.
The golden ratio connects to the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21...) where consecutive terms approach φ as the sequence grows. Architects, artists, and designers use φ to create compositions that feel naturally balanced — from the Parthenon to modern logos.
Kullanılan Formüller & Denklemler
Bu Golden Ratio Calculator aracı 5 temel denklem kullanır:
1 Golden Ratio Value ▼
Phi is derived from the quadratic equation x² - x - 1 = 0. The positive solution is the golden ratio.
2 Golden Section (Longer Side) ▼
Given the shorter side is 100, the longer side = 100 × 1.618 = 161.80. Together they form a golden rectangle.
3 Golden Section (Shorter Side) ▼
Given the longer side is 200, the shorter side = 200 / 1.618 = 123.61.
Bu Hesaplayıcı Nasıl Kullanılır?
Bu Oran Hesaplayıcıyı kullanmak için 3 adımı takip edin:
Değerleri Girin
Bilinen oran değerlerini giriş alanlarına yazın. Bir alanı boş bırakın — Oran Hesaplayıcının çözdüğü bilinmeyen değer budur.
Mod Seçin
Oran modunu seçin — Çöz, Basitleştir veya Ölçeklendir. Her mod, giriş değerlerinize farklı denklemler uygular.
Sonuçları Alın
Hesapla'ya tıklayın. Sonuç ekranı, cevabı görsel bir oran çubuğu, pasta grafiği ve adım adım çözüm dökümü ile görüntüler.
Örnek Problemler & Adım Adım Çözümler
İşte bu Oran Hesaplayıcıyı kullanan adım adım çözümlü 3 örnek problem:
Giriş 1 Find the golden rectangle from a 500px side
Giriş 2 Divide a 1000px canvas using the golden ratio
Giriş 3 Find golden ratio in Fibonacci: F(10)/F(9)
Sıkça Sorulan Sorular
What is phi (φ) in mathematics? ▼
Phi (φ) is the golden ratio, approximately 1.6180339887. It is an irrational number defined as (1 + √5) / 2. It has the unique property that φ² = φ + 1 and 1/φ = φ - 1.
How is the golden ratio used in design? ▼
Designers use φ to set proportions for layouts, typography scales, spacing, and composition. A common technique is the golden spiral, where rectangles are subdivided in golden proportions to guide visual flow.
Is the golden ratio found in nature? ▼
Yes. Spiral patterns in sunflower seeds, nautilus shells, hurricanes, and galaxies approximate the golden ratio. Leaf arrangement (phyllotaxis) often follows Fibonacci numbers, which converge to φ.
What is a golden rectangle? ▼
A golden rectangle has sides in the ratio 1 : φ (1 : 1.618). When you remove a square from a golden rectangle, the remaining rectangle is also a golden rectangle — this property continues infinitely.
How does the Fibonacci sequence relate to the golden ratio? ▼
Each consecutive Fibonacci ratio (F(n+1)/F(n)) gets closer to φ. 2/1=2, 3/2=1.5, 5/3=1.667, 8/5=1.6, 13/8=1.625, 21/13=1.615... The limit is exactly φ.