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.
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.
القوانين والمعادلات المستخدمة
تستخدم Golden Ratio Calculator هذه 5 معادلات أساسية:
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.
كيفية استخدام هذه الحاسبة
لاستخدام حاسبة النسب هذه، اتبع 3 خطوات بسيطة:
أدخل القيم
اكتب قيم النسبة المعروفة في حقول الإدخال. اترك حقلاً واحداً فارغاً — هذا هو المتغير المجهول الذي تحله حاسبة النسب.
اختر الوضع
حدد وضع النسبة — حل، تبسيط، أو تغيير الحجم. يطبق كل وضع معادلات مختلفة على قيم الإدخال الخاصة بك.
احصل على النتائج
انقر فوق احسب. تعرض شاشة النتائج الإجابة مع شريط نسبة مرئي، ومخطط دائري، وتفصيل حل خطوة بخطوة.
أمثلة على مسائل وحلول خطوة بخطوة
فيما يلي 3 مسائل توضيحية مع حلول مفصلة خطوة بخطوة باستخدام حاسبة النسب هذه:
المدخلات 1 Find the golden rectangle from a 500px side
المدخلات 2 Divide a 1000px canvas using the golden ratio
المدخلات 3 Find golden ratio in Fibonacci: F(10)/F(9)
الأسئلة الشائعة
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.