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.
Използвани Формули и Уравнения
Този калкулатор използва 5 основни уравнения:
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.
Как се Използва този Калкулатор
За да използвате този Калкулатор за Отношения, следвайте 3 лесни стъпки:
Въведете Данни
Въведете известните стойности на съотношението в полетата за въвеждане. Оставете едно поле празно — това е неизвестното, което калкулаторът ще реши.
Изберете Режим
Изберете режим на съотношение — Реши, Опрости или Мащабирай. Всеки режим прилага различни уравнения към вашите входни стойности.
Получете Резултати
Кликнете върху Пресметни. Екранът с резултати показва отговора с цветна скала, кръгова диаграма и пошагово решение.
Примерни Задачи с Решения Стъпка по Стъпка
Ето 3 практически примера с подробно математическо обяснение на стъпките:
Вход 1 Find the golden rectangle from a 500px side
Вход 2 Divide a 1000px canvas using the golden ratio
Вход 3 Find golden ratio in Fibonacci: F(10)/F(9)
Често Задавани Въпроси
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.