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.
Формулы и Используемые Уравнения
В калькуляторе заложены 5 основных уравнений:
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 Пользоваться Калькулятором
Чтобы использовать этот Калькулятор Отношений, выполните 3 простых шага:
Введите Данные
Введите известные числа в поля ввода. Оставьте одно поле пустым — калькулятор вычислит это неизвестное значение.
Выберите Режим
Выберите режим работы — Решение пропорций, Упрощение отношений или Масштабирование. В каждом режиме используются свои математические формулы.
Получите Результат
Нажмите кнопку Вычислить. На экране отобразится ответ с цветной шкалой отношения, круговой диаграммой и пошаговым решением.
Примеры Задач с Пошаговыми Решениями
Вот 3 практических примера расчетов с подробным математическим описанием действий:
Ввод 1 Find the golden rectangle from a 500px side
Ввод 2 Divide a 1000px canvas using the golden ratio
Ввод 3 Find golden ratio in Fibonacci: F(10)/F(9)
Часто Задаваемые Вопросы
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.