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.
Rumus & Persamaan Yang Digunakan
Golden Ratio Calculator ini menggunakan 5 persamaan inti:
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.
Cara Menggunakan Kalkulator Ini
Untuk menggunakan Kalkulator Rasio ini, ikuti 3 langkah berikut:
Masukkan Nilai
Ketik nilai rasio yang diketahui ke dalam bidang input. Biarkan satu bidang kosong — itu adalah nilai tidak diketahui yang diselesaikan oleh Kalkulator Rasio.
Pilih Mode
Pilih mode rasio — Pecahkan, Sederhanakan, atau Skala. Setiap mode menerapkan persamaan yang berbeda ke nilai input Anda.
Dapatkan Hasil
Klik Hitung. Layar hasil menampilkan jawaban dengan batang rasio visual, diagram lingkaran, dan rincian solusi langkah-demi-langkah.
Contoh Masalah & Solusi Langkah-demi-Langkah
Berikut adalah 3 contoh masalah dengan solusi langkah-demi-langkah menggunakan Kalkulator Rasio ini:
Input 1 Find the golden rectangle from a 500px side
Input 2 Divide a 1000px canvas using the golden ratio
Input 3 Find golden ratio in Fibonacci: F(10)/F(9)
Pertanyaan yang Sering Diajukan
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.