Golden Ratio (Phi) Calculator
Find golden rectangle dimensions, split any length into the golden section, or check how close two numbers are to Phi (φ ≈ 1.618) — instantly and for free.
Phi Ratio Calculator
Calculate golden ratio dimensions and splits
Phi (φ) ≈ 1.6180339887 — choose the type of golden ratio calculation you need
In a golden rectangle, the longer side ÷ the shorter side = φ
The other side will be calculated to complete a golden rectangle
Controls how many decimal places your results are rounded to
Ratio Results
Your golden ratio calculation breakdown
Choose a calculation type, enter your values, then click Calculate to see your golden ratio breakdown.
What Is the Golden Ratio?
The golden ratio is a mathematical constant, approximately 1.6180339887, written using the Greek letter Phi (φ). Two lengths are said to be in the golden ratio when dividing the longer one by the shorter one gives the same result as dividing their total by the longer one. Unlike a simple fraction such as 3:2, Phi is irrational — its decimal digits continue forever without ever settling into a repeating pattern.
Phi is calculated using the formula φ = (1 + √5) ÷ 2. It also emerges naturally from the Fibonacci sequence: dividing any number in the sequence by the one before it produces a value that gets closer and closer to Phi the further along the sequence you go (for example, 144 ÷ 89 ≈ 1.6180).
Where It’s UsedCommon Uses of the Golden Ratio
- Graphic & web design — sizing layout columns, logos, and typography so proportions feel naturally balanced.
- Photography & composition — placing focal points along golden ratio lines, a refinement of the rule of thirds.
- Architecture — proportioning façades, windows, and floor plans, a practice dating back to classical and Renaissance buildings.
- Art — composing canvases and sculptures around golden rectangles and golden spirals.
- Nature — describing spiral patterns such as sunflower seed heads, pinecones, nautilus shells, and hurricane formations.
Golden Ratio FAQ
What is the golden ratio?
The golden ratio is an irrational mathematical constant, approximately 1.6180339887 and represented by the Greek letter Phi (φ). Two quantities are in the golden ratio when the ratio between the larger and smaller quantity equals the ratio between their sum and the larger quantity.
How do you calculate the golden ratio?
Phi is calculated algebraically as one plus the square root of five, divided by two, which equals roughly 1.6180339887. It can also be approximated by dividing consecutive numbers in the Fibonacci sequence, with the result getting closer to Phi as the numbers get larger.
What is a golden rectangle?
A golden rectangle is a rectangle whose longer side divided by its shorter side equals Phi. If you remove the largest possible square from a golden rectangle, the leftover piece is itself a smaller golden rectangle, which is why the shape is closely linked to the golden spiral.
Where is the golden ratio used?
Designers, photographers, and architects often use the golden ratio to plan layouts, crop images, and proportion buildings because the resulting shapes are widely considered visually balanced. It also describes natural growth patterns, such as the spiral arrangement of seeds in a sunflower head.
Is the golden ratio the same as the Fibonacci sequence?
They’re closely related but not identical. The Fibonacci sequence is a list of whole numbers where each term is the sum of the two before it, and dividing consecutive Fibonacci numbers produces a ratio that gets progressively closer to the golden ratio without ever exactly reaching it.