Math & Stats

Golden Ratio Calculator

Calculate golden ratio proportions (φ = 1.618) for design, art and layout. Enter one length to find the golden-ratio partner and the whole.

Golden Ratio Calculator

Value

This value is the…

Method

How this calculator works

φ = (1 + √5) / 2 ≈ 1.618. Long side a and short side b satisfy a / b = φ and (a + b) / a = φ.

Examples

Worked examples

Real numbers, end-to-end results.

Whole length = 100

long ≈ 61.80, short ≈ 38.20

100 ÷ 1.618 = 61.80; 100 − 61.80 = 38.20.

Short side = 50

long ≈ 80.90, whole ≈ 130.90

50 × 1.618 = 80.90.

FAQ

Frequently asked questions

What is the golden ratio?

The golden ratio, φ (phi), is approximately 1.6180339887. Two quantities are in the golden ratio if the ratio of the larger to the smaller equals the ratio of their sum to the larger: a/b = (a+b)/a = φ.

How is the golden ratio calculated?

φ = (1 + √5) / 2 ≈ 1.618. To split a length into golden proportions, the longer part = whole ÷ φ and the shorter part = whole − longer.

Where is the golden ratio used?

It appears in art, architecture, logo and web design, photography (the golden spiral), typography scales, and even in nature such as sunflower seeds and shell spirals.

What is the difference between the golden ratio and the rule of thirds?

Both are composition guides. The rule of thirds divides a frame into equal thirds, while the golden ratio uses the 1:1.618 proportion, which many designers find more organic.

How do I use golden ratio in design?

Pick a base size (for example a body font of 16px or a container width) and multiply or divide by 1.618 to generate harmonious secondary sizes.