Golden Ratio Calculator
Divide any length into golden proportions or scale a segment by φ to find its larger and smaller golden parts.
Mode
The larger golden section
- 1
Golden ratio φ = (1 + √5) ÷ 2
1.618φ is the unique ratio where the whole is to the larger part as the larger part is to the smaller. - 2
Longer part = total ÷ φ
100 ÷ 1.618 = 61.8034
How does this calculator work?
The golden ratio is φ = (1 + √5) / 2 ≈ 1.618. To split a total length, the longer part is total ÷ φ and the shorter part is what remains. To scale a known segment, multiply by φ for the larger part and divide by φ for the smaller. The longer-to-shorter ratio always equals φ.
Formula
How this is calculated
The golden ratio φ equals (1 + √5) / 2 ≈ 1.6180339887. Two quantities are in the golden ratio when the ratio of the larger to the smaller equals the ratio of their sum to the larger. This calculator works in two modes selected by the Mode field, and the length can be in any consistent unit (the result carries the same unit).
In "Total length to split" mode you give a total length T, and the calculator finds the longer part as T / φ and the shorter part as T − longer (equivalently T / φ²). The two parts sum back to the original total, and their ratio equals φ. In "Known segment to scale" mode you give one segment length a and the calculator returns the larger golden part a · φ and the smaller golden part a / φ, treating your input as the middle term of a golden progression.
The input must be a positive number; zero or negative lengths are rejected and return no result. Because φ is irrational, displayed values are rounded to four decimal places while the underlying computation uses full precision. The ratio of longer to shorter always approximates φ ≈ 1.618 regardless of the chosen mode or unit.
Frequently asked questions
It is the irrational number φ = (1 + √5) / 2 ≈ 1.618, the proportion where the whole is to the larger part as the larger part is to the smaller.
Total mode splits a single length into longer and shorter golden parts that sum to your input. Segment mode treats your input as one part and scales it up by φ and down by 1/φ.
No. The golden ratio is dimensionless, so the parts come out in whatever unit you entered, whether centimeters, pixels, or inches.
Also known as
TG we-Calculate Editorial Team. (2026). Golden Ratio Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/golden-ratio-calculator
TG we-Calculate Editorial Team. "Golden Ratio Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/golden-ratio-calculator.
TG we-Calculate Editorial Team, "Golden Ratio Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/golden-ratio-calculator
@misc{wecalculate_golden_ratio_calculator, title = {Golden Ratio Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/golden-ratio-calculator}}, year = {2026}, note = {TG we-Calculate} }
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