# Golden Ratio Calculator

URL: https://speedycalculator.com/calculators/math/golden-ratio/
Last updated: 2026-10-25

> The golden ratio calculator splits a length into two parts in the golden ratio (about 1.618 : 1), or extends a length by the golden ratio. Designers use it for layouts, logos and proportions.

## Inputs

- Total length

## Results

- Longer part
- Shorter part
- Golden extension of total

## Formula

```
φ = (1 + √5) ÷ 2 ≈ 1.6180339887
```

## Explanation

Two lengths are in the golden ratio when the whole relates to the larger part as the larger part relates to the smaller.

### How to use the Golden Ratio Calculator

- **Total length**
- Want to work backwards? Type a value into **Longer part** and **Total length** is calculated for you.

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Divide the total by φ for the longer part; the remainder is the shorter part.

### What each result means

- **Longer part** = [Total length] ÷ ((1 + sqrt(5))÷2)
- **Shorter part** = [Total length] - [Longer part]
- **Golden extension of total** = [Total length] × (1 + sqrt(5))÷2

### Example values

How the main result changes when **Total length** changes and everything else stays at the example values above:

Total lengthLonger part5030.90177546.352510061.803412577.254215092.7051200123.6068

## Worked example

Inputs — Total length: 100.

Results — **Longer part = 61.803399**; Shorter part = 38.196601; Golden extension of total = 161.803399.

## FAQ

**Is the golden ratio really everywhere in nature?**
It appears in some patterns, but many claims are exaggerated.

**How is it linked to Fibonacci?**
Ratios of consecutive Fibonacci numbers approach φ.

**What formula does the Golden Ratio Calculator use?**
φ = (1 + √5) ÷ 2 ≈ 1.6180339887.

**Can I work backwards from the result?**
Yes. Type the result you want into Longer part and the calculator finds the matching total length.