Golden Ratio Calculator
Golden split of any length with phi shown.
What it does
The golden ratio cuts a length so the whole relates to the longer part exactly as the longer relates to the shorter. Designers, woodworkers, and photographers use the split for layouts that read balanced without measuring twice.
The tool above takes any total length. It returns the longer and shorter golden parts with phi beside them, in inches or centimeters.
The default 100 splits into 61.8 with 38.2, summing back to 100. A 50 length splits 30.9 with 19.1 under the same proportion.
Phi matches OpenStax Contemporary Mathematics with OEIS confirming the expansion: (1 + root 5) / 2 at 1.6180339887, squared 2.6180339887, reciprocal 0.6180339887.
How to use
- Pick imperial (in) or metric (cm).
- Enter the total length.
- Read the longer part first.
- Read the shorter part.
- Check the two sum to total.
- Lay out longer first in designs.
Formula
- phi
- 1.618034, positive root of x^2 - x - 1 = 0.
- L
- Total length in either unit.
- phi^2
- 2.618034, phi plus one.
Display rounding can sum to 99.99 or 100.01 on odd lengths; the math underneath still balances. Fibonacci neighbor ratios approach phi but only reach it in the limit.
Worked example
Example: length 100
Defaults: imperial, total length 100 in.
- Phi: (1 + 2.2360679775) / 2 = 1.618034.
- Longer: 100 / 1.618034 = 61.8.
- Shorter: 100 / 2.618034 = 38.2.
- Check: 61.8 + 38.2 = 100.
- Tool shows 61.8 in, 38.2 in, 1.618034.
- Metric 100 cm splits the same digits.
Reference table
| Total | Longer | Shorter |
|---|---|---|
| 100 | 61.8 | 38.2 |
| 50 | 30.9 | 19.1 |
| 10 | 6.18 | 3.82 |
Limits
- Display rounding only at the end.
- Zero and negative lengths rejected.
- Proportion is exact; beauty is taste.
- Fibonacci ratios only approximate phi.
Common mistakes
- Using 0.618 where 1.618 belongs.
- Splitting before converting units.
- Rounding mid way then summing.
- Forcing golden on every layout.
- Reading shorter as the longer part.
Try it yourself
Quick checks. Answers sit tucked under each question.
Length 50 splits how?
30.9 with 19.1.
Length 10 splits how?
6.18 with 3.82.
Check rule?
Whole over longer equals longer over shorter.
Questions
What is the golden ratio?
(1 + root 5)/2, about 1.618034.
How to split a length golden?
Divide by 1.618 for longer, by 2.618 for shorter.
Fibonacci link?
Neighbor ratios converge to phi as terms grow.
Phi squared?
2.618034, exactly phi plus one.
Reciprocal?
0.618034, exactly phi minus one.
Where is it used?
Art, architecture, logos, photo crops, and nature spirals.