Calculator
Choose a mode, enter values, and compute instantly.
Example data table
These examples show typical inputs and the expected golden outputs.
| Scenario | Input | Golden output | Check |
|---|---|---|---|
| Split total | Total = 100 | Larger ≈ 61.8034, Smaller ≈ 38.1966 | 61.8034 / 38.1966 ≈ 1.6180 |
| From larger section | Larger = 50 | Smaller ≈ 30.9017, Total ≈ 80.9017 | 50 / 30.9017 ≈ 1.6180 |
| From smaller section | Smaller = 25 | Larger ≈ 40.4508, Total ≈ 65.4508 | 40.4508 / 25 ≈ 1.6180 |
| Golden rectangle | Width = 160 (larger) | Height ≈ 98.8854 | 160 / 98.8854 ≈ 1.6180 |
| Compare pair | A = 34, B = 55 | Observed ratio ≈ 1.6176 | Error vs φ is very small |
Formula used
- Golden ratio: φ = (1 + √5) / 2 ≈ 1.6180339887…
- Split a total: if L = a + b and a / b = φ, then a = L / φ and b = L / φ².
- From larger: if larger is a, then smaller b = a / φ, and total L = a·φ.
- From smaller: if smaller is b, then larger a = φ·b, and total L = φ²·b.
- Rectangle: for a golden rectangle, width / height = φ.
How to use this calculator
- Pick a mode that matches your problem.
- Enter the required value(s) shown for that mode.
- Set decimal places and optional units.
- Click Calculate to view results above.
- Use Download CSV or Download PDF to save.
FAQs
1) What is the golden ratio?
It is a special proportion where the larger part divided by the smaller equals φ, about 1.6180339887. It appears in geometry, design, and many growth patterns.
2) How do I split a length using φ?
Use the “Split a total” mode. Enter the total L, then the calculator returns larger L/φ and smaller L/φ². Both parts add back to L.
3) Can this compare two numbers to φ?
Yes. The “Compare two numbers” mode computes max/min, then reports percent error versus φ. It also suggests ideal values if you want one number adjusted to match φ.
4) What does percent error mean here?
It measures how far your observed ratio is from φ. The formula is ((ratio − φ) / φ) × 100. Smaller absolute values mean closer alignment with the golden ratio.
5) How does the golden rectangle calculation work?
A golden rectangle satisfies width/height = φ. If you know the larger side, divide by φ to get the smaller side. If you know the smaller side, multiply by φ to get the larger.
6) Why does φ² appear in the split formulas?
Because φ has the identity φ + 1 = φ². When you solve a + b = L with a = φb, you get L = (φ + 1)b = φ²b, leading to b = L/φ².
7) Is Fibonacci really related to φ?
The ratio F(n+1)/F(n) approaches φ as n grows. The “Fibonacci approximation” mode shows that ratio for your chosen n and reports how close it is to φ.
8) Does rounding change the correctness?
Rounding only affects displayed numbers. Internally the calculations use floating-point values. If you need more precision, increase decimal places and export the result.