Golden Ratio Calculator
Split a length in the golden ratio, or find the whole from either part (φ = 1.6180339887…).
Change the values and press Calculate to work out your own figures.
Enter one of the longer segment, the shorter segment or the whole.
Show the working
- (a + b) ÷ a = a ÷ b = φ = (1 + √5) ÷ 2
How to use it
Enter one of the longer segment, the shorter segment or the whole.
Number boxes accept whole numbers, decimals, fractions (3/4), powers (2^10), roots (sqrt(2)) and the constants pi and e. Show the working lists the steps.
Key facts
(a + b) ÷ a = a ÷ b = φ = (1 + √5) ÷ 2
φ
φ = 1.61803398874989…, and φ² = φ + 1.
Questions
If the short side is 1, what is the long side?
1.61803398875.
Formulas
(a + b) ÷ a = a ÷ b = φ = (1 + √5) ÷ 2
Sources
Limitations
- Expressions up to 500 characters; matrices up to 10 × 10.
- Big-number results up to 100,000 digits; factorials up to 10,000!.
- Numbers in words up to 10^102 (short scale).