Golden Ratio Calculator

Worked example

Enter 100 as the smaller value (B), find the larger value (A):

• A = B × φ = 100 × 1.618033988749895 = 161.803
• Total (A + B) = 161.803 + 100 = 261.803
• Ratio A ÷ B = 161.803 / 100 = 1.618034 ≈ φ

The defining property of the golden ratio is that A/B equals (A+B)/A — check it here: 261.803 / 161.803 also comes out to 1.618034. That self-similar identity is why the golden rectangle can be split into a square plus a smaller rectangle with the same proportions as the original, which is what the tool's diagram draws.

Where φ actually comes from

φ = (1 + √5) / 2 = 1.6180339887498949... — an irrational number, so the calculator uses a fixed 15-digit approximation (1.618033988749895) rather than computing √5 fresh each time. For any practical input size this makes no visible difference.

Input rules

Only positive numbers are accepted; zero, negative values, or blank input return an error instead of a result. The radio buttons control which direction the multiplication goes — "find larger" multiplies your input by φ, "find smaller" divides it by φ — so entering 100 under each option gives a different pair: 161.8 & 100 versus 100 & 61.8.