Enter a number, select mode, then click Calculate.

The golden ratio (φ ≈ 1.61803398875) is an irrational number that appears in mathematics, art, architecture, and nature. Two quantities a and b are in the golden ratio if (a + b) / a = a / b = φ. It is the solution to the equation x² = x + 1. The golden ratio is closely related to the Fibonacci sequence, where the ratio of consecutive terms approaches φ. This calculator finds the proportional values for any number: given a smaller value, it finds the larger value (smaller × φ); given a larger value, it finds the smaller value (larger / φ). The golden rectangle, with sides in this ratio, is considered aesthetically pleasing and is widely used in design, photography, and architecture.

1. Enter a Number (positive value).
2. Select Find Larger (input is the smaller value) or Find Smaller (input is the larger value).
3. Click Calculate to compute the golden ratio proportions.
4. The result shows both values, their sum, difference, and the ratio.
5. Golden rectangle dimensions and Fibonacci sequence terms are also displayed.
6. Click Reset to restore default example values.