The Golden Ratio & Fibonacci Sizer determines proportional golden rectangle dimensions and calculates arbitrary terms of the Fibonacci sequence for web layout grids, typographic hierarchies, and visual framing.

### Mathematical Principles & Golden Proportions The golden ratio represents the geometric proportion where the ratio of the sum of two quantities to the larger quantity equals the ratio of the larger to the smaller: - **Golden Ratio Constant (Phi)**: $$\phi = \frac{1 + \sqrt{5}}{2} \approx 1.6180339887$$ - **Golden Height (Subdivision)**: $$\text{Golden Height} = \text{round}\left(\frac{\text{Base Dimension}}{\phi}\right)$$ - **Golden Width (Expansion)**: $$\text{Golden Expansion} = \text{round}(\text{Base Dimension} \times \phi)$$ - **Fibonacci Sequence Recurrence**: $$F_0 = 0, \quad F_1 = 1, \quad F_n = F_{n-1} + F_{n-2}$$

### Worked Calculation Example Applying the golden ratio to an initial container width of 960 pixels: - **Golden Subdivision Height**: $960 / 1.618034 \approx 593\text{ px}$ (forms a 960×593 px Golden Rectangle). - **Golden Expansion Scale**: $960 \times 1.618034 \approx 1{,}553\text{ px}$. - **12th Fibonacci Term**: The 12th sequence term $F_{12}$ evaluates to exactly $144$.

### In-Browser Processing & Privacy Calculations execute locally inside your web browser. No layout dimensions, design coordinates, or numerical inputs are transmitted across the network.