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Golden Ratio Calculator — result sheet
Calculate the golden ratio and its complementary reciprocal relationships from a positive reference length.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: φ=(1+√5)/2; long segment=φ×reference; short complement=reference/φ; φ²=φ+1.
The golden ratio is the positive solution to φ²=φ+1. Scaling a reference length by φ gives the corresponding longer segment in a golden-section construction.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Reference length — length units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Reference length | 10 |
φ≈1.618034; long segment≈16.18034; reciprocal-scale segment≈6.18034.
Assumptions and limits
- The reference length is positive and both segments use the same unit.
- The calculator treats the reference as the shorter segment for its long-segment output.
- Aesthetic or design claims are not inferred from the ratio alone.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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