The golden ratio φ is about 1.618.
About this calculator
The golden ratio φ is about 1.618. Divide a line so the longer part is to the shorter as the whole is to the longer — that ratio is φ. It shows up in pentagons, Fibonacci limits, and design grids.
This calculator multiplies or divides any number by φ, raises φ to an integer power, or checks whether two segment lengths approximate a golden cut.
Designers and students use φ for layout proportions. For Fibonacci-style sequences try the [[number-sequence]] calculator. For square roots underlying φ see the [[root]] calculator. For general powers use the [[exponent]] calculator.
Common uses
- Scale a layout dimension by φ for design grids
- Verify whether two lengths form a golden section
- Compute φⁿ for Fibonacci limit exercises
- Convert between complementary golden segments
Frequently asked questions
What is the golden ratio numerically?
φ = (1 + √5) / 2 ≈ 1.6180339887. Its reciprocal 1/φ ≈ 0.618, and φ² = φ + 1.
How do you check a golden segment?
If parts a and b satisfy (a+b)/a ≈ a/b ≈ φ, the cut is golden. Use segment mode with your two lengths.
Is the golden ratio the same as Fibonacci?
Related but not identical. The ratio of consecutive Fibonacci numbers approaches φ as n grows — see the number sequence calculator.
Why multiply by φ in design?
Scaling by φ or 1/φ produces visually balanced rectangles and spacing without arbitrary guesswork.