Golden Ratio Calculator

The Golden Ratio Calculator computes Long segment (b = aφ) from 1 input: short segment (a). Compute the golden ratio from any value.

Mathematics shows up in every corner of daily life — budgeting, cooking, construction, engineering, even reading a bus schedule. A calculator like this lets you skip the scratch-paper step and move straight to the answer, without the arithmetic mistakes that creep in when the numbers get messy. The Golden Ratio Calculator sits in that toolkit — it compute the golden ratio from any value. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

Where

a

Short segment (a)

Long segment (b = aφ)

Output value

Total (a+b)

Output value

1. 01Start by noting the input — Short segment (a): 1.
2. 02Substitute these values into the formula: Long segment (b = aφ) = e.a × (1+√(5)) / 2 | Total (a+b) = t+t × (1+√(5)) / 2
3. 03Compute Long segment (b = aφ): the calculator returns 1.61803.
4. 04Compute Total (a+b): the calculator returns 2.61803.
5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.