Each Fibonacci number is the sum of the two before it: 0, 1, 1, 2, 3, 5, 8, 13, …
How to use the Fibonacci Calculator
- Position (n)
Results update as you type, and every field accepts the units shown in its menu.
How it works
Binet’s formula gives Fₙ directly without listing all earlier terms.
What each result means
- Fₙ = round([Golden ratio]^[Position (n)] ÷ sqrt(5))
- Fₙ₋₁ = round([Golden ratio]^([Position (n)]-1) ÷ sqrt(5))
- Fₙ₊₁ = round([Golden ratio]^([Position (n)]+1) ÷ sqrt(5))
- Fₙ₊₁ ÷ Fₙ = [Fₙ₊₁] ÷ [Fₙ]
Formula
Fₙ = round(φⁿ ÷ √5), φ = (1 + √5) ÷ 2Worked example
Inputs — Position (n): 20.
Results — Fₙ = 6765; Fₙ₋₁ = 4181; Fₙ₊₁ = 10946; Fₙ₊₁ ÷ Fₙ = 1.6180339985.
Frequently asked questions
Why stop at n = 78?
Larger Fibonacci numbers exceed the precision of standard floating-point numbers.
Where does the golden ratio appear?
The ratio of consecutive Fibonacci numbers approaches 1.618…
What formula does the Fibonacci Calculator use?
Fₙ = round(φⁿ ÷ √5), φ = (1 + √5) ÷ 2.