Mathematical Calculators

Fibonacci Calculator

This Fibonacci calculator can be used to calculate the terms arbitrarily of the Fibonacci sequence.

Fibonacci Calculator

Table of contents

What is the Fibonacci sequence and how does it work?
Formula for the n-th term
The Golden Ratio

What is the Fibonacci sequence and how does it work?

Fibonacci sequence refers to a series of numbers that follows a specific rule: Each term in the sequence must equal the sum of the two preceding terms. Each term can be expressed using this equation:
բₙ ₌ բₙ₋₂ ₊ բₙ₋₁
Fibonacci sequences typically have F0 = 0, F1 = 1, and F2 = 1. You can also choose F1 = 1, or F2 = 1 to start the sequence. You will need at least two terms consecutively to solve the arithmetic series.
Negative terms can also be covered by the Fibonacci sequence rule. For example, F-1 can be found to be equal to 1.
The Fibonacci sequence's first 15 terms are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377...
Fibonacci numbers are interestingly consistent with the well-known Benford’s law.

Formula for the n-th term

The good news is that you don't need to calculate all the preceding terms in order to calculate the next term of a sequence. You can find an arbitrary term in a sequence with a simple formula:
բₙ ₌ ₍φⁿ ₋ ψⁿ₎ / √₅
բₙ: the n-th term of the sequence
φ: golden ration equal to (1 + √5)/2, or 1.618...)
The Fibonacci Sequence is a sequence of numbers.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
You can find the next number by adding up both numbers before it.
Add the two numbers immediately before the 2 to get the 2 (+1).
Add the two numbers immediately before the number (3+2) to get the 3,
The 5 is (2+3)
You can go on and on!
Here's a more extensive list:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ...
n = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...
xn = 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 ...

The Golden Ratio

The gold ratio " is a unique mathematical relationship. Two numbers can be considered to be in the "golden ratio" if the proportion of both the numbers (a+b), and the larger number (a), is equal to that of the larger number and the smaller number (a/b). The golden ratio can be represented by the Greek letter "phi", φ.
The Fibonacci Number best describes the golden ratio. Fibonacci number are a never ending sequence that begins with 1 and goes on to add the next two numbers. The next numbers in Fibonacci's sequence are, for example, 1,2,3, and 5.

Parmis Kazemi
Article author
Parmis Kazemi
Parmis is a content creator who has a passion for writing and creating new things. She is also highly interested in tech and enjoys learning new things.

Fibonacci Calculator English
Published: Tue Mar 08 2022
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