# Fibonacci Sequence Calculator

Written by:
PK

One this page is a Fibonacci number calculator and Fibonacci sequence calculator. Enter which Fibonacci number to find (starting from 0th = 0) and we'll return the number and optionally the entire series to that point.

## What is a Fibonacci Number or the Fibonacci Sequence?

The Fibonacci sequence is an increasing sequence of numbers in which a number in the series is calculated by adding the two previous numbers, starting with 0 and 1.

A Fibonacci number is either a number which appears in the Fibonacci sequence, or the index of a number in the series. For example, the 6th Fibonacci number is 8, and 8 is also a Fibonacci number as it appears in the sequence.

0 is considered the '0' index of the formula, followed by 1. Therefore, Fibonacci numbers 0 through 10 (11 numbers) are:

0,1,1,2,3,5,8,13,21,34,55

### Fibonacci Numbers and the Golden Ratio

The Fibonacci numbers converge to the Golden Ratio – a ratio which occurs when the ratio of two sizes is the same as the ratio of the sum of both sizes to the larger size.

It's expressed as the Greek letter Phi (φ) and the ratio is approximately equal to 1.61803.

\phi=\frac{a+b}{a}=\frac{a}{b}

As first observed by Johannes Kepler, as numbers get increasingly larger in the Fibonacci sequence consecutive numbers converge on the ratio. For example:

6th\ Fibonacci = 8\\7th\ Fibonacci = 13\\~\\13/8= 1.625\\~\\ 20th\ Fibonacci = 6765\\21st\ Fibonacci = 10946\\~\\10946/6765= 1.61803

## Using the Fibonacci Number and Fibonacci Sequence Calculator

To use the Fibonacci sequence calculator, first enter which Fibonacci Number (n) you are interested in, where 0 = 0 and 1 = 1.

Then, you can either hit Compute Fibonacci to see the number in the sequence at that position, or hit Show Fibonacci Sequence to see all numbers up that that index.

Next, you might want to see the closely related Lucas series calculator. Afterwards, try the other calculators and tools.

### PK

PK started DQYDJ in 2009 to research and discuss finance and investing and help answer financial questions. He's expanded DQYDJ to build visualizations, calculators, and interactive tools.

PK lives in New Hampshire with his wife, kids, and dog.

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