# Fibonacci Calculator

**Created By :** Abhinandan Kumar

**Reviewed By :** Rajashekhar Valipishetty

**Last Updated :** Mar 21, 2023

Fibonacci calculator is an online & handy tool for calculating the arbitrary terms of the Fibonacci sequence. Give your input number in the input field and tap on the calculate button to obtain solution with steps in the blink of an eye.

### What is Meant by Fibonacci Sequence?

In Maths, the list of numbers which maintains the specific pattern is called sequence. Fibonacci sequence is one of the types of sequences. The definition of fibonacci sequence is a set of numbers that proceed with the rule ie., each term is equal to sum of two preceding terms.

The resultant number is called fibonacci number and each number in series or sequence of fibonacci is represented as F_{n}. The other name of fibonacci sequence is recursive sequence. Also, it is a sequence of whole numbers organized as 0,1,1,2,3,5,8,13,...

### How to Find Fibonacci Sequence?

The simple steps that need to be followed to find the Fibonacci sequence when n is given is listed below:

- Firstly, know the given fibonacci numbers in the problem, if F
_{0}=0, F_{1}=1 then calculating the Fn is very easy. - Simply apply the formula of fibonacci number ie., F
_{n}= F_{n-1}+ F_{n-2} - If you want to find the F
_{n}by using given n term then make use of the Fibonacci sequence formula ie.,F_{n}= ( (1 + √5)^n - (1 - √5)^n ) / (2^n × √5) - By simplifying the equation, you will find the required term of the Fibonacci sequence.

Learn the complete fibonacci sequence concept from this fibonacci calculator and also understand the steps on how to find fibonacci series manually with steps from below solved example.

**Example: **

Find the fibonacci sequence number for F_{46}?

**Solution: **

By applying the formula of fibonacci sequence ie., F_{n} = ( (1 + √5)^n - (1 - √5)^n ) / (2^n × √5), we can easily calculate the exact result.

F_{46} = ( (1 + √5)^46 - (1 - √5)^46 ) / (2^46 × √5)

F_{46}=(1.61803...)^46−(−0.61803...)^46 / 2^46 X√5

F_{46} = 1836311903.

### Formula to Calculate Fibonacci Numbers

Numbers that follow a specific pattern is called fibonacci numbers. To calculate the fibonacci numbers in the sequence, we make use of the fibonacci formula. When the position is given, the relationship between the successive number and the two preceding numbers can be used in the formula to find any specific Fibonacci number in the series or sequence.

The formula to find the (n+1)th number in the sequence of fibonacci numbers is given as,

**F _{n} = F_{n-1} + F_{n-2}**

where, n>1

F_{n-1} is nth Fibonacci number

F_{n-2} is (n-1)th Fibonacci number

**Example:**

If the fibonacci sequence starts from F_{0}=0, F_{1}=1 then calculate F_{5}.

**Solution:**

Given numbers are F_{0}=0, F_{1}=1

To calculate the given nth term of the sequence, we use the fibonacci nuumber formula ie.,

F_{n} = F_{n-1} + F_{n-2}

F_{5} = F_{5-1} + F_{5-2}

F_{5} = F_{4} + F_{3}

F_{5} = 3+2

F_{5} = 5.

#### Fibonacci Sequence Formula

To calculate the single fibonacci number, we use the fibonacci sequence formula which is given as

**F _{n} = ( (1 + √5)^n - (1 - √5)^n ) / (2^n × √5)** for positive and negative integers n.

For only positive interger of n, a simplified equation or formula to find a fibonacci number is

**F _{n} = [( (1 + √5)^n ) / (2^n × √5)]**

The compact version of the formula to use is

**F _{n} = ( φ^n - ψ^n ) / √5**

where φ, the Greek letter phi, is the Golden Ratio φ = (1 + √5) / 2 ≈ 1.618034... and ψ, the Greek letter psi, is ψ = (1 - √5) / 2 ≈ -0.618034...

#### Negative Fibonacci Sequence Formulas

If you want to find the negative terms of fibonacci numbers in the sequence, you can easily use the above formulas and calculate F-n. But it can be more prominent to solve the negative terms by using the following formula or equation ie.,

**F _{-n} = (−1)^n+1 * F_{n}**

In other way, when -n is odd, **F _{-n} = F_{n}** and when -n is even,

**F**.

_{-n}= -F_{n}In case you are originating a sequence of -n manually and working toward negative infinity, you can iterate the sequence equation above and utilie this as start point.

F_{0} = 0, F_{1} = F_{2} = 1, and

F_{n}=F_{n+2}−F_{n+1}

For example, F_{-5} = F_{5} * (-1)^5+1 = F_{5} * (-1) = -5

### List of Fibonacci Numbers From F0 to F10

The Fibonacci Numbers list from F0 to F19 is formed by using the Fibonacci numbers formula and the method to find the successive terms in the sequence discussed above. The list of Fibonacci numbers is as shown below,

- F0 = 0
- F1 = 1
- F2 = 1
- F3 = 2
- F4 = 3
- F5 = 5
- F6 = 8
- F7 = 13
- F8 = 21
- F9 = 34
- F10 = 55

### FAQs on Fibonacci Calcuator - Online Free

**1. What is Fibonacci sequence formula?**

Fibonacci numbers are a sequence of whole numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... This infinite sequence is called the Fibonacci sequence. Here each term is the sum of the two preceding ones, starting from 0 and 1. The formula of fibonacci sequence F_{n} = F_{n-1} + F_{n-2}

**2.How do you calculate Fibonacci?**

Calculating fibonacci is very simple if you follow the steps furnished on our page.

**3. What is a Fibonacci calculator?**

Fibonacci calculator is a free online tool that helps students to find the fibonacci numbers sequence within fraction of seconds by entering the input terms.

**4. What is the Fibonacci of 5?**

The fibonacci of 5 isF_{5}= 5 check out the detailed steps on SequenceCalculators.com offered Fibonacci Calculator.