Fibonacci Sequence Calculator

Welcome to the Fibonacci Sequence Calculator. Here, you can easily solve 3 problems:

The sum of the Fibonacci sequence.
The Nth term of the Fibonacci sequence.
Checking if a number is a Fibonacci number.

Eg, what is the 500th Fibonacci number? Enter 500 into the input box and click Calculate button.

Calculate Reset

Fibonacci Number Checker

Eg, Is 101 a Fibonacci number? Enter 101 into the input box and click Calculate button.

Calculate Reset

What is the Fibonacci sequence?

Similar to Lucas numbers, the Fibonacci sequence has a recursive relationship where each term in the series is the sum of the previous two terms. The first two terms of the Fibonacci sequence are 0 and 1, while the first two in the Lucas numbers are 1 and 2. Usually, F_n is used to represent the Fibonacci numbers.

The formula for Fibonacci numbers is as follows:

Fibonacci numbers formula For example, the 5th Fibonacci number.

F₅ = F₄ + F₃

F₄ = F₃ + F₂

F₃ = F₂ + F₁

F₂ = F₁ + F₀

F₅ = F₄ + F₃ = F₃ + F₂ + F₃ = 2 * F₃ + F₂ = 2 * (F₂ + F₁) + F₂ = 3 * F₂ + 2 * F₁ = 3 * (F₁ + F₀) + 2 * F₁ = 5 * F₁ + 3 * F₀ = 5 * 1 + 3 * 0 = 5

So, the 5th Fibonacci number is 5.

First 100 Fibonacci numbers

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
514229
832040
1346269
2178309
3524578
5702887
9227465
14930352
24157817
39088169
63245986
102334155
165580141
267914296
433494437
701408733
1134903170
1836311903
2971215073
4807526976
7778742049

12586269025
20365011074
32951280099
53316291173
86267571272
139583862445
225851433717
365435296162
591286729879
956722026041
1548008755920
2504730781961
4052739537881
6557470319842
10610209857723
17167680177565
27777890035288
44945570212853
72723460248141
117669030460994
190392490709135
308061521170129
498454011879264
806515533049393
1304969544928657
2111485077978050
3416454622906707
5527939700884757
8944394323791464
14472334024676221
23416728348467685
37889062373143906
61305790721611591
99194853094755497
160500643816367088
259695496911122585
420196140727489673
679891637638612258
1100087778366101931
1779979416004714189
2880067194370816120
4660046610375530309
7540113804746346429
12200160415121876738
19740274219868223167
31940434634990099905
51680708854858323072
83621143489848422977
135301852344706746049
218922995834555169026

How to use the Fibonacci sequence calculator

The calculator consists of two parts, one to calculate the sum and Nth term of the Fibonacci sequence, and the other to is used to check if a given number is a Fibonacci number.

The sum and Nth term of the Fibonacci sequence calculator

1Enter the positive integer in the first input box (Number less than 2000).
2Click Calculate button to calculate the sum and Nth term of the Fibonacci sequence.
3Click the Reset button to start a new calculation.

Fibonacci Number checker

1Enter the positive number in the first input box.
2Click Calculate button to verify whether the input number is a Fibonacci number.
3Click the Reset button to start a new verification.

Solved examples using the Fibonacci sequence calculator

Example 1: What is the 200th Fibonacci number?

In an Fibonacci sequence calculator, enter 200 into the input box and click Calculate button, as shown in the figure, the 200th Fibonacci number is 280571172992510140037611932413038677189525.

Example 2: What is the sum of the first 20 Fibonacci numbers?

In the Fibonacci sequence calculator, enter 20 into the input box and click Calculate button, as shown in the figure, the sum of the first 20 Fibonacci numbers is 17710.

Example 3: Is 101 a Fibonacci number?

In the Fibonacci Number checker, enter 101 into the input box and click Calculate button, as shown in the figure, 101 is not a Fibonacci number.

Fibonacci Sequence Calculator