Calculator that checks if a number is in the Fibonacci sequence

Use the calculator below to check if almost any number is a Fibonacci one.

Is a Fibonacci Number? Calculator

Please fill in a number to check if it is a Fibonacci number:

Result:

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What is a Fibonacci number?

A Fibonacci number should obey this sequence of numbers:

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

The first Fibonacci number (F0) is zero and the second (F1) and the third (F1) are one.

To get the next Fibonacci number, we just need to addup the two numbers before it. For Example:

  • The 4th (F3) is found by adding the two numbers before it (1+1)
  • The 5th (F2) is also found by adding the two numbers before it (1+2);
  • The 6th (F4) is 2+3 = 5
  • ...
  • The 10th (F9) is (13+21) = 34

and so on ...

You get the idea!

So, we can derive the following formula to calculate any fibonacci number:

F0 = 0, F1 = 1

and

Fn = Fn - 2 + Fn - 1

for n > 1.

Fibonacci Chart

n Fn
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610

The fibonacii sequence grows very fast. For example:

F0 = 0,
F10 = 34,
F20 = 4181,
F30 = 514229,
F40 = 63245986,
F50 = 7778742049,
F100 = 218922995834555169026,
F200 = 173402521172797813159685037284371942044301,
F500 = 86168291600238450732788312165664788095941068326060883324529903470149056115823592713458328176574447204501,
F1000 = 26863810024485359386146727202142923967616609318986952340123175997617981700247881689338369654483356564191827856161443356312976673642210350324634850410377680367334151172899169723197082763985615764450078474174626,
You get the idea!

That is why the best way to work with Fibonacci numbers is by using a calculator or a table.

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