The Fibonacci Calculator requires Javascript (which is NOT the same as Java).
Fibonacci and Lucas Number Calculator 1.2     For help, see lower down.
Series? Value or Range for i? Action buttons
From i=
To i=

The calculator is     <<< ready for you     <<< computing - please wait...


[Links followed will open in a new window.]
  1. Select a series:
    Fibonacci(i), Lucas(i), Rabbit(i).
      For Fibonacci(i) and Lucas(i) you have a choice of Precision: exact or approximate.
      Exact: the calculator will find Fibonacci(i) and Lucas(i) for i into the thousands. However, if i is too large, the browser may quit unexpectedly! (Sorry - I cannot predict or prevent this! 'i' values up to i=2000 (Fib(2000) has 400+ digits) should be OK.
      Approximate: Immediate result. The length of the answer decreases as i gets larger, but the index i itself may have up to digits!

    The Eval box lets you input an expression which uses i. Details below.
  2. Type in a whole number value for i, which can be negative except for Rabbit(i), in the From i= box.
  3. If you want to find all the values in a certain range, type a value in the To i= box also.
  4. Select an action:
    Show series
    outputs the numbers in the selected series for i in the chosen range.
    Initial digits
    Benford's Law relates to the distribution of the initial digits of Fibonacci and Lucas numbers. (Precision buttons are ignored.)
    Amaze me!
    produces a correct, random expression equal to 1 and involving two nth-roots, as mentioned on The Lucas numbers page.
    Clear all
    clears all values and the output area.


This calculator requires JavaScript (not the same as Java!) and Internet Explorer 4 or Netscape Navigator 4 or Communicator 4 or later versions.

Netscape Navigator:

Make sure JavaScript is enabled in Navigator version 4 or later:
In Edit Menu - Preferences - Advanced, make sure the box marked 'JavaScript' is checked.

Microsoft Internet Explorer 4+

Make sure Scripting is enabled in version 4 or later:
In Edit Menu - Preferences - Web Content, make sure 'Enable Scripting' is checked in the "Active Content" section.


The Eval box lets you type in a mathematical expression involving i. It is evaluated in the i range that you give and values printed in the Output area.
NaN means the output is Not a Number (there is an error in your expression, or you've given an impossible value to a function, such as sqrt(-1).
Infinity - the Calculator has generated a value that is too large for it.


E , PI, Phi, phi


+ - * /
% ( x%y is the integer remainder when integer x is divided by integer y)
< > <= >=     equal to is == and not equal to is !=
NB There is no "to-the-power-of" operator - see pow function below.


abs(x)the absolute value of x (always positive)
acos(x)the angle (in radians) whose cosine is x
asin(x)the angle (in radians) whose sine is x
atan(x)the angle (in radians) whose tangent is x
ceil(x) round up to the next integer (if not already an integer)
cos(x)the cosine of angle x (x in radians)
exp(x)E to the power of x; same as pow(E,x)
Fib(i) Fibonacci(i)
floor(x)x, if x is an integer, otherwise the next integer less than x
log(x) the natural log of x (log to the base E)
log10(x)the common log of x (log to base 10)
Luc(i) Lucas(i)
pow(x,p) xp
Rab(i) Rabbit(i)
randint(LO,HI) a random integer between LO and HI (inclusive)
random() a random number between 0.0 and 1.0
round(x)the nearest integer to x
sin(x)the sine of angle x (x in radians)
sqrt(x)the square root of x
tan(x)the tangent of angle x (x in radians)

Conditional Expressions

( C ? T : E ) C is an expression with a true or false result;
T is the value returned if C evaluates to true;
E is the value returned if C evaluates to false

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6 May 1999<