Fibonacci Calculator

    Calculate the Fibonacci number at a zero-based index, generate the sequence through that index, and show the running sum and golden-ratio approximation.

    Zero-based indexing is used: F0 = 0 and F1 = 1. Enter a whole number from 0 to 1,500.

    Nth Fibonacci number and sequence

    English Fibonacci calculator intent usually combines two jobs: find the nth term and generate the sequence up to that term. This page uses zero-based indexing, so F0 is 0 and F1 is 1.

    Each term after F1 is the sum of the previous two terms.

    1. Enter a nonnegative integer index.
    2. Read the exact Fibonacci number.
    3. Use the table to inspect the sequence through that index.

    Golden ratio connection

    The ratio of neighboring Fibonacci numbers approaches the golden ratio as n grows.

    IndexValue
    1055
    206,765
    5012,586,269,025
    The calculator uses integer iteration for the exact value. Binet's formula is useful for explanation, but floating-point arithmetic is not reliable for large exact terms.

    Frequently Asked Questions

    Sources and References

    Calculations are based on the listed reference sources. Links open in a new tab.

    Updated:

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