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Calculation Machine

Fibonacci Calculator

Fibonacci terms and the golden ratio.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
F(20)
6,765
Sum of first n terms
17,710
Ratio to previous term
1.61803396
Golden ratio
1.61803399
Sequence
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377

Quick answer

Each Fibonacci number is the sum of the previous two, and consecutive ratios converge to the golden ratio 1.618.

The formula

F(n) = F(n−1) + F(n−2)

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Term number n20

Result

  • F(20)6,765
  • Sum of first n terms17,710
  • Ratio to previous term1.61803396
  • Golden ratio1.61803399
  • Sequence0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377

How to use the Fibonacci Calculator

  1. 1Enter which Fibonacci term you want.
  2. 2Read the value and running sum.
  3. 3Compare the ratio to the golden ratio.

Frequently asked questions

Where does Fibonacci appear in nature?

Sunflower spirals, pine cones and branching patterns approximate it.

Does it start at 0 or 1?

This tool uses F(0)=0, F(1)=1, the standard mathematical convention.

About this calculator