Fibonacci Calculator

The start. Position 1 is 1 and position 2 is 1. Each later term is the sum of the two before it. Position 7 is 13. Position 10 is 55. There is no rounding. If your list starts at 0, your seventh term is not 13. Match the start before you compare. Forty is the cap. The loop is exact integer addition.

Position 7 is 13. Position 10 is 55. Position 1 and position 2 are both 1, which is the start this page uses. Some books start 0, 1. Those books will disagree at every index. The result names the start so the disagreement is visible. Forty is the cap because the numbers stay comfortable and the loop stays short. There is no closed form and no rounding. The value is an integer. You can check a small position by writing the sequence. If your handwritten 7th term is not 13, you started at 0 or you counted from zero. Match the start before you call the page wrong.

Write 1, 1, 2, 3, 5, 8, 13 and stop at the seventh term. It should be 13. Continue to the tenth and you should reach 55. If you wrote a 0 at the start, cross it out before you count. The page will not switch starts. Position 40 is the last index. The value is still an ordinary integer at that index and the addition does not round. There is no Binet approximation. If you need a closed form, you are past this page. Use the integer. Check position 1 and position 2 once. Both are 1. After that the recurrence is the whole definition.

This page starts the sequence at 1, 1. Position 1 is 1 and position 2 is 1. Each later position is the sum of the two before it. Position 3 is 2, position 4 is 3, position 5 is 5, position 6 is 8, position 7 is 13, and position 10 is 55. Write that list when you check the tool. Books that start at 0, 1 will disagree at every index. The result names the start so the disagreement is visible. There is no switch to the other start. Position 40 is the last index the form accepts. The value is an integer from addition, not a rounded closed form. There is no Binet formula on this page. If your handwritten seventh term is not 13, you either started at 0 or you counted the first 1 as position 0. Match the start before you call the result wrong. Reset restores position 7. Change it to 10 for the second example. The addition is exact at these sizes.

Memorise the two positions as sentences: position 7 is 13, and position 10 is 55, with the sequence starting 1, 1. Write the terms in between if you want to see the additions. Position 3 is 2, position 4 is 3, position 5 is 5, and position 6 is 8. Stop when the term matches the page. If it does not, your start was 0, 1. This page will not change its start to match that book. Reset returns position 7 so you can repeat the first sample without retyping it.

Position 7

Inputs: Position: 7

Leave the position as 7 and press Find. The value is 13.

Result: Position: 7 Value: 13 Sequence starts 1, 1, 2, 3, 5. Position 1 and position 2 are both 1.

Position 10

Inputs: Position: 10

Change the position to 10 and press Find. The value is 55.

Result: Position: 10 Value: 55 Sequence starts 1, 1, 2, 3, 5. Position 1 and position 2 are both 1.

Why is position 7 equal to 13?

The sequence starts 1, 1, 2, 3, 5, 8, 13. The seventh term is 13.

Why might a book disagree?

Some books start 0, 1. Those indexes are shifted. This page starts 1, 1.

What are position 1 and 2?

Both are 1.

Is the value rounded?

No. It is an integer sum.

Can I ask for position 100?

No. The cap is 40.

Is the position uploaded?

No. The sum runs in the browser.