Calculators

Pell Number Calculator

Calculate exact Pell numbers for indices 0 to 1000 privately in your browser, with the next term and digit count.

Calculate a term in the Pell sequence and the following term. Exact BigInt arithmetic keeps every digit. Your data stays in your browser.

Enter a whole number from 0 to 1000 using digits only. Zero returns 0. The sequence starts 0, 1, 2, 5, 12, 29.

Your Pell number will appear here.

Calculate exact terms in the Pell sequence.

Pell numbers start with P(0) = 0 and P(1) = 1. Each later term is twice the previous term plus the term before it: P(n) = 2 × P(n − 1) + P(n − 2). The sequence begins 0, 1, 2, 5, 12, 29, 70, 169. For example, P(5) = 2 × 12 + 5 = 29. Unlike Fibonacci numbers, the preceding term is doubled before addition. Enter an index from 0 to 1000 using one to four digits; leading zeros and surrounding whitespace are accepted. Signs, decimals, separators and scientific notation are rejected. Exact BigInt arithmetic preserves every digit. Results include the selected term, its decimal digit count and the next term. Zero has one digit. All calculations stay in your browser.

Frequently Asked Questions

Everything you need to know about this tool, how it works, and privacy.

How are Pell numbers calculated?

Start with P(0) = 0 and P(1) = 1. Each subsequent term is twice the preceding term plus the earlier term. For example, P(5) = 2 × 12 + 5 = 29.

How do Pell and Fibonacci numbers differ?

Pell numbers double the preceding term before adding the earlier term. Fibonacci numbers simply add the preceding two terms.

Are large results exact?

Yes. BigInt arithmetic preserves every digit. Results include the selected term, its decimal digit count and the next term without rounding.

Which inputs are supported?

Enter an index from 0 to 1000 using one to four digits. Leading zeros and surrounding whitespace are accepted. Signs, decimals, separators and scientific notation are rejected. Calculations stay in your browser.