Calculators
Lucas Number Calculator
Calculate the exact nth Lucas number, its digit count and the next term locally in your browser.
Calculate exact terms of the Lucas sequence.
The Lucas sequence starts with L(0) = 2 and L(1) = 1. Each later term adds the previous two: L(n) = L(n − 1) + L(n − 2). Its first terms are 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123. For index 10, L(10) is 123 and the next term is 199. Lucas numbers use the same recurrence as Fibonacci numbers but different starting values. Enter an index from 0 to 10,000 using at most five digits; leading zeros and surrounding whitespace are accepted. Signs, decimal points, separators and scientific notation are not supported. Browser BigInt addition produces exact integers without rounding. The output includes the number of decimal digits and the next term. This calculator finds terms by zero-based index; it does not test sequence membership. All calculations and copy actions stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
Where does the Lucas sequence start?
This calculator uses L(0) = 2 and L(1) = 1. The next terms are 3, 4, 7 and 11. At index 10, the Lucas number is 123.
How do Lucas numbers differ from Fibonacci numbers?
Both sequences add the two preceding terms. Lucas numbers start with 2 and 1, while Fibonacci numbers start with 0 and 1. For n ≥ 1, L(n) = F(n − 1) + F(n + 1).
Are large Lucas numbers exact?
Yes. Repeated BigInt addition gives exact integers for indices from 0 to 10,000. Long numbers wrap in the output and can be copied in full.
What input formats are supported?
Use at most five digits for an index from 0 to 10,000. Leading zeros and surrounding whitespace are accepted. Decimals, signs, commas and exponent notation are rejected. Values remain in your browser.