Lucas Number Calculator

About this calculator

This calculator finds the nth term of the Lucas sequence, defined by the same recurrence as Fibonacci (Lₙ = Lₙ₋₁ + Lₙ₋₂) but with different starting values L₀=2, L₁=1, producing 2, 1, 3, 4, 7, 11, 18, 29, … Lucas numbers share the same golden-ratio-based closed form (Binet-like formula) as Fibonacci and satisfy several identities linking the two sequences, such as L(n) = F(n−1) + F(n+1).

Math students and recreational mathematicians use it to explore number theory identities and the golden ratio, and it appears in some algorithm analyses (like worst-case Euclidean algorithm inputs) and in a small number of primality tests (Lucas-Lehmer variants). Enter n to compute Lₙ.