In this paper, adaptive Lagrangian multiplier λ estimation in Larangian R-D optimization for video coding is presented that is based on the ρ-domain linear rate model and distortion model. It yields that λ is a function of rate, distortion and coding input statistics and can be written as λ(R, D, σ2) = β(ln(σ2/D) + δ)D/R + k0, with β, δ and k0 as coding constants, σ2 is variance of prediction error input. λ(R, D, σ2) describes its ubiquitous relationship with coding statistics and coding input in hybrid video coding such as H.263, MPEG-2/4 and H.264/AVC. The lambda evaluation is de-coupled with quantization parameters. The proposed lambda estimation enables a fine encoder design and encoder control.