Smooth approximations to half-perimeter wire-length are being investigated actively because of the recent increase in interest in analytical placement. It is necessary to not just provide smooth approximations but also to provide error analysis and convergence properties of these approximations. We present a new approximation scheme which uses a non-recursive approximation to the MAX function. We also show the convergence properties and the error bounds. The accuracy of our proposed scheme is better than those of the popular Logarithm-Sum-Exponential (LSE) wirelength model [7] and the recently proposed Weighted Average(WA) wirelength model[3]. We also experimentally validate the comparison by using global and detail placements produced by NTU Placer [1] on ISPD 2004 benchmark suite. The experimentations on benchmarks validate that the error bounds of our model are lower, with an average of 4% error in the total wirelength. © 2013 EDAA.