This work presents a compact methodology for power distribution network design in a nanometer scale VLSI chip using a noise-area tradeoff analysis which considers on-chip inductance effects. This methodology is used to quantitatively demonstrate the importance of considering on-chip power grid inductance, and how its impact scales with technology. While increasing power supply noise levels (which become worse with on-chip inductance) are expected to adversely impact the chip's power supply grid design, this work demonstrates that a power grid optimized with on-chip inductance considerations can lead to significant improvement in the wiring resource utilization.