Analytical calculations are made for the scaling and design parameters for the generation of a multi-pico Coulomb and multi-GeV electron beam from a laser Wakefield acceleration (LWFA). The numerical values are optimized for electron acceleration from a cm-scale gas cell and self-guided laser plasma in the bubble domain, where the low-density plasma serves as an accelerating medium. A graphical analysis of the matched parameters is presented for 1–10 GeV electron beam energy gain, where the laser pulse is powered between 30 ∼ 700 TW with delivery capabilities of 1–100 J pulse energy, 25–150 fs pulse duration, and 15–95 μm spot size operating with 1018–19 W cm−2 laser intensity at a plasma density ∼1017 cm−3. The result shows the generation of multi-pico-Coulomb and multi-GeV electron beams. These parameters will be helpful for the future LWFA related experiments using cm scale gas cells in the bubble regime.