Amidst rising interest in biogas as a sustainable alternative to traditional energy vectors like natural gas, this study focuses on its role in achieving net-zero targets-where carbon emissions are balanced with sequestration. Biogas, derived from carbon-neutral organic waste, significantly reduces greenhouse gas (GHG) emissions. Life cycle assessments (LCA) are crucial for evaluating the global warming potential (GWP) of biogas, ensuring its effectiveness in offsetting fossil fuel equivalents. Due to renewed interest in anaerobic digestion in offsetting carbon, new robust easily calculable algebraic equations are proposed. Our study introduces two complementary sets of equations, grounded in published literature and Ecoinvent databases. Despite their differing structures in lifecycle activity considerations, both sets yield closely aligned estimations, reinforcing confidence in these models. The GWP is sensitive to the feedstock type, electricity and heat consumption, and fugitive emissions. The statistical distributions show the mean GWP (kg CO2e) of 0.54 per m3 biogas, 0.09 per kWh biomethane and 0.73 per kWh electricity production rates of cradle-to-grave systems. The lowest GWP meets the UK's 50 g CO2e per kWh biomethane target by 2030 for gas grid injection. The GWP in g CO2e per kg AD feedstock is 93-104 (manure), 16-26 (sludge), and 273 (grass silage), etc. Further, the GWP savings from the natural gas displacement and biogenic CO2 in biowaste feedstock can offset its AD systems' GWP giving a net GWP saving of 0.5-0.7 kg CO2e per kWh of electricity generated.